Holt Pre Algebra Teacher's Practice Workbook

Copyright © by Holt, Rinehart and Winston. 1 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 1-1 Variables and Expressions LESSON Evaluate each expression for the given value of the variable. 1. 5x 3 for x 4 2. 23 b for b 16 3. 12y for y 22 4. 19 3x for x 6 5. 7b 9 for b 9 6. 8.6 9y for y 7 7. 78 14k for k 5 8. 9(a 3) for a 6 Evaluate each expression for the given value of the variables. 9. 3x y for x 6 and y 9 10. 5a b for a 6 and b 8 11. 7m 8n for m 10 and n 7 12. 7r 6s for r 12 and s 14 13. 10(x y) for x 14 and y 8 14. m(18 x) for m 9 and x 6 A caterer determines 14pound of roast beef is needed to serve each guest at a party. How many pounds of roast beef are needed for each number of guests? 15. 8 guests 16. 12 guests 17. 18 guests 18. 25 guests 6144lb 122 lb 3 lb lb 60 108 14 168 27 22 8 81 54 71.6 11 117 7 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 2 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 1-2 Writing Algebraic Expressions LESSON Write an expression for each word phrase. 1. a number x divided by 7 2. the sum of 10 and a number n 3. a number b decreased by 14 4. the product of a number x and 8 5. 12 times the difference of a number 6. 11 minus the product of 5 and a r and 7 number k 7. a. Grace wants to divide the job of writing x invitations to the party equally among 4 committee members.Write an expression to determine the number of invitations she will have each committee member write. 4 x b. If Grace has 220 invitations for the committee members to write, how many will she have each member write? 55 invitations Write an algebraic expression and use it to evaluate each word problem. 8. Arturo purchased a package of 50 blank CDs. After he used x CDs, he had x less than 50 CDs remaining. How many CDs did he have left after using 31 CDs? 19 CDs 9. At the grocery store, Henry bought c pounds of cashews for $4.99 per pound. If he buys 2 pounds, how much will they cost? $9.98 12(r 7) 11 5k b 14 8x 10 n 7 x Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 3 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 1-3 Solving Equations by Adding or Subtracting LESSON Determine which value is a solution of the equation. 1. x 8 14; x 6, 20, or 22 2. 8 a 19; a 7, 11, or 27 3. y 14 22; y 8, 12, or 36 4. d 17 52; d 25, 35, or 69 Solve. 5. m 9 14 6. 7 x 16 7. k 12 31 8. y 14 46 9. 13 r 29 10. 17 t 19 11. b 39 57 12. p 27 27 13. 0 w 45 14. 8.7 s 12.1 15. x 3.7 0.8 16. n 3.41 5.40 17. The school library is combining books from two storage units into a newly designed area for the library. The first original unit held 186 books and the second unit had 307 books.Write and solve an equation to find the number of books in the new area of the library. 186 307 b; b 493 18. Amelia wanted to buy a new computer and printer which had a total cost of $1099.95. She had saved $389.85 for her purchase. How much more does she need to save to buy the computer and printer she wants? 389.85 x 1099.95; x 710.10 s 3.4 x 4.5 n 8.81 b 18 p 0 w 45 y 60 r 16 t 2 m 23 x 9 k 19 y 36 d 35 x 22 a 11 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 4 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 1-4 Solving Equations by Multiplying and Dividing LESSON Solve. 1. 7n 49 2. 6w 48 3. 3a 39 4. b510 5. 7x13 6. 2c46 7. 12n 96 8. 57 3k 9. 22x 176 10. 2w217 11. 1h6 16 12. 13 3t3 13. 572 26m 14. 2x418 15. 46v 828 16. 2x 3 19 17. 2r7 14 18. 3 4s 5 19. Ashley saves $32 from her weekly paycheck for her college education. This is 15of her weekly salary. How much does she earn each week? Write and solve an equation to determine the amount Ashley earns each week. 5 c 32; c 160 20. Hunter bought a package of 24 pencils for $3.12. Write and solve an equation to determine the cost of each pencil in the package. 24p 3.12; p 0.13 x 8 r 14 s 2 m 22 x 432 v 18 w 374 h 256 t 429 n 8 19 k x 8 b 50 x 91 c 144 n 7 w 8 a 13 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 5 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 1-5 Solving Simple Inequalities LESSON Use , , or to compare each inequality. 1. 8 13 20 2. 23 3(7) 3. 28 9 18 4. 67 9(8) 5. 52 37 15 6. 78 12(6) Solve and graph each inequality. 7. x 3 7 8. y 5 1 9. 4n 20 10. h 1 6 11. 5x3 12. 3t4 13. 9d 45 14. 17 m 23 15. 128 16x 16. Philippe wants to drink at least 72 ounces of water every day while at work. He works 6 hours a day. How many ounces of water must Philippe drink each hour? Write and solve an inequality to answer the question. 6w 72; w 12 17. Glynn’s car has a 18 gallon gas tank. He travels 450 miles. What is the least miles per gallon Glynn’s car will get on this trip? Write and solve an inequality to answer the question. 18x 450; x 25 d 5 m 6 x 8 2 0 2 4 6 8 2 0 2 4 6 8 10 2 0 2 4 6 8 10 h 7 x 15 t 12 2 0 2 4 6 8 101214 2 0 2 4 6 8 10121416 2 0 2 4 6 8 10 12 14 x 4 y 6 n 5 2 0 2 4 6 8 2 0 2 4 6 8 2 0 2 4 6 8 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 6 Holt Middle School Math All rights reserved. Name Date Class Combine like terms. 1. 11b 6b 2. 9m 3m 3. 5x 8x 7 4. 8w 9x 7w 5. 13r 10r 8t 6. 9g 4m 8g 7. 12b 14p 7 8. 7a 11a a 9. 15 3x 9 8x 10. 6x y x 9y 11. 8m 14 7m 11 12. 13x 4 12x 9 Simplify. 13. 5(x 4) 7 14. 9(6 y) 3y 15. 6(7 2a) 8a Solve. 16. 5r 2r 21 17. 15t 9t 54 18. 6x 8x 42 19. Janelle has d dimes and n nickels. Her sister has 5 times as many dimes and 6 times as many nickels as Janelle has.Write the sum of the number of coins they have, and then combine like terms. d n 5d 6n; 6d 7n 20. If Janelle has 9 dimes and 18 nickels, how many total coins do Janelle and her sister have? 180 coins r 3 t 9 x 3 5x 13 54 12y 42 4a 7x 10y 15m 3 x 5 12b 14p 7 17a 6 11x 15w 9x 23r 8t g 4m 17b 6m 13x 7 Homework and Practice 1-6 Combining Like Terms LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 7 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 1-7 Ordered Pairs LESSON Determine whether each ordered pair is a solution of y 5 3x. 1. (1, 8) 2. (3, 7) 3. (2, 10) 4. (0, 5) Determine whether each ordered pair is a solution of y 4x 1. 5. (0, 1) 6. (1, 3) 7. (3, 11) 8. (5, 19) Use the given values to complete the table of solutions. 9. y x 4 for x 0, 1, 2, 3, 4 10. y 2x 3 for x 0, 1, 3, 5, 7 11. y 4x 1 for x 1, 2, 4, 5, 8 12. y 5x 2 for x 0, 2, 4, 6, 8 13. Mrs. Frank had 150 customers when she began her delivery route. Each month she adds 5 new customers. The equation that gives the total number of customers, t, in her route is t 150 5m, where m is the number of months since she began the route. How many customers will Mrs. Frank have after 12 months? 210 no yes yes yes yes no no yes x x4 y (x, y) 0 0 4 4 (0, 4) 1 1 4 5 (1, 5) 2 2 4 6 (2, 6) 3 3 4 7 (3, 7) 4 4 4 8 (4, 8) x 2x 3 y (x, y) 0 2(0) 3 3 (0, 3) 1 2(1) 3 5 (1, 5) 3 2(3) 3 9 (3, 9) 5 2(5) 3 13 (5, 13) 7 2(7) 3 17 (7, 17) x 4x 1 y (x, y) 1 4(1) 1 3 (1, 3) 2 4(2) 1 7 (2, 7) 4 4(4) 1 15 (4, 15) 5 4(5) 1 19 (5, 19) 8 4(8) 1 31 (8, 31) x 5x 2 y (x, y) 0 5(0) 2 2 (0, 2) 2 5(2) 2 12 (2, 12) 4 5(4) 2 22 (4, 22) 6 5(6) 2 32 (6, 32) 8 5(8) 2 42 (8, 42) Holt Pre-AlgebraGive the coordinates of each point. 1. A 2. D 3. H 4. C 5. B 6. T 7. M 8. R Graph each point on a coordinate plane. Label points A–F. 9. A(3, 5) 10. B(–6, 3) 11. C(0, –4) 12. D(–4, –6) 13. E(5, –2) 14. F(2, 0) Complete the table of ordered pairs. Graph the equation on a coordinate plane. 15. y 2x 16. A doctor sees 4 patients each hour. Use the equation y 4x, where the y-value represents the many patients that the doctor may see in x hours. Graph, if necessary. How many patients will the doctor see in a 5-hour day? 20 (–4, 5) (7, 5) (2, –6) (0, 6) (–2, 1) (–1, –5) (4, 0) (3, –4) Copyright © by Holt, Rinehart and Winston. 8 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 1-8 Graphing on a Coordinate Plane LESSON y x O 2 4 62 6 4 2 46 2 4 6 A D HC B T M R B F C D E y x O 2 42 4 2 4 2 4 A x x y (x, y) 1 (1) 2 (1, 2) 2 (2) 4 (2, 4) 3 (3) 6 (3, 6) 6543210 1 2 3 4 5 6 y x Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 9 Holt Middle School Math All rights reserved. The table gives the prices of three different stocks over the first few hours of trading. Tell which stock corresponds to each situation described below. 1. A stock opens and rises steadily over the first few hours of trading. Stock 3 2. A stock opens and declines steadily over the first few hours of trading. Stock 1 Tell which graph corresponds to each situation in Exercises 1–2. 3. 4. 5. Create a graph that illustrates the hours students spent studying for exams. Exercise 2 (Stock 1) Name Date Class Homework and Practice 1-9 Interpreting Graphs and Tables LESSON Time 9:30 10:30 11:30 12:30 1:30 Stock 1 $26.50 $26.00 $25.00 $24.00 $22.50 Stock 2 $38.25 $36.50 $39.75 $37.25 $41.00 Stock 3 $55.00 $55.25 $55.50 $56.00 $57.00 $27.00 9:30 10:30 11:30 12:30 1:30 $26.00 $25.00 $24.00 $23.00 $22.00 $21.00 $20.00 Exercise 1 (Stock 3) $57.50 9:30 10:30 11:30 12:30 1:30 $57.00 $56.50 $56.00 $55.50 $55.00 $54.50 $54.00 Samantha 0 0.51 1.52 2.53 3.54 4.5 Seth Simon Susan Number of Hours Studying for Exams Number of Hours Student Studying for Exams Samantha 3 hours Seth 3.5 hours Simon 4 hours Susan 2.5 hours Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 10 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 2-1 Adding Integers LESSON Use a number line to find the sum. 1. 2 3 2. 5 3 Add. 3. 6 15 4. 28 (7) 5. 31 (19) 6. 34 21 Evaluate each expression for the given value of the variables. 7. a 9 for a 5 8. x 7 for x 8 9. y 6 for y 13 10. 5 r for r7 11. 9 w for w12 12. m 8 for m11 13. 6 k for k9 14. t (5) for t8 15. b (7) for b7 16. 11 x for x 15 17. g (15) for g 15 18. 16 j for j18 19. The music club had 328 members. This year 103 new members joined. How many members does the music club have now? 431 members 20. Rosetta is playing a board game with her friends. She rolls doubles of five on her first roll of the number cubes. If a player rolls doubles, they roll again after moving forward. However if they roll doubles again they must move backwards. Rosetta rolls doubles of six on her second roll. How many spaces is Rosetta from her starting place? 2 back 4 0 34 15 13 14 12 21 3 14 15 199 35 12 13 5 2 7654321 2 3 0 1 2 3 4 5 6 7 7654321 5 3 0 1 2 3 4 5 6 7 Holt Pre-AlgebraName Date Class Subtract. 1. 9 3 2. 12 4 3. 9 16 4. 19 12 5. 7 15 6. 18 4 7. 8 12 8. 11 14 9. 25 49 10. 18 36 11. 101 52 12. 76 (12) Evaluate each expression for the given value of the variables. 13. a 10 for a 7 14. x 13 for x 20 15. 17 y for y 6 16. 15 b for b9 17. 14 t for t18 18. d 24 for d17 19. 16 w for w15 20. 10 r for r22 21. 14 g for g19 22. x (18) for x25 23. y (14) for y14 24. n (17) for n 21 25. The largest island in the world is Greenland with an area of 839,999 square miles. The second largest island is New Guinea with an area of 316,615 square miles. What is the difference in the areas of the two islands? 523,384 square miles 26. Justin weighed 223 pounds and lost 45 pounds.What is Justin’s new weight? 178 pounds 7 0 38 1 12 5 6 32 41 3 7 1124 18 153 64 8 14 20 25 6 8 7 7 Homework and Practice 2-2 Subtracting Integers LESSON Copyright © by Holt, Rinehart and Winston. 11 Holt Middle School Math All rights reserved. Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 12 Holt Middle School Math All rights reserved. Name Date Class Multiply or divide. 1. 7 9 2. 321 3. 9 5 4. 287 5. 4626. 11(8) 7. 5868. 4(13) Simplify. 9. 6(4 5) 10. 9(10 3) 11. 7(13 4) 12. 8(17 11) 13. 14(5 3) 14. 10(5 14) 15. 11(15 9) 16. 12(7 3) Complete the table for the equation y 2x 3. Then plot the points on the coordinate plane. 22. Mr. Sweeney’s stock portfolio lost $125 for 3 consecutive days. What was the total dollar amount the stock lost over the 3 days? lost $375 23. The temperature was –2, –3, 1, and –4 on four consecutive days.What was the average temperature for those days? 2 28 90 66 120 54 63 63 48 7 88 7 52 63 7 45 4 Homework and Practice 2-3 Multiplying and Dividing Integers LESSON x 2x 3 y (x,y) 17. 2 2(2) 3 1 (2, 1) 18. 1 2(1) 3 1 (1, 1) 19. 0 2(0) 3 3 (0, 3) 20. 1 2(1) 3 5 (1, 5) 21. 2 2(2) 3 7 (2, 7) y x Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 13 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 2-4 Solving Equations Containing Integers LESSON Solve. 1. x 8 3 2. y 4 9 3. 7w 35 4. n2 8 5. 8 t6 6. a6 7 7. 9 k15 8. 9d 36 9. c 817 10. m78 11. 8 b11 12. x 19 19 13. 5x 65 14. r6 4 15. h 1712 16. x6 6 17. s 1515 18. 648v 19. Austin High School had an enrollment of 1,428 students. In May, they graduated 418 students. How many students are still enrolled in the school? 1,010 students 20. Mr. Otten saved $32 each week for 26 weeks. How much did he save in that time? $832 x 36 s 0 8 v x 13 r 24 h 5 m 56 b 3 x 38 k 6 d 4 c 9 n 16 t 2 a 42 x 5 x 13 w 5 Holt Pre-AlgebraHomework and Practice 2-5 Solving Inequalities Containing Integers LESSON Copyright © by Holt, Rinehart and Winston. 14 Holt Middle School Math All rights reserved. Name Date Class Solve. 1. x 5 13 2. 6y 36 3. w4 8 4. t 9 12 5. x (8) 16 6. a87 7. b (13) 5 8. 7r 49 Solve and graph. 9. 17 x 13 10. w3 4 11. t (12) 7 12. 11y 33 Write an inequality for each of the following. 13. A number increased by negative fifteen is less than twenty-eight. x (15) 28 14. A number multiplied by sixteen is less than or equal to negative thirty. 16x 30 15. A number divided by twelve is greater than or equal to negative thirty-four. 1x234 16. A number decreased by forty-two is greater than thirty-seven. x 42 37 t 5 y 3 x 4 w 12 x 24 a 56 b 18 r 7 x 8 y 6 w 32 t 3 7654321 0 1 2 3 4 5 6 7 2 1 0 1 2 3 4 5 6 7 8 9 1011121314 7654321 0 1 2 3 4 5 6 7 7654321 0 1 2 3 4 5 6 7 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 15 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 2-6 Exponents LESSON Write using exponents. 1. 8 8 8 8 2. (5) (5) 3. 9 9 9 8 8 8 (5) (5) 9 9 9 Evaluate. 4. 104 5. (4)3 6. (6)2 7. 92 8. 142 9. (8)2 10. (12)2 11. (3)4 Simplify. 12. 33 15 13. (4)4 7 14. 72 25 15. 78 62 16. 112 34 3 17. 16 33 4 18. 62 10 24 19. 3 (43 92) Evaluate for the given value of the variable. 20. x 3 for x3 21. 6y 2 for y 4 22. w 4 17 for w 3 23. Write an expression for eight times a number used as a factor four times. 8x 4 24. If the length of a side of a regular cube is 12 cm, find its volume. (Hint: V l 3). 1728 cm3 27 96 6443 92 196 435 12 263 17 42 196 64 144 81 10,000 64 36 81 87 (5)4 96 Holt Pre-AlgebraHomework and Practice 2-7 Properties of Exponents LESSON Copyright © by Holt, Rinehart and Winston. 16 Holt Middle School Math All rights reserved. Name Date Class Multiply.Write the product as one power. 1. 106 109 2. a 8 a 6 3. 156 1512 4. 1112 117 5. (w)8 (w)12 6. (12)18 (12)13 7. 1310 1315 8. w14 w12 Divide.Write the quotient as one power. 9. a a 2158 10. ( (1133))194 11. 1 144182 12. 1 188151 13. 1 199145 14. 2 2112220 15. ( (xx))177 16. 225538 Write the product or quotient as one power. 17. r 9 r 8 18. 1 1662100 19. x x195 20. (17)8 (17)7 21. 277 276 22. mm1106 23. (b)21 (b)14 24. 2 266157 25. (s)11 (s)4 26. Hampton has a baseball card collection of 56 cards. He organizes the cards into boxes that hold 54 each. How many boxes will Hampton need to hold the cards? Write the answer as one power. 52 27. Write the expression for a number used as a factor seventeen times being multiplied by a number used as a factor fourteen times. Then write the product as one power. x 17 x 14 x 31 (b)35 2612 (s)15 (17)15 2713 m6 r 17 1610 x 6 1911 212 (x)10 255 a 7 (13)5 144 186 (w)20 (12)31 1325 w26 1015 a14 1518 1119 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 17 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 2-8 Looking for a Pattern in Integer Exponents LESSON Evaluate the powers of 10. 1. 106 2. 104 3. 103 4. 105 5. 101 6. 108 7. 105 8. 102 Evaluate. 9. (7)3 10. 1 11125 11. aa184 12. (8)4 13. 63 • 62 14. 55193 15. 142 • 145 16. 1 19979 17. ((1155))4 18. (17)3 • (17)6 19. 2 21124 20. (20)3 • (20)5 Express the answer using powers of 10 and negative numbers. 21. 1 meter 10100 km km. 22. Find the volume of a cube with a side that measures 0.01 cm. (Hint: V s 3). 106 cm3 103 4010 4411 4,913 3,3175 3611 2,744 6215 7,7176 4,0196 a16 1,3131 3413 0.1 100,000,000 0.00001 100 0.000001 10,000 0.001 100,000 Holt Pre-AlgebraHomework and Practice 2-9 Scientific Notation LESSON Copyright © by Holt, Rinehart and Winston. 18 Holt Middle School Math All rights reserved. Name Date Class Write each number in standard notation. 1. 6.12 102 2. 7.9 103 3. 4.87 104 4. 9.3 102 5. 8.06 103 6. 5.7 104 7. 3.17 105 8. 9.00613 102 9. 9.85 105 10. 6.004 107 11. 8.23 104 12. 1.48 106 Write each number in scientific notation. 13. 108,000,000 14. 0.5943 15. 42 16. 0.0000673 17. 0.0056 18. 6004 19. 0.00852 20. 24,631,500 21. 89450 22. 0.005702 23. 8,005,000,000 24. 0.00012805 25. The mass of the Earth is 5,980,000,000,000,000,000,000,000 kilograms. Write this number in scientific notation. 5.98 1024 26. The mass of a dust particle is 7.53 1010. Write this number in standard notation. 0.000000000753 kg 8.945 104 5.702 103 8.005 109 1.2805 104 5.6 103 6.004 103 8.52 103 2.46315 107 1.08 108 5.943 101 4.2 101 6.73 105 0.0000985 60,040,000 82,300 0.00000148 8,060 0.00057 0.0000317 0.0900613 612 0.0079 48,700 0.093 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 19 Holt Middle School Math All rights reserved. Simplify. 1. 162 2. 264 3. 13264. 382 5. 12576. 12647. 19268. 5142Write each decimal as a fraction in simplest form. 9. 0.56 10. 3.2 11. 0.036 12. 2.05 13. 3.502 14. 0.064 15. 8.4 16. 0.004 17. 0.70 18. 5.25 19. 0.128 20. 0.0004 Write each fraction as a decimal. 21. 3822. 5923. 28124. 118725. 13926. 121027. 7528. 356429. Make up a fraction that cannot be simplified that has 25 as its denominator. sample answer: 2356.333 0.55 1.4 1.5 0.375 0.555 2.625 0.944 2,5100 11265 514170 2510 8251285 3520510 2210 2590 3152145 2918235914131412Name Date Class Homework and Practice 3-1 Rational Numbers LESSON Holt Pre-Algebra1. Benjamin paid his cell phone bill that was $25.95. He wrote a check that cost $0.75 to pay the bill. When he mailed it, Benjamin put a $0.37 stamp on the letter. What was the total cost for Benjamin to pay his cell phone bill? $27.07 2. Dannika is preparing a recipe that calls for 234cups of flour. If Dannika has only 214cups left in the flour container, how much flour must she add from a new bag to complete the recipe? 12cup Use a number line to find each sum. 3. 0.3 0.8 4. 4553Copyright © by Holt, Rinehart and Winston. 20 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 3-2 Adding and Subtracting Rational Numbers LESSON 0.3 0.8 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0 15 15 25 35 45 25 35 45 45 1 1 35 Add or subtract.Write answers in simplest form. 5. 57176. 18587. 152 112 8. 136 156 9. 125 185 10. 270 230 11. 158 178 12. 235 2151Evaluate each expression for the given value of the variable. 13. 92.7 x for x 4.8 14. 27.3 x for x 9.5 15. 254 x for x 274 112 97.5 17.8 285 23152512133467150.5 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 21 Holt Middle School Math All rights reserved. Multiply.Write each answer in simplest form. 1. 6232. 9133. 8136 4. 14375. 152 265 6. 112 1587. 131288. 152 1659. 56122010. 274 132511. 1294152712. 13835141Multiply. 13. 3.1(2.6) 14. 0.72(0.05) 15. (8)(5.8) 16. 4(5.56) 17. 0.08(6.02) 18. 0.7(9.3) 19. (1.14)(9.5) 20. (6.5)(3.6) 21. 18(0.15) 22. (4.32)(7.1) 23. 11.3(6.2) 24. (8.516)(3.25) Evaluate 314x for each value of x. 25. x 3 26. x 2327. x 2 28. x 1229. Blaine repaired a damaged car in 812hours. He received $26.50 an hour for his work. How much was Blaine paid for repairing the car? $225.25 1586122169342.7 30.672 70.06 27.677 0.4816 6.51 10.83 23.4 8.06 0.036 46.4 22.24 1916110 12163 130 110 16 124 3 Name Date Class Homework and Practice 3-3 Multiplying Rational Numbers LESSON Holt Pre-AlgebraDivide.Write each answer in simplest form. 1. 14582. 56152 3. 25170 4. 134675. 79566. 290 347. 111245448. 133034959. 20 4910. 78(21) 11. 10 4512. 2215(14) Divide. 13. 32 0.4 14. 6.58 0.08 15. 7.26 (0.03) 16. 3.333 0.66 17. 0.0096 (1.2) 18. 25.28 1.6 19. 17.5 0.07 20. 279.4 12.7 21. 71.46 9 22. 36.3 (1.6) 23. 984.6 2.4 24. 601.96 2.02 Evaluate each expression for the given value of the variable. 25. 5x2for x 0.16 26. 14x.52 for x 5.5 27. 54x.72 for x 0.003 28. A 3.6-pound beef roast cost $10.62. What is the cost of the beef roast per pound? $2.95 per pound 325 2.64 18,2407.94 22.6875 410.25 298 0.008 15.8 250 22 80 82.25 242 5.05 530 1212214 45 12118351145 14472 25Copyright © by Holt, Rinehart and Winston. 22 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 3-4 Dividing Rational Numbers LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 23 Holt Middle School Math All rights reserved. Add or subtract.Write the answer in simplest form. 1. 12382. 35143. 79152 4. 59325. 130 126. 172 155 7. 145258. 152 529. 78152 10. 21831411. 43512312. 61345613. 7 57814. 816172 15. 16 8916. 4170 11 Evaluate each expression for the given value of the variable. 17. 258x for x 31418. 112x for x 25619. 749x for x 7 20. 958x for x 63421. 1538x for x 13422. 1529x for x122323. Brendan practiced soccer for 112hours on Monday, 114hours on Tuesday, 116hours on Wednesday and 34hours on Thursday in preparation for the game on Friday. How many total hours did Brendan practice soccer in this week? 423hours 2591358163849113586130 16897172 11811221145 5382114 610 231445193136 2170 18Name Date Class Homework and Practice 3-5 Adding and Subtracting with Unlike Denominators LESSON Holt Pre-AlgebraSolve. 1. y 3.2 4.7 2. x 5.61 3.89 3. 0.4d 8.2 4. b 2 17.5 5. a 101 14.2 6. 3.3x 108.9 7. 19.48 x 28.03 8. 10m.1 3.5 9. 217.25 39.5w 10. 4t.714.7 11. b 29.15 17.73 12. 7r .6 3.05 Solve. Write each in simplest form. 13. 58y 23814. 1225m 590 15. 365 r 215816. x 170 33517. y 111842918. 294 w 312819. Jessica baked 10 dozen cookies. She left 18of the baked cookies home and took the rest to school for the bake sale. How many cookies did Jessica take to school? 105 cookies 20. Doug must take 1.25 milliliters of medicine every day. How many days will the medicine last if Doug was given a prescription of the medicine in a bottle containing 50 milliliters? 40 days w 112y 456x 2190 r 415m 38y 134t 69.09 b 11.42 r 23.18 x 8.55 m 35.35 w 5.5 b 19.5 a 115.2 x 33 y 1.5 x 1.72 d 20.5 Copyright © by Holt, Rinehart and Winston. 24 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 3-6 Solving Equations with Rational Numbers LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 25 Holt Middle School Math All rights reserved. Solve. 1. 15.7 y 9.4 2. 2x.5 1.54 3. 6.2t 14.57 4. 4.x56 18.5 5. 16.87 h 15.92 6. 8.3w 350.26 Solve. Write answers in simplest form. 7. w 194 154 8. x 1115459. 1201n 24710. 423y 24911. x14 125812. a 1178 26513. d 2185 3170 14. x 3172 35915. 438y 17316. Mr. Conner’s students made kites in science class. He bought a 500-yd bolt of twine to tie to the kites. If he wants to give each student a piece of twine 3313yards long, what is the maximum number of pieces of twine Mr. Conner will be able to make from the bolt of twine? 15 pieces y 4169 x 316 d 6370 a 149x 712y 2111 n 525x 1185 w 27x 84.36 h 0.95 w 42.2 y 25.1 x 3.85 t 2.35 Name Date Class Homework and Practice 3-7 Solving Inequalities with Rational Numbers LESSON Holt Pre-AlgebraFind the two square roots for each number. 1. 16 2. 9 3. 64 4. 121 5. 36 6. 100 7. 225 8. 400 Evaluate each expression. 9. 2737 10. 4159 11. 12241 12. 16723 13. 38119 14. 2525 15. 169 36 16. 196 25 17. 98118. 4.96419. 2225520. 120.5021. Find the product of six and the sum of the square roots of 100 and 225. 150 22. Find the difference between the square root of 361 and the square root of 289. 2 23. If a replica of the ancient pyramids were built with a base area of 1,024 in.2, what would be the length of each side?( Hint: s A) 32 in. 24. The maximum displacement speed of a boat is found using the formula: Maximum Speed in km/h 4.5 thewaterlinelengthoftheboatinmeters. Find the maximum displacement speed of a boat that has a waterline length of 9 meters. 13.5 km/h 1 39.2 3 4 30 20 7 39 8 10 9 12 6, 6 10, 10 15, 15 20, 20 4, 4 3, 3 8, 8 11, 11 Copyright © by Holt, Rinehart and Winston. 26 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 3-8 Squares and Square Roots LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 27 Holt Middle School Math All rights reserved. Each square root is between two integers. Name the integers. 1. 102. 243. 514. 395. 666. 307. 788. 87Use a calculator to find each value. Round to the nearest tenth. 9. 1810. 6311. 1912. 4113. 5314. 9815. 5416. 7217. 8318. 12019. 20020. 48921. The distance a person can see at sea is measured in miles by using the formula d 32h, where h is the height in ft above sea level. About how many miles can a person see that is 8 feet above sea level? Round the answer to the nearest tenth of a mile. 3.5 miles 22. The length of the hypotenuse of a right triangle is the square root of the sum of the squares of the measures of the other two legs of the triangle. Approximate the length of the hypotenuse of a right triangle if the legs have measures 12 and 15. 19.2 23. At an accident scene, a police officer may determine the rate of speed, r, in mi/h, of the car by using the following formula r 20, where is length of the skid marks. How fast was a car going if the skid marks at the scene are 180 ft long? 60 mph 9.1 11 14.1 22.1 7.3 9.9 7.3 8.5 4.2 7.9 4.4 6.4 8 66 9 5 30 6 8 78 9 9 8710 3 10 4 4 24 5 7 51 8 6 39 7 Name Date Class Homework and Practice 3-9 Finding Square Roots LESSON Holt Pre-AlgebraWrite all names that apply to each number. 1. 34 62. 136 3. 0.81 4. 81 5. 7.233 6. 95State if the number is rational, irrational, or not a real number. 7. 498. 1449. 9310. 89111. 20112. 28013. 10014. 8.67 Find a real number between each pair of numbers. 15. 425and 43516. 7.25 and 12517. 58and 3418. Give an example of a rational number between 36and 36sample answer; 1 19. Give an example of an irrational number less than 0. sample answer; 320. Give an example of a number that is not real. sample answer; 54 sample answer: 170 sample answer: 4sample answer: 7.3 12not real rational not real rational rational rational irrational rational integer, rational, real rational, real irrational, real rational, real rational, real integer, rational, real, whole Copyright © by Holt, Rinehart and Winston. 28 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 3-10 The Real Numbers LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 29 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 4-1 Samples and Surveys LESSON Identify the population and sample. Give a reason why the sample could be biased. 1. The customers at a diner are surveyed to determine the number of times that local people eat out in a week. population local people sample all the customers of the diner possible bias people already eating out are more likely to eat out 2. At a school with school colors of purple and white, the male students are asked to name their favorite color. population students at the school sample male students surveyed possible bias will say their school colors 3. The first one thousand adults at a professional baseball game are surveyed and asked to name their favorite sport. population all the people at the game sample adults surveyed possible bias already at a baseball game Identify the sampling method used. 4. The supervisor of the recreational committee visits 5 of the city’s pools and collects water samples from the pools at various times of the day. stratified 5. Commuters on a subway are selected at random and asked to name their favorite flavor of ice cream. random 6. The register receipt of every 10th shopper at a grocery store is automatically compiled into a data base of the total amount spend and the items purchased. systematic Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 30 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 4-2 Organizing Data LESSON 1. Use the given data to make a table. Two hundred people were asked which was their favorite type of movie—comedy, drama, or action. The men’s choices were 10 for comedy, 35 for drama and 55 for action. The women’s choices were 45 for comedy, 50 for drama and 5 for action. List the data values in the stem-and-leaf plot. 2. 3. 4. Use the given data to make a stem-and-leaf plot. 5. Use the given data to make a back-to-back stem-and-leaf plot. 44, 46, 48, 50, 52, 54, 56, 67, 81, 83, 85, 87 12, 15, 17, 18, 20, 20, 26, 31, 31, 32, 32, 45, 46 Choice Comedy Drama Action Men 10 35 55 Women 45 50 5 1 2 5 7 8 2 0 0 6 3 1 1 2 2 4 5 6 key:45 45 4 4 6 8 5 0 2 4 6 6 7 8 1 3 5 7 key:81 81 6 7 7 2 5 7 8 0 1 5 6 6 9 2 4 4 key: 9 2 92 Wins Losses 6 5 67 1 7 9 5 3 8 1 9 6 7 key: 9 6 represents 96 3 8 represents 83 Michael’s Test Scores 86 85 92 75 72 94 81 86 94 77 67 80 MLB American League—Central Division 2000–2001 Final Standings MLB Team Wins Losses Cleveland 91 71 Minnesota 85 77 Chicago 83 79 Detroit 66 96 Kansas City 65 97 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 31 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 4-3 Central Tendency LESSON Find the mean, median, and mode of each data set. 1. 9, 5, 8, 5, 9, 8, 4, 8, 7 2. 8.3, 3.8, 4.2, 6.4, 3.9, 7.7, 4.2 mean: mean: median: median: mode: mode: 3. 41, 43, 44, 42, 44, 45, 42, 47, 43, 46 4. 2, 27, 6, 47, 22, 6, 11, 8, 52, 6, 25, 19 mean: mean: median: median: mode: mode: 5. The Baylus family’s food bills for the last 6 months were $362, $354, $412, $415, $354 and $353. What is the mean, median, and mode of the food bills for this time period? mean: $375; median: $358; mode: $354 Use the data to find each answer. 6. Find the mean of the areas in square miles. 31,638,800 sq. mi. 7. Find the median of the area in square miles. 28,557,500 sq. mi. 8. Find the mean and median of the greatest known depth in feet. mean: 27,340 ft; median: 27,353 ft 42, 43, 44 643.5 15 43.7 19.25 8 4.2 8 4.2 7 5.5 Oceans Area in sq. mi. Greatest Known Depth in ft. Pacific Ocean 64,000,000 36,198 Atlantic Ocean 31,815,000 30,246 Indian Ocean 25,300,000 24,460 Artic Ocean 5,440,200 18,456 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 32 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 4-4 Variability LESSON Find the range and the first and third quartiles for each data set. 1. 52, 36, 41, 48, 55, 31, 57 2. 26, 28, 42, 43, 22, 56, 51, 36 range: range: first quartile: first quartile: third quartile: third quartile: Use the given data to make a box-and-whisker plot. 3. 44, 56, 30, 73, 34, 55, 62, 51 4. 26, 37, 45, 62, 55, 11, 27, 72, 51, 48, 43, 38, 47 Use the box-and-whisker plots to compare the data sets. 5. Compare the ranges and medians. The range of data set 2 is greater than the range of data set 1. The median of data set 1 is greater than the median of data set 2. 6. Compare the ranges of the middle half of the data for each. The range of the middle half of data set 1 is greater than the middle half of data set 2. 10 20 30 40 50 60 70 80 90 100 Data Set 2 Data Set 1 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 55 47 36 27 26 34Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 33 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 4-5 Displaying Data LESSON 1. Organize the data into a frequency table and make a bar graph. 5 3 8 4 7 8 8 4 8 4 5 7 4 6 5 3 8 7 7 4 8 2. Use the data to make a histogram with intervals of 5. 3. Make a line graph of the given data. Use the graph to estimate the percent of food expenses away from home in 1993. In 1993, approximately % of food expenses were away from the home. 37 Number Frequency 3 2 4 5 5 3 6 1 7 4 8 6 76543210 3 4 5 6 7 8 876543210 1–5 6–10 11–15 16–20 21–25 Percent of Food Expenses Away from Home Percent of Spending 45 40 35 30 25 20 15 1050 1960 1965 1970 1975 1980 1985 1990 1995 Minutes it takes students to travel to school 6 10 15 18 10 20 25 20 15 10 8 5 20 15 10 15 18 6 20 15 Percent of Food Expenses Away from Home 1960 19.9% 1980 32.2% 1965 22.8% 1985 35.8% 1970 26.3% 1990 36.7% 1975 28.5% 1995 38.2% Minutes it takes students to travel to school Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 34 Holt Middle School Math All rights reserved. Name Date Class Explain why each graph is misleading. 1. This graph is misleading because the vertical axis does not begin at zero. Also, several of the month’s sales figures are missing. This does not give a true picture of increases and decreases or total sales for the year. 2. This graph is misleading because the vertical axis does not begin at zero. This does not give a true comparison of the gas mileage for these vehicles. Explain why the statistic is misleading. 3. A toothpaste company advertises that 9 out of 10 dentists surveyed recommend their brand of toothpaste to their patients. This statistic is misleading because the company does not say how many dentists were surveyed to ask what brand of toothpaste they recommend. Also, it is important if these dentists were paid for their responses or if they received and distributed free samples to their patients. Homework and Practice 4-6 Misleading Graphs and Statistics LESSON Sales Report in Millions 400 350 300 250 200 150 100 January FebruaryMarch April May June JulyAugust September October November December Gas Mileage for 2002 Cars 33 32 31 30 29 28 27 26Chrysler Sebring Pontiac Grand Prix Honda AccordChevrolet Monte Carlo Oldsmobile Alero Chevrolet Cavalier Toyota Camry Pontiac Sunfire Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 35 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 4-7 Scatter Plots LESSON 1. Use the given data to make a scatter plot. Do the data sets have a positive, a negative, or no correlation? 6. Use the data to predict the percent of U.S. Households with a computer in 1998. In 1998, about % of U.S. households had a computer. 36 1. The type of car a person drives and the color of their hair. no correlation 4. The number of innings completed in a baseball game and the number of runs scored. positive correlation 3. The number of people working on a job and the hours to completion. negative correlation 5. The number of shares of stock owned and the amount received in dividends. positive correlation Total Fat Sandwich Calories Grams Chicken Breast 318 2 Chicken Teriyaki 374 1.5 Club 323 2 Cold Cut 441 7 Ham 288 1.5 Meatball 527 10 Roast Beef 293 2 Tuna 445 6 Turkey Breast 281 1.5 Veggie 226 1 Total Fat Grams Calories 12 10864200 100 200 300 400 500 600 Percent of U.S. Households with a Computer Year 1985 1990 1995 2000 Percent 8.2% 15% 24.1% 51% Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 36 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 5-1 Points, Lines, Planes, and Angles LESSON 11. If m 1 103, find m 2. m 2 10312. If m 2 115, find m 1. m 1 115In the figure, 1 and 2 are vertical angles. 1. Name four points in the figure. W, X, Y, Z 2. Name a line in the figure. WX3. Name the plane in the figure. WXY 4. Name three segments in the figure. WX, XY, or WZ6. Name a right angle in the figure. AXB 7. Name two acute angles in the figure BXC and CXD 8. Name two obtuse angles in the figure. AXC and CXE 9. Name a pair of complementary angles in the figure. BXC and CXD Z Y W XA BE D X C 12 Possible answers are given. 5. Name four rays in the figure. WX, XW, XY, or WZ10. Name three pair of supplementary angles in the figure. AXB and BXD, DXE and AXE, AXB and EXD Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 37 Holt Middle School Math All rights reserved. Name Date Class 1. Measure the angles formed by the transversal and the parallel lines.Which angles seem to be congruent. 1 3 5 7 and 2 4 6 8 In the figure, line x || line y. Find the measure of each indicated angle, if the m 8 34. 2. 2 3. 3 4. 4 5. 6 6. 7 7. 1 In the figure, line m || line n. Find the measure of each angle, if m 1 131. 8. 2 9. 3 10. 4 11. 5 12. 6 13. 7 In the figure, line a || line b. 14. Name all angles congruent to 5. 1, 3, 7 15. Name all angles congruent to 4. 2, 6, 8 16. Name three pairs of angles with sums of 180. 1 2, 3 4, 5 6, 7 8, 1 8, 2 7, 3 6, or 4 5 17. Which line is the transversal? line m 131491314913149341461463414634Homework and Practice 5-2 Parallel and Perpendicular Lines LESSON 1 2 4 35 6 8 7 xr s 1 2 4 35 6 8 7 xy a 8 7 5 64 3 1 2 n x m 8 7 5 6 4 3 1 2 a b m Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 38 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 5-3 Triangles LESSON 1. Find a in the right triangle. 2. Find b in the acute triangle. 3. Find m in the acute triangle. 4. Find y in the right triangle. 5. Find t in the right triangle. 6. Find x in the obtuse triangle 7. Find a in the right triangle. 8. Find x in the right triangle. 454248° x ° 45° a ° 4438113° 29° x ° 46° t ° 684347° y ° 55° m° 57° 387858° 44° b° 52° a° Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 39 Holt Middle School Math All rights reserved. Find the sum of the angle measures in each figure. 1. 2. 3. 4. 5. 6. Find the angle measure in each regular polygon. 7. 8. 9. 10. 11. 12. Write all the names that apply to each figure. 13. 14. 15. rectangle rhombus trapezoid parallelogram parallelogram quadrilateral quadrilateral quadrilateral 1441351089060120360540360180360720Name Date Class Homework and Practice 5-4 Polygons LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 40 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 5-5 Coordinate Geometry LESSON Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. 1. AD2. BC3. MW4. TD5. SV6. RS7. Which lines are parallel? BC||SV8. Which lines are perpendicular? MWRS;ADBC;TDXYADSVGraph the quadrilaterals with the given vertices. Write all the names that apply to each quadrilateral. 9. (3, 2), (6, 4), (4, 2), (6, 4) quadrilateral, trapezoid 10. (2, 6), (6, 5), (2, 5), (6, 6) quadrilateral, parallelogram, rectangle positive; 1 undefined negative; 230 negative; 1 positive; 1 X x C y V R Y A T BD W S M y x Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 41 Holt Middle School Math All rights reserved. Write a congruence statement for each pair of polygons. 1. triangle ABW triangle CDX 2. rectangle BDMR rectangle ACNS 3. pentagon DMSXW pentagon BRNTZ 4. rhombus DMTX rhombus KNSY Find the value of the variable if triangle ABC is congruent to triangle XYZ. 5. Find a. 6. Find b. 7. Find c. 8. Find x. 9. Find y. 10. Find z. 21 14 3118 41108DT X M NY K S D N T R Z B W M X S B D C N R M A S A W B 48° 48° 42° 42° D CX Name Date Class Homework and Practice 5-6 Congruence LESSON B Y 21 14 18 A C Z X x a ° c ° y b ° 108° z 31° 41° Holt Pre-AlgebraIdentify each as a translation, rotation, reflection, or none of these. 1. 2. 3. 4. Draw the image of the triangle after each transformation. 5. reflection across BC6. translation along ABso that C' coincides with B. Draw the image of the rectangle with vertices (1, 6), (3, 4), (3, 6), (5, 4) after each transformation. 7. translation 5 units down 8. 270clockwise rotation around (0, 0) y x y x A B ABCCA BBACCrotation reflection translation or reflection rotation Copyright © by Holt, Rinehart and Winston. 42 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 5-7 Transformations LESSON A BC Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 43 Holt Middle School Math All rights reserved. Complete the figure. The dashed line is the line of symmetry. 1. 2. 3. 4. 5. 6. Complete the figure. The point is the center of rotation. 7. 8. 9. 10. Name Date Class Homework and Practice 5-8 Symmetry LESSON Holt Pre-Algebra1. Name a possible combination of squares and triangles that would form a semiregular tessellation. 3 triangles, 2 squares 2. Create a semiregular tessellation that uses squares and triangles. sample answer: 3. Create another semiregular tessellation that uses squares and triangles. sample answer: 4. Create a tessellation with quadrilateral ABCD. sample answer: 5. Use rotations to create a variation of the tessellation in Exercise 4. sample answer: Copyright © by Holt, Rinehart and Winston. 44 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 5-9 Tessellations LESSON A B C D Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 45 Holt Middle School Math All rights reserved. Find the perimeter of each figure. 1. 2. 3. Graph each figure with the given vertices. Then find the area of each figure. 104 units 82 units 71.5 units 16.25 16.25 19.5 19.5 24 24 17 17 33 33 19 19 Name Date Class Homework and Practice 6-1 Perimeter and Area of Rectangles and Parallelograms LESSON 4. (4, 3), (7, 3), (4, 3), (7, 3) 66 units2 5.(7, 7), (7, 7), (7, 7), (7, 7) 196 units2 y x y x 6. Mrs. Delfina is having new carpet installed in a room and hall in her home. The diagram at the right shows the dimensions of the area. If the carpet costs $1.95 a square foot, how much will it cost Mrs. Delfina to carpet the area? $532.35 18 ft 16 ft 12.5 ft 3 ft Holt Pre-AlgebraFind the perimeter of each figure. 1. 2. 3. Graph and find the area of each figure with the given vertices. 1011 1212units 7858.3 units units 334 111 12 258258 512 414318 21.7 9.2 11.6 15.8 Copyright © by Holt, Rinehart and Winston. 46 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 6-2 Perimeter and Area of Triangles and Trapezoids LESSON 4. (6, 7), (2, 7), (3, 4) 44 units2 6. (1, 7), (4, 7), (3, 4), (6, 4) 5. (5, 0), (1, 4), (5, 0), (2, 4) 26 units2 7. (6, 2), (6, 2), (6, 4) y x y x y x y x 77 units2 36 units2 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 47 Holt Middle School Math All rights reserved. Find the length of the hypotenuse in each triangle. 1. 2. 3. 4. Graph the triangle formed with coordinates (7, 0), (7, 6), (1, 0) and find the length of the hypotenuse. Solve for the unknown side in each right triangle. Round the answers to the nearest hundredth. 10 15 26 45 27 36 24 10 9 12 Name Date Class Homework and Practice 6-3 The Pythagorean Theorem LESSON y x 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Use the Pythagorean Theorem to find the height of the triangle at the right. Then use the height to find the area of the triangle. h 25; area 750 units2 21.93 48.17 36.06 34 12 36 32 20 9 26.63 35 35.38 26 24 28 21 22 15 50 4.5 18.36 16 9 2.7 14 3.6 48 65 60 Holt Pre-Algebra1. circle with diameter 12 cm 12cm or 37.7 cm 3. circle with radius 17 ft 34ft or 106.8 ft 5. circle with radius 10.8 in. 21.6in. or 67.8 in. 2. circle with radius 11 in. 22in. or 69.1 in. 4. circle with diameter 28 yd 28yd or 87.9 yd 6. circle with diameter 23.6 m 23.6m or 74.1 m Copyright © by Holt, Rinehart and Winston. 48 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 6-4 Circles CHAPTER Find the circumference of each circle, both in terms of and to the nearest tenth of a unit. Use 3.14 for . Find the area of each circle, both in terms of and to the nearest tenth of a unit. Use 3.14 for . 7. circle with diameter 12 yd 36yd2 or 113.0 yd2 9. circle with radius 30 ft 900ft2 or 2,826 ft2 11. circle with radius 8.9 m 79.2m2 or 248.7 m2 13. Graph a circle with center (0, 0) that passes through (0, 5). Find the area and circumference, both in terms of and to the nearest tenth of a unit. Use 3.14 for . A 25units2 or 78.5 units2; C 10units or 31.4 units 8. circle with radius 16 cm 256cm2 or 803.8 cm2 10. circle with diameter 38 m 361m2 or 1,133.5 m2 12. circle with diameter 56 m 784m2 or 2,461.8 m2 y x 14. If a circle has an area of 7,850 yd2, what is the diameter of the circle? Use 3.14 for . 50 yd Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 49 Holt Middle School Math All rights reserved. 1. Use isometric dot paper to sketch a rectangular box that is 4 units long, 2 units wide, and 3 units tall. 2. Use isometric dot paper to sketch a cube that is 3 units on each edge. 3. Sketch a one-point perspective drawing of a triangular prism. sample answer: 4. Sketch a two-point perspective drawing of a rectangular box. sample answer: Name Date Class Homework and Practice 6-5 Drawing Three-Dimensional Figures LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 50 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 6-6 Volume of Prisms and Cylinders LESSON Find the volume to the nearest tenth of a unit. Use 3.14 for . 1. 2. 3. 4. 5. 6. 7. 8. 9. 3,048.6 in.3 480 m3 1,056 cm3 5.5 cm24 cm 12 m 8 cm 5 m 16 m 14.5 in. 14.5 in. 14.5 in. 56,160 mm3 2,208 in.3 4,220.2 cm3 21 cm 8 cm 23 in. 16 in. 12 in. 36 mm 65 mm 48 mm 512 ft3 1,177.5 cm3 1,120 yd3 20 yd 7 yd 8 yd 10 cm 15 cm 8 ft 8 ft 8 ft 10. A cylinder has a radius of 8 cm and a height of 20 cm. Explain whether tripling the height will triple the volume of the cylinder. The original cylinder has a volume of 1,280cm3. If you triple the height the volume is 3,840cm3, which is triple the original volume. 11. Find the height of a cylinder if the volume is 2,512 in.3 and the radius is 10 in. Use 3.14 for . 8 in. 12. What is the volume of a can of peanuts with a height of 5 in. and a lid that is 4 in. wide? Use 3.14 for . Round the answer to the nearest tenth of an inch. 62.8 in.3 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 51 Holt Middle School Math All rights reserved. Find the volume of each figure to the nearest tenth of a unit. Use 3.14 for . 1. 2. 3. 4. 5. 6. 7. A funnel has a diameter of 8 in. and is 21 in. deep.What is the volume of the funnel to the nearest tenth of a unit? Use 3.14 for 351.7 in.3 8. The radius of a cone is 13 ft and its height is 27 ft. Find the volume of the cone to the nearest tenth. Use 3.14 for . 4,775.9 ft3 9. Find the volume of a rectangular pyramid if the height is 35 cm and the base sides are 21 cm and 28 cm. 6,860 cm3 10. The base of a regular pyramid has an area of 135 in.2. The height of the pyramid is 8.5 in. Find the volume. 382.5 in.3 760 m3 942 cm3 7,500 cm3 36 cm 25 cm 25 cm 16 cm 15 cm 10 m 9.5 m 24 m 75.4 in.3 48 m3 12.6 ft3 2 ft 3 ft 4 m6 m 6 m 8 in. 6 in. Name Date Class Homework and Practice 6-7 Volume of Pyramids and Cones LESSON Holt Pre-AlgebraFind the surface area of each figure to the nearest of a tenth unit. Use 3.14 for . 1. 2. 3. 4. 5. 6. 7. 8. 9. 480 cm2 2,524.6 ft2 2007.6 in2 12.5 in. 18.6 in. 24.8 in. 12 ft 24 cm 21.5 ft 26 cm 10 cm 4 cm 8,664 cm2 251.2 m2 308 m2 13 m 6 m 4 m 3 m 5 m 38 cm 38 cm 38 cm 1,752 ft2 4,615.82 in. 2,820 yd2 20 yd 42 yd 15 yd 25 yd 34 in. 15 in. 22 ft 12 ft 18 ft Copyright © by Holt, Rinehart and Winston. 52 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 6-8 Surface Area of Prisms and Cylinders LESSON 10. Find the surface area to the nearest tenth of a unit of a cylinder 84.5 m tall that has a diameter of 50 m. Use 3.14 for . 17,191.5 m2 11. Find the surface area to the nearest tenth of a unit of a rectangular prism with height 24 cm and sides 18 cm and 14 cm. 2,040 cm2 12. A recipe calls for a 9 13 2 in. baking dish to have the inside of the baking dish coated before adding the recipe contents. What is the surface area of the baking dish that will be coated? 205 in.2 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 53 Holt Middle School Math All rights reserved. Find the surface area of each figure to the nearest of a tenth unit. Use 3.14 for . 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Find the length of the slant height of a square pyramid if the one side of the base is 26 cm and the surface area is 2,236 cm2. 30 cm 11. Find the surface area of a regular square pyramid with a slant height of 27 in. and a base perimeter of 96 in. 1,872 in.2 12. Find the length of the slant height of a cone with a radius of 40 ft and a surface area of 9,420 ft2. Use 3.14 for . 35 ft 2,355 in.2 2001 cm2 1,403.4 m2 19.6 m 19.6 m 26 m 23 cm 23 cm 32 cm 35 in. 30 in. 36 m2 1,912.3 yd2 693.8 ft2 12.5 ft 12.5 ft 21.5 ft 29.5 yd 3 m 3 m 14 yd 4.5 m 3,768 cm2 1,425 in.2 2,508.9 ft2 17 ft 30 ft 19 in. 19 in. 20 cm 28 in. 40 cm Name Date Class Homework and Practice 6-9 Surface Area of Pyramids and Cones LESSON Holt Pre-AlgebraFind the volume of each sphere, both in terms of and to the nearest tenth of a unit. Use 3.14 for . 1. r 12 yd 2. r 27 ft 3. d 36 m 4. d 48 ft 5. r 4.5 m 6. r 7.5 cm 7. r 33 cm 8. d 32.02 ft 9. d 60 m Find the surface area of each sphere, in terms of and to the nearest tenth of a unit. 10. 11. 12. 13. 14. 15. 16. Estimate to the nearest tenth of an inch the surface area of a baseball with a 3 in. diameter. Use 3.14 for . 28.3 in.2 4,069.4 ft2 624.3 cm2 5,805.9 in.2 1,296ft2198.8cm21,849in.221.5 in. 36 ft 14.1 cm 393.8 in.2 482.9 yd2 7,850 cm2 125.4in.2153.8yd22,500cm225 cm 12.4 yd 5.6 in. 150,456.2 cm3 17,180.8 ft3 113,040 m3 47,916cm35,471.6ft336,000m357,876.5 ft3 381.5 m3 1,766.3 cm3 18,432ft3121.5m3562.5cm37,234.6 yd3 82,406.2 ft3 24,416.6 m3 2,304yd326,244ft37,776m3Copyright © by Holt, Rinehart and Winston. 54 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 6-10 Spheres LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 55 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 7-1 7-1 Ratios and Proportions LESSON Find two ratios that are equivalent to each given ratio. 1. 375 2. 146 3. 41864. 785. 2646. 217. 13408. 1669. 4255Simplify to tell whether the ratios form a proportion. 10. 1600and 122 11. 1204and 370212. 287 and 156613. 396 and 410314. 1247and 482115. 1255and 230016. 1268and 230517. 1678and 516418. Mr. Blackwell had two ties for every five shirts he owned. If he owned 25 shirts, how many ties did he own? 10 ties 19. The school had the classroom walls painted. Seven out of 10 people surveyed liked the new color of the walls. Of the 250 people surveyed, how many people liked the new color of the walls? 175 yes, 1414yes, 4747no, 3523yes, 12472147 no, 144130 no, 28727yes, 152152 yes, 1616sample 59, 1108 sample 3122, 83sample 175, 4215 sample 36, 150 sample 82, 1482 sample 1146, 2214 sample 13, 3100 sample 14, 382 sample 15, 7140 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 56 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 7-2 Ratios, Rates and Unit Rates LESSON For exercises 1–3, use the bar graph to find each rate. 1. Helena’s salary per week $650 2. Aisha’s salary per day $145 3. Nani’s salary per hour $22.50 4. Of the 405 students who took the test, 162 of them passed. Write a ratio in simplest form for the number of students who passed the test to the number of students who took the test. 525. A lawn care company charges a homeowner $1,625 a year to maintain a lawn that is 65 ft by 50 ft. What is the maintenance fee per square foot? $0.50 per square foot 6. A 12 oz container of soda has 180 calories, how many calories are in one ounce of the soda? 15 calories Determine the better buy. 7. a 500-count ream of paper for $8.25 or a 1250-count ream of paper for $20 1250-count ream for $20 8. a 1.5 lb bag of carrots for $2.85 or a 2 lb bag of carrots for $3.84 1.5 lb bag for $2.85 9. Morgan paid $16.74 for 12.4 gallons of gasoline. What was the cost per gallon? $1.35 per gallon Yearly Gross Salary Based on 52 Weeks, 5 Days a Week, 8 Hours a Day $50,000 $40,000 $30,000 $20,000 $10,000 $0 AishaHelenaJenniferLianLyndaNaniTe r e s e $37,700 $33,800 $39,000 $45,500 $42,900 $46,800 $35,100 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 57 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 7-3 Problem Solving Skill: Analyze Units LESSON Find the appropriate factor for each conversion. 1. millimeters to meters 2. inches to yards 3. days to minutes 4. Oliver constructs a fence around a garden that is 24 feet by 36 feet. How many yards of fencing does Oliver need? 40 yards 5. Marci drinks four 48 ounce glasses of water a day. How many pints of water does she drink every day? 12 pints 6. Christopher wrestles for his high school in the light heavyweight division. Christopher weighs 175 pounds. How many ounces does he weigh? 2800 ounces 7. Mari bought 912yards of ribbon. How many inches of ribbon did she buy? 342 inches 8. A bag of frozen vegetables weighs 64 ounces. How many pounds does the package of vegetables weigh? 4 pounds 9. The 18th hole on the local golf course is 543 yards long. How many feet is the distance of this par 5 hole? 1,629 feet A Boeing 777-300 commercial jetliner has a maximum take-off weight of 660,000 pounds, wing span of 199 feet 11 inches, overall length of 242 feet 4 inches, and an interior cabin width of 19 feet 3 inches. Find the following dimensions of the plane. 10. What is the maximum take-off weight in tons? 330 tons 11. What is the measure of the wing span in inches? 2,399 inches 12. What is the overall length of the plane in yards? 80.77 yards 14140damyin 316 yind. 10010mmm Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 58 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 7-4 Solving Proportions LESSON Tell whether each pair of ratios are proportional. 1. 56? 33062. 280 ? 164 3. 1227? 188 4. 1135? 43595. 186 ? 15000 6. 2419? 13467. 1284? 195 8. 148 ? 81189. 1160? 226010. 2144? 326111. 2156? 5412. 1171? 3531Solve each proportion. 13. 145 4a5 14. 1168w815. 1m1342416. 1t27417. 9b277218. 3x6221719. 6y158120. 13021x521. 48512n7 22. 22814t423. 4d2 14497 24. 1r71 708225. The Orlemann family planted 3 rows of corn this year and harvested 270 ears. How many rows should they plant if they want to harvest 360 ears of corn? 4 rows 26. Find the number of times a heart beats in 2 minutes if it beats 576 times in 8 minutes. 144 times 27. David is making chocolate-chip cookies. Chocolate chips cost $1.79 for 12 ounces. David buys 60 ounces of chocolate chips for the cookies. How much did the chocolate chips cost? $8.95 n 15 t 33 d 14 r 13 b 24 x 28 y 17 x 48 a 12 w 9 m 8 t 21 no yes no yes yes no no yes yes no yes yes Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 59 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 7-5 Dilations LESSON Tell whether each transformation is a dilation. 1. 2. Dilate each figure by the given scale factor with P as the center of dilation. 3. scale factor is 2 4. scale factor is 31Dilate each figure by the given scale with the origin as the center of dilation. What are the coordinates of the image? 5. scale factor is 2 6. scale factor is 317. scale factor is 3 8. scale factor is 41(6,6), (6,6), (6,6), (6,6) (3,3), (2,3), (2,1), (3,1) A BD C y x O BDCAA BD C BDCy x O A(1,8), (8,0), (8,8) (0,0), (4,0), (2,2), (0,2) A B D C BDCy O x AA B C ABCy x O A P C B ACBP A BD C ABDCdilation not a dilation Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 60 Holt Middle School Math All rights reserved. Name Date Class 1. Which figures are similar to ABCD? all figures are similar 2. If a tree casts a 22-ft shadow at the same time a 6-ft tall person casts a 4-ft shadow, how tall is the tree? 33 ft 3. In RST, RS 28 cm, ST 20 cm, RT 24 cm. If DKM is similar to RST and the ratio of the corresponding sides of DKM to RST is 3 to 4, find the lengths of DK, KM, and DM. DK 21 cm, KM 15 cm, DM 18 cm 4. A nickel is approximately 20 mm in diameter and a quarter is approximately 25 mm in diameter. If the nickel is enlarged to a diameter of 128 mm, what would be the diameter of the quarter using the same scale? 160 mm 5. The students gave their school a gift of an American flag that measures 30 ft by 50 ft. They wanted to make a scale drawing of the flag to place on a plaque acknowledging the gift. What would the dimensions of the flag on the plaque be if it were made to a scale of 10 ft 1 in.? 3 in. 5 in. 6. Lilly is enlarging a photo that is 4 in. wide and 6 in. long to a photo that is 24 in. wide. What would be the length of the new photo after the enlargement? 36 in. 7. A 4 ft tall child is standing by The Leaning Tower of Pisa in Italy. The child casts a 15 ft shadow at the same time the tower casts a 675 ft shadow. Approximate the height of the Leaning Tower of Pisa. 180 ft Homework and Practice 7-6 Similar Figures LESSON A B D C14 16 W X M L S Z F G RN P Y21 28 21 24 32 24 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 61 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 7-7 Scale Drawings LESSON The scale of a drawing is 14in. 12 ft. Find the actual measurement. 1. 8 in. 2. 11 in. 3. 16 in. 4. 18 in. 5. 22 in. 6. 27 in. 7. 21.5 in. 8. 38.5 in. The scale is 2 cm 15 m. Find the length each measurement would be on a scale drawing. 9. 180 m 10. 585 m 11. 330 m 12. 420 m 13. 225 m 14. 622.5 m 15. 547.5 m 16. 682.5 m 17. On a map the distance between Charleston and Mt. Pleasant is 3.2 cm. The scale is 1 cm 25 mi.What is the actual distance in miles between these two towns? 80 mi 18. Blueprints of a building are drawn with a scale of 1 cm 25 ft. If the base of the building is a square with a perimeter 700 feet, what is the length of one side of the base of the building on the scale drawing? 7 cm 19. If the scale drawing of a room has measurements of 8 cm by 4.5 cm and the scale of the drawing is 1 cm 8 ft, what are the actual measurements of the room? 64 ft 36 ft 30 cm 83 cm 73 cm 91 cm 24 cm 78 cm 44 cm 56 cm 1,056 ft 1,296 ft 1,032 ft 1,848 ft 384 ft 528 ft 768 ft 864 ft Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 62 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 7-8 Scale Models LESSON Tell whether each scale reduces, enlarges, or preserves the size of the actual object. 1. 1 in.:15 in. 2. 3 ft:1 yd. 3. 1 cm:1 in. 4. 40 cm:10 in. 5. 1,760 yd:1 mi 6. 1 mi:1 km Change both measurements to the same unit of measure, and find the scale factor. 7. 2-in. model of a 5-ft desk 8. 4-ft model of a 120-yd field 9. 30-cm model of a 7.5-m wall 10. 50-in. model of a 7,000-ft volcano 11. The museum has a 2-ft model of a 10-yard shark. What is the scale factor of the model? 1:15 12. Marina made a scale model of her yard. Her yard is 40 ft 28 ft 9 in. Her drawing is 16 in. 11.5 in. What scale factor did she use? 1:30 13. A 17 in. model of a 2002 Buick Rendezvous is made with a scale factor of 111 . Estimate the actual length of a 2002 Buick Rendezvous? 187 in. 14. A miniature fireplace for a dollhouse is 4.5 in. by 6.75 in. If the scale factor is 112 , what size fireplace does the miniature represent? 54 in. 81 in. 1:25 1:1,680 1:30 1:90 enlarges preserves enlarges reduces preserves reduces Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 63 Holt Middle School Math All rights reserved. A 15-in. cube is built from small cubes, each 1 in. on a side. Compare the following values. 1. the side lengths of the two cubes The sides of the 15-in. cube are 15 times as long as the sides of the 1-in. cube. 2. the surface area of the two cubes The surface area of the 15-in. cube is 1,350 or 152 times that of the 1-in. cube. 3. the volumes of the two cubes The volume of the 15-in. cube is 3,375 or 153 times that of the 1-in. cube. A 20-in. cube is built from small cubes, each 1 in. on a side. Compare the following values. 4. the side lengths of the two cubes The sides of the 20-in. cube are 20 times as long as the sides of the 1-in. cube. 5. the surface area of the two cubes The surface area of the 20-in. cube is 2,400, or 202 times that of the 1-in. cube. 6. the volumes of the two cubes The volume of the 20-in. cube is 8,000, or 203 times that of the 1-in. cube. 7. The dimensions of a warehouse are 180 ft long, 225 ft wide, and 90 ft high. The scale model used to build the warehouse is 15 in. long. Find the width and height of the model of the warehouse. 18.75 in. wide and 7.5 in. high 8. A 4-cm 3-cm 5-cm solid figure is built with centimeter cubes. If each dimension is doubled, how many cubes are used to build the larger solid? 480 cubes Name Date Class Homework and Practice 7-9 Scaling 3-Dimensional Figures LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 64 Holt Middle School Math All rights reserved. Name Date Class Find the missing ratio or percent equivalent for each letter on the number line. 1. a 2. b 3. c 4. d 5. k 6. n 7. s 8. w Find each equivalent value. 9. 44% as a fraction 10. 530 as a decimal 11. 1430as a percent 12. 35as a percent 13. 1119% as a fraction 14. 38as a decimal 15. At Eduardo’s party, 18 friends attended but 6 friends could not come.What percent of the people invited could come to the party? 75% 16. On a math quiz, Ande answered 34 out of 40 questions correctly.What percent did she answer correctly? 85% 17. There are 300 students and 25 tables in the school cafeteria. If the students are seated equally at the tables, what percent of the students are seated at one table? 4% 0.375 1960% 32.5% 0.06 2115 270 5390 20% 12.5% 2130 215 48% 90% 0%4% 35% 65% 78% 100% c n k w a d s b 181512 25 9 10 Homework and Practice 8-1 Relating Decimals, Fractions, and Percents LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 65 Holt Middle School Math All rights reserved. Name Date Class Find each percent. 1. What percent of 60 is 45? 2. 45 is what percent of 90? 3. What percent of 45 is 18? 4. What percent of 75 is 15? 5. 21 is what percent of 84? 6. 51 is what percent of 85? 7. What percent of 60 is 27? 8. What percent of 90 is 27? 9. 18 is what percent of 60? 10. 24.2 is what percent of 110? 11. What percent of 42 is 35? 12. What percent of 64 is 24? 13. What percent of 78 is 27.3? 14. 105 is what percent of 60? 15. An airplane completed 900 miles of a 1200-mile flight. What percent of the trip remains to be completed? 25% 16. Cloe had 36 of the 45 questions on the math test correct. What percent of problems did Cloe have correct? 80% 17. Lincoln received $55 for his birthday. He puts $22 of it in his savings account.What percent of the money did Lincoln deposit in his savings account? 40% 18. Chico bought a jacket for $42. The cost of the jacket including tax, was $44.31. What was the percent of sales tax on the purchase? 5.5%35% 175% 8337.5% 13% 30% 22% 45% 30% 25% 60% 40% 20% 75% 50% Homework and Practice 8-2 Finding Percents LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 66 Holt Middle School Math All rights reserved. Name Date Class Find each number. 1. 25% of what number is 12? 2. 27 is 54% of what number? 3. 51 is 60% of what number? 4. 32% of what number is 8? 5. 80% of what number is 16? 6. 76 is 95% of what number? 7. 27 is 18% of what number? 8. 24% of what number is 72? 9. 104 is 65% of what number? 10. 12 is 3% of what number? 11. 5% of what number is 12.2? 12. 16% of what number is 4.8? 13. 90 is 6623% of what number? 14. 40.5 is 150% of what number? 15. Meredith bought a bicycle that cost $385.89. In addition, she had to pay 7% sales tax on her purchase.What was the amount of sales tax Meredith paid? Round the answer to the nearest cent. $27.01 16. Wilson answered 92% of a 25 question test correctly. How many questions did he answer correctly? 23 17. Rodriquez had $84.60 of his salary withheld for taxes. This was 15% of his gross pay. What is his gross pay? $564 18. A car dealer receives an order of 340 new cars. Thirty percent of the cars are silver in color. How many of the cars received by the dealership are silver? 102 135 27 244 30 160 400 150 300 20 80 85 25 48 50 Homework and Practice 8-3 Finding a Number When the Percent Is Known LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 67 Holt Middle School Math All rights reserved. Name Date Class Find each percent increase or decrease to the nearest percent. 1. from 16 to 12 2. from 40 to 46 3. from 20 to 26 4. from 50 to 38 5. from 75 to 45 6. from 30 to 45 7. from 27 to 35.1 8. from 35 to 22.75 9. from 84 to 54.6 10. from 35 to 42.7 11. from 39 to 97.5 12. from 108 to 86.4 13. from 63 to 39 14. from 81 to 124 15. from 72 to 98 16. The regular price of track shoes is $49.75. They are on sale for $39.80. What is the percent of decrease for the sale price? 20% 17. An electronics store pays a $255.50 for a TV and sells it for $357.70. What is the percent of increase in the price of the TV? 40% 18. The Globe Company has laid off 1,220 employees of the company’s 24,400 employees.What is the percent of decrease in the company’s work force? 5% 19. Brooke is given a 4% raise which makes her salary $754 a week. What was Brooke’s salary before the salary increase? $725 20. Clyde weighed 200 pounds and lost 15 pounds.What was the percent of decrease in his weight? 7.5% decrease 38% increase 53% increase 36% increase 22% increase 150% decrease 20% increase 30% decrease 35% decrease 35% decrease 24% decrease 40% increase 50% decrease 25% increase 15% increase 30% Homework and Practice 8-4 Percent Increase and Decrease LESSON Holt Pre-AlgebraEstimate. 1. 26 out of 51 2. 24% of 42 3. 19% of 20 4. 30% of 73 5. 68% of 103 6. 61 out of 82 7. 32 out of 98 8. 34 out of 84 9. 50% of 19.6 Estimate each number or percent. 10. 10% of 81.2 is about what number? 11. 18 is 26% of about what number? 12. About what number is 33% of 46? 13. 32 is 39% of about what number? 14. On Tuesday, 453 students attend school. This is about 91% of the total enrollment. Estimate the school’s total enrollment. about 500 students 15. Suzette bought dinner for her friends. The total cost of the meals was $73.95. Suzette left a tip of $15. Approximate the percent of the tip to the cost of the meals. about 20% 16. Of the 294 students who took the state test, 31 of them must retake the test. Estimate the percent of students who need to retake the test. about 10% 17. The usual markup on shoes at Fast Times Department Store is 240%. During a 25%-off sale, the store sold a pair of shoes for $39.95. Estimate the amount of the store’s profit on the shoes. about $20 about 15 about 80 about 8 about 70 about 33% about 40% about 10 about 25 about 70 about 75% about 50% about 10 about 4 Homework and Practice 8-5 Estimating with Percents LESSON Copyright © by Holt, Rinehart and Winston. 68 Holt Middle School Math All rights reserved. Name Date ClassHolt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 69 Holt Middle School Math All rights reserved. Name Date Class Complete the table to find the amount of sales tax for each sale amount to the nearest cent. 1. Complete the table to find the commission for each sale amount to the nearest cent. 2. 3. Mr. Darney bought a house for $58,000. He made a down payment of 20% and got a loan for the rest.What was the amount of his loan? $46,400 4. Elijah buys three pens for $1.89 each and a notebook for $3.95. The sales tax rate is 6%.What is Elijah’s total cost? Round the answer to the nearest cent. $10.20 5. Seth is a real estate agent. He receives 8% commission on the selling price of any home he sells. If the last house he sold had a selling price of $145,900, what was Seth’s commission? $11,672 Homework and Practice 8-6 Applications of Percents LESSON 6% sales tax 7% sales tax 5.5% sales tax $53.50 $3.21 $3.75 $2.94 $80.50 $4.83 $5.64 $4.43 $219.95 $13.20 $15.40 $12.10 $2,640.00 $158.40 $184.80 $145.20 5% commission 8% commission 7.5% commission $365.00 $18.25 $29.20 $27.38 $2,140.00 $107.00 $171.20 $160.50 $16,300.00 $815.00 $1304.00 $1222.50 $94,750.00 $4,737.50 $7,580.00 $7,106.25 Holt Pre-AlgebraHomework and Practice 8-7 Simple Interest LESSON Copyright © by Holt, Rinehart and Winston. 70 Holt Middle School Math All rights reserved. Name Date Class Find the missing value. 1. principal $175 2. principal ? rate 4% rate 6% time 5 years time 6 years interest ? interest $81 3. principal $210 4. principal $125 rate 5% rate ?% time ? years time 4 years interest $31.50 interest $35 5. principal ? 6. principal ? rate 541% rate 6.5% time 2 years time 3 years interest $126 interest $165.75 7. Scott deposits $1,000 in an account that earns 5% simple interest. What will the account be worth after two years? $1,100 8. A bank pays 5.5% simple interest per year. Find the total amount at the end of one year on a principal of $3,000. $3,165 9. Mr.Womer borrowed $1,100 to start his own business. National Bank charged him 15% interest per year. Mr.Womer paid $330 in interest. For what period of time did he borrow the money? 2 years 10. Ms. Lang borrows $2,300 for 30 months at 13% interest per year. How much interest will Ms. Lang pay? What is the total amount she will repay? interest $747.50; total amount repaid $3,047.50 $1,200 $850 3 years 7% $35 $225 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 71 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 9-1 Probability LESSON The following table indicates the inventory totals for a shoe store. Find the probability for choosing the following types of shoes. 1. P(two-tone high-top) 2. P(black low cut) 3. P(white high top) 4. P(black shoe) 5. P(two-tone) 6. P(two-tone low cut) 7. P(blue shoe) 8. P(black or white) 9. P(low cut or high top) Find the probability of drawing the following colored candies from a jar containing 25 red, 15 blue, 20 green, 30 yellow, and 10 orange pieces of candy. 10. P(yellow) 11. P(red) 12. P(orange) 13. P(blue) 14. P(purple) 15. P(blue or green) 16. P(candy) 17. P(red or yellow) 18. There are 25 red, 16 green, 30 purple, 14 white, 20 black, and 15 orange marbles in a bag. What is the probability of picking a marble that is not purple? 4319. What is the probability of tossing a 4 on a regular numerical cube? 162110 1 270 0 230 110 14130 1 1115 0 110 145 2135 570 245 16Two-Tone Black White High-Top 25 54 21 Low Cut 15 24 11 Holt Pre-Algebra1. A number cube was thrown 125 times. The results are shown in the table below. Complete the table with the experimental probability for each outcome. The school spirit wear shop sells special sweatshirts with the school logo imprinted on them in sizes small, medium, large, x-large and xx-large. In the first hour the store is open, the first 50 customers buy 2 small, 4 medium, 5 large, 15 x-large, and the rest buy xx-large. Find the probability of the purchase of each of the different size sweatshirts from the store. 2. P(x-large sweatshirt) 3. P(medium sweatshirt) 4. P(xx-large sweatshirt) 5. P(small or large sweatshirt) If the store has 225 customers in the second hour they are open, predict how many sweatshirts of each size will be sold based on the purchases during the first hour. 6. number of small sweatshirts sold 7. number of medium sweatshirts sold 8. number of xx-large sweatshirts sold 9. number of large and x-large sweatshirts sold 10. Jay practiced his foul shots for the upcoming basketball game. He attempted 45 shots and made 36 of them.What is the probability that Jay would make the foul shot? 11. If Jay took 20 foul shots in the basketball game, predict how many shots he would make based on his practicing. 108 90 9 18 570 or 14% 1225or 48% 225 or 8% 130 or 30% Copyright © by Holt, Rinehart and Winston. 72 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 9-2 Experimental Probability LESSON Outcome 1 2 3 4 5 6 Frequency 15 25 20 26 18 21 Probability 12% 20% 16% 20.8%14.4% 16.8% 80% 16% Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 73 Holt Middle School Math All rights reserved. Use the table of random numbers for the problems below. Ms. Patrick gave the same math test to all three of her math classes. In the first two classes, 70% of the students received a grade above C. Estimate the probability that at least 13 of 20 students will receive a grade above C in the third class. 1. Using the first row as the first trial, count the successful outcomes and name the unsuccessful outcomes. 13 out of 20 successful; 96, 85, 96, 72, 98, 89, 87 2. Using the second row, count the successful outcomes and name the unsuccessful outcomes. 12 out of 20 successful; 93, 95, 74, 88, 86, 97, 80, 73 Determine the successful outcomes in the remaining rows of the random number table. 3. third row 4. fourth row 5. fifth row 6. sixth row 7. seventh row 8. eighth row 9. ninth row 10. tenth row 11. Based on the simulation, estimate the probability that at least 13 of 20 students will receive a grade above C. 50%14 8 12 16 13 13 12 10 Name Date Class Homework and Practice 9-3 Problem Solving Strategy: Use a Simulation LESSON 2596 3623 1053 2161 8550 9672 1044 9852 8935 8727 2393 1231 2795 2036 5138 7488 5814 2086 5397 8073 5086 9057 2050 7424 1706 1391 3585 3124 4164 9498 3274 5099 1789 7021 5636 2404 7180 3395 4734 0395 1387 7460 9196 0463 1388 5104 6408 7463 3289 9321 5891 8081 6222 9656 5606 8739 8698 3982 4974 9961 1544 2817 5296 1340 9750 3943 5697 1585 1097 8365 0442 3881 9080 7964 9357 8202 9987 5681 1288 7894 7170 4188 7099 7590 2158 0242 5299 4095 6986 3935 6039 5890 3996 0217 4045 6545 3744 8368 2034 8670 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 74 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 9-4 Theoretical Probability LESSON An experiment consists of rolling two fair dice. Find each probability. 1. P(total shown 4) 2. P(total shown 6) 3. P(total shown 10) 4. P(total shown 11) 5. P(total shown 1) 6. P(total shown 5) 7. P(total shown 2) 8. P(total shown 7) 9. P(total shown 8) Find the theoretical probability of having a thrown dart land in the indicated area. 10. P(landing in area A) 11. P(landing in area B) 12. P(landing in area C) 13. P(landing in area D) 14. P(landing in areas A or C) 15. What is the theoretical probability of winning a raffle if 375 tickets were sold and you bought 25? 115 16. The second place winner of the raffle could choose between 12 envelopes each with money in them. Two of the envelopes contained a $20 bill, 4 contained $10 bills, and 6 contained $5 bills.What is the theoretical probability that the winner will choose an envelope with a $20 bill in it? 165818181412158 172 1 190 118 112 356 112 A B CD Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 75 Holt Middle School Math All rights reserved. School identification codes at Truman School contain 1 letter followed by 3 numbers. All codes are equally likely. 1. Find the number of possible identification codes. 26,000 2. Find the probability that an ID code of the school does not contain the number 0. 1 286905040 1702090 0.729 3. The Dairy King Shop serves 3 flavors of ice cream: vanilla, chocolate, and vanilla/chocolate swirl. The ice cream can be served in a dish, sugar cone, or waffle cone and may be a small, medium, large, or jumbo size. Make a tree diagram indicating the possible outcomes for each ice cream served. 4. How many different ice cream selections does the Dairy King Shop have? 36 Find the probability for each of the following. Assume all selections are equally likely. 5. P(dish of ice cream) 6. P(vanilla and small ice cream) 7. P(medium size) 8. P(not a dish) 230.666 140.25 1120.083 130.333 Name Date Class Homework and Practice 9-5 The Fundamental Counting Principle LESSON small medium large jumbo small medium large jumbo small medium large jumbo small medium large jumbo small medium large jumbo small medium large jumbo small medium large jumbo small medium large jumbo small medium large jumbo dish dish dish vanilla sugar chocolate sugar vanilla/chocolate sugar swirl waffle waffle waffle Holt Pre-AlgebraEvaluate each expression. 1. 12! 2. 9! 3. 13! 10! 4. 11! 8! 5. 2 129!! 6. 1250!!7.(24 18!12)! 8.(2121! 5)! 9.(23 17!14)! 10. How many different 3 people committees can be formed from a group of 25 people? 2,300 11. From a class of 28 students, how many different ways can 4 students be selected to serve on the student council as president, vice president, secretary and treasurer? 491,400 12. The boys’ volleyball team has 24 players. If the coach chooses 9 boys to play at a time, how many different teams can be formed? 1,307,504 13. The golf tournament has 120 players signed up to play. How many different 4-person sets can be formed? 8,214,570 14. Mr. Cruz bought new tires for his car. The dealer advised Mr. Cruz to have the tires rotated every 5,000 miles. If Mr. Cruz takes the advice of the dealer and has the tires rotated a different way every 5,000 miles, how many possible miles would he drive before using all the possible rotations? 120,000 miles 13,366,080 2,441,880 980,179,200 39,876,480 9,240 1,860,480 479,001,600 362,880 6,223,392,000 Copyright © by Holt, Rinehart and Winston. 76 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 9-6 Permutations and Combinations LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 77 Holt Middle School Math All rights reserved. Determine if the events are dependent or independent. 1. spinning a spinner and rolling a numerical cube 2. drawing a card from a deck and not replacing it and then drawing another card 3. selecting a piece of cake and selecting a drink A jar contains 4 white chips, 5 purple chips, and 1 black chip. Chips are selected randomly one at a time, and are not replaced. Find the probability of the following. 4. P(purple then black) 5. P(black then white) 6. P(white then purple) 7. P(purple then white) 8. P(2 whites) 9. P(2 purples) 10. P(2 black chips) 11. P(white, then purple, 12. P(3 whites) then black) 13. Mrs. Benedict offers extra credit when she gives a math test. She writes the first 5 prime numbers on 5 separate cards and places them in a box. Students are permitted to draw one card to determine their extra credit when the test is finished. The cards are replaced after each student draws. What is the most extra credit a student can receive on a test? What is the probability of drawing that card? 11 extra credit points; probability is 51310 0.033 316 0 0.0277 290.22 125 0.133 290.22 290.22 425 0.044 118 0.055 independent dependent independent Name Date Class Homework and Practice 9-7 Independent and Dependent Events LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 78 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 9-8 Odds LESSON 1. If the probability of Courtney winning the raffle is 172 , what are the odds in favor of Courtney winning the raffle? 2. The odds in favor of the New York Yankees winning the World Series are 5 to 3. What is the probability that the Yankees will win the World Series? A bag contains 18 red jelly beans, 12 green jelly beans, 10 purple jelly beans, 6 yellow jelly beans, and 4 orange jelly beans. 3. Find P(green jelly bean) 4. Find P(red jelly bean) 5. Find P(yellow jelly bean) 6. Find the odds in favor of choosing a red jelly bean. 7. Find the odds against choosing a red jelly bean. 8. Find the odds in favor of choosing an orange jelly bean. 9. Find the odds against choosing a purple jelly bean. 10. Find the odds in favor of choosing a green jelly bean. 11. Find the odds against choosing a yellow jelly bean. 12. Find the odds in favor of not choosing an orange jelly bean. 23 : 2 22 : 3 6 : 19 4 : 1 2 : 23 16 : 9 9 : 16 235 0.12 295 0.36 265 0.24 580.625 7 : 5 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 79 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 10-1 Solving Two-Step Equations LESSON Write and solve a two-step equation to answer the following questions. 1. Sue wants to buy a new printer that costs $189. She has $125 saved. She has a job that pays $8 an hour. How many hours must she work to earn enough to buy the printer? x number of hours 189 8x 125 189 125 8x 125 125 64 8x 6 8488x8 x 2. Corbin’s car payment is $289. This is $37 less than 13of his monthly income. What is Corbin’s monthly income? x monthly income 289 13x 37 289 37 13x 37 37 326 13x 326 3 13x3 978 x Solve. 3. 13 3a 14 4. 13k 4 1 5. 8 3x5 6. 6 5d 1 7. 15y 936 8. 14x 6 11 9. w493 10. 0.3m 5 7 11. x7 53 12. 7 4a.23.5 13. 5r 234 14. 12.95.73d 15. Nineteen more than five times a number is eighty-four. Find the number. 13 16. Mr. Cruz buys some wood and pays $245. Each bundle of wood costs $15 and there is a delivery charge of $35. How many bundles of wood did Mr. Cruz buy? 14 bundles x 16 a 14.7 r 1 d 6.2 y 3 x 20 w 24 m 40 a 9 k 15 x 9 d 1 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 80 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 10-2 Solving Multistep Equations LESSON Solve. 1. 8y 4 7y 11 2. 2x 2 5x 23 3. 8 7a 8 3a 4. r 5r 525 5. 9w 12w 2 7 6. 38 24 7x 5x 7. 27y 5657y 1168. 58x 1 78x 439. 6x 16 15x11 10. 49w 6 13w 4 11. 0.05d 0.2d 17 13 12. 0.6m4.44.8m2.4 13. 8.2s 4 13.7s7 14. 11y 7.5 6y 2 15. 13x 4.6x 3.9 8.7 16. The measure of an angle is 34less than its supplement. Find the measure of each angle. angle 73; supplement 10717. The measure of an angle is 9more than twice its complement. Find the measure of each angle. angle 63; complement 2718. If the perimeter of the triangle is 139. Find the measure of each side. RS 24; ST 48; RT 67 s 2 y 1.9 x 1.5 w 18 d 200 m 1.62 y 2 x 1 x 3 r 5 w 3 x 7 y 15 x 3 a 4 T SR 2x 3x 5 x Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 81 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 10-3 Solving Equations with Variables on Both Sides LESSON Solve. 1. 5x 1 21 3x 2. 9y 3 6y 15 3. 7w 3 w 12.6 4. 12 8a 3a 3 5. 29n 5 2 59n 6. 1.8d 31 3.4d 19 7. 2b 30 4b 3 8. 4x 2.3 2x 3.7 9. 3(m 5) m 7 10. 5(3h 2) 2(h 8) 11. 5 12y 38y 6 12. 2x 124x 1413. 4(3r 2) 4 12r 14. 14x 7 13x 8 15. 3a245 2a 16. Mandy and Mackenzie spent the same amount of money at the arcade. They both played the same number of games. Mandy played $0.50 games and spent $10 on refreshments. Mackenzie played $0.75 games and spent $6 on refreshments. How many games did each person play? 16 17. The square and the equilateral triangle at the right have the same perimeter. Find the lengths of the sides of the square. 21 r x 180 a 2 12h 2 y 8 x 1 b 13.5 x 3 m 4 a 3 n 21 d 7.5 x 11 y 6 w 1.6 2x 1 3x 2 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 82 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 10-4 Solving Multistep Inequalities LESSON Solve and graph. 1. 5x 3 28 2. 10 12w 12 3. 7y 15 4y 18 4. 7a 12a 10 5. 19 4m 4m 11 6. 56d 8 13 7. 2(3x 1) 4(2x 3) 8. 14.1 25h 13.9 130 h 9. Six more than three-fourths a number is greater than or equal to one more than twice the number. Find the number. x 4 10. Ms. Garcia wants to carpet her bedroom which requires 24 square yards. Her budget will allow her to spend no more than $600 for the project. If the installation of the carpet will cost $162, what is the most she can pay per square yard for the carpeting? $18.25 per square yard 2101 2 3 4 5 6 7 8 9 1011 12 7654321 0 1 2 3 4 5 6 7 x 7 h 2 7654321 0 1 2 3 4 5 6 7 7654321 0 1 2 3 4 5 6 7 m 1 d 6 7654321 0 1 2 3 4 5 6 7 7654321 0 1 2 3 4 5 6 7 y 1 a 2 7654321 0 1 2 3 4 5 6 7 7654321 0 1 2 3 4 5 6 7 x 5 w 4Copyright © by Holt, Rinehart and Winston. 83 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 10-5 Solving for a Variable LESSON Solve each equation for the indicated variable. 1. If the formula of changing Celsius, C, temperature to Fahrenheit, F, temperature is C 59(F 32), solve for F. F 95C 32 2. If the formula for a man’s shoe size, s, is s 3f 24, where f is the foot length in inches, solve for f. 13s 8 f 3. If the volume of a cylinder is V r 2h, where r is the radius of the base and h is the height of the cylinder, solve for h. Vr2 h Solve each equation for y and graph. 4. 2x y 3 5. 2y 6x 8 y 2x 3 y 3x 4Copyright © by Holt, Rinehart and Winston. 84 Holt Middle School Math All rights reserved. Name Date Class Determine if the ordered pair is a solution of each system of equations. 1. (1, 3) 2. (1, 2) 3. (3, 5) yx 2 y 2x xy 8 y x 4 y x 1 x y 2 4. (1, 4) 5. (2, 4) 6. (2, 8) x 4y 3x 2y 14 2x y 4 3x 4y 4 2x y 3x y 2 7. (1, 2) 8. (0, 0) 9. (1, 3) 3x y 1 y 3x 4 2x y 5 6x 2y 2 y 3x 4 2x y 1 Solve each system of equations. 10. x y 12 11. 2x y 10 x y 0 x y 4 12. x y 8 13. 3x 2y 0 2x y 4 x 2y 8 14. The sum of two numbers is 206. The second number is 48 more than the first. Find the numbers.Write a system of equations and solve. x y 206; y x 48; (79,127) 15. Ryan and Juan collect baseball cards. Together they have 880 cards. Juan has 125 less than twice as many as Ryan. How many cards does each have? Write a system of equations and solve. x y 880; y 2x 125; (335,545); Ryan has 335 cards and Juan has 545 cards. (4, 4) (4, 6) (6, 6) (2, 6) no no yes no yes no yes yes no Homework and Practice 10-6 Systems of Equations LESSONCopyright © by Holt, Rinehart and Winston. 85 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 11-1 Graphing Linear Equations LESSON 1. y 3x 4 linear 2. y x 2 2 not linear Graph each equation and tell whether it is linear. y x 4 2 O 2 4 6 6 2 246 4 6 y x 4 2 O 2 4 6 6 2 246 4 6 x 3x 4 y (x, y) 4 3(4) 4 8 (4, 8) 3 3(3) 4 5 (3, 5) 2 3(2) 4 2 (2, 2) 1 3(1) 4 1 (1, 1) 0 3(0) 4 4 (0, 4) 1 3(1) 4 7 (1, 7) 2 3(2) 4 10 (2, 10) x x2 2 y (x, y) 3 (3)2 2 11 (3, 11) 2 (2)2 2 6 (2, 6) 1 (1)2 2 3 (1, 3) 0 (0)2 2 2 (0, 2) 1 (1)2 2 3 (1, 3) 2 (2)2 2 6 (2, 6) 3 (3)2 2 11 (3, 11) 3. A pharmaceutical representative sells $48,000 in a one month period. The rep earns 5.5% commission plus base salary of $400 a month. How much is the rep paid that month? $3,040 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 86 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 11-2 Slope of a Line LESSON Find the slope of the line passing through each pair of points. 1. (5, 7), (6, 9) 2. (2, 8), (8, 2) 3. (2, 6), (2, 4) 4. (8, 7), (9, 1) Use the graph of each line to determine its slope. 5. 6. Tell whether the lines passing through the given points are parallel or perpendicular. 7. line 1: (1, 2), (4, 8) 8. line 1: (6, 8), (6, 10) line 2: (6, 7), (7, 5) line 2: (5, 9), (3, 9) 9. Graph the line passing through the 10. Graph the line passing through the point (1, 4) with slope 12. point (1, 3) with slope 3. parallel perpendicular 344 y x 4 2 O 2 4 2 24 4 y x 4 2 O 2 4 2 24 4 2 1 undefined 6 y x 4 2 O 2 4 2 24 4 y x 4 2 O 2 4 2 24 4 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 87 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 11-3 Using Slopes and Intercepts LESSON Find the x-intercept and y-intercept of each line. Use the intercepts to graph the equation. 1. x y 5 2. 3x 2y 6 Write each equation in slope-intercept form and then find the slope and y-intercept. 3. 2x y 4 4. 4x 3y 9 5. x 4y 8 Write the equation of the line that passes through each pair of points in slope-intercept form. 6. (1, 7), (4, 3) 7. (2, 5), (8, 15) 8. (8, 4), (10, 5) 9. Thad’s father gives him $10 for a passing report card plus $5 for every grade of A. Write an equation of a line in slope-intercept form to express y, the amount received with x grades of A. State the slope, x-intercept, and y-intercept of the equation. y 5x 10; m 5; b 10; x-intercept is 2, y-intercept is 10 y 21y 2x 5 y x 7 x y 14x 2; m 14; b 2 y 43x 3; m 43; b 3 y 2x 4; m 2; b 4 x-intercept is 2; y-intercept is 3 x-intercept is 5; y-intercept is 5 y x 4 2 O 2 4 2 24 4 y x 4 2 O 2 4 2 24 4 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 88 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 11-4 Point-Slope Form LESSON Identify a point the line passes through and the slope of the line, given the point-slope form of the equation. 1. y 6 3(x 2) 2. y 42(x 1) 3. y 51(x 8) 4. y 3 4(x 2) 5. y 76(x 1) 6. y 4 9(x 6) 7. y 57(x 9) 8. y 7 13(x 9) 9. y 3 3.2(x 8) Write the point-slope form of the equation with the given slope that passes through the indicated point. 16. Write an equation of a line in point-slope form that is parallel to y 4x 7 and passes through the (8, 5) y 54(x 8) m 3.2; (x1, y1) (8, 3) m 13; (x1, y1) (9, 7) m7; (x1, y1) (9, 5) m 9; (x1, y1) (6, 4) m2; (x1, y1) (1, 7) m 4; (x1, y1) (2, 3) m1; (x1, y1) (8, 5) m2; (x1, y1) (1, 4) m 3; (x1, y1) (2, 6) 10. the line with slope 3 passing through (4, 3) y 33(x 4) 12. the line with slope 5 passing through (7, 1) y 1 5(x 7) 14. the line with slope 2 passing through (9, 6) y 6 2(x 9) 11. the line with slope 1 passing through (6, 2) y 21(x 6) 13. the line with slope 7 passing through (8, 4) y 4 7(x 8) 15. the line with slope 8 passing through (7, 3) y 38(x 7) Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 89 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 11-5 Direct Variation LESSON Make a graph to determine whether the data set shows direct variation. 1. The data set shows a direct variation. 2. Write the equation of direct variation for exercise 1. y 0.75x or y 34x Find each equation of direct variation, given that y varies directly with x. 3. y is 27 when x is 3 4. y is 8 when x is 40 5. y is 54 when x is 12 6. y is 21 when x is 49 7. y is 31.5 when x is 14 8. y is 180 when x is 216 9. Bridgett’s gross pay per year is $40,300. Her net pay is $27,001 as a result of her payroll deductions. Last year Bridgett’s gross salary was $37,700. Her net pay was $25,259. Write an equation of direct variation indicating Bridgett’s gross pay, x, versus her net pay, y. y 0.67x y65y 2.25x x y 73y x 29x y51y 9x x x y 4 3 8 6 0 0 4 3 y x 4 2 O 2 4 6 6 2 246 4 6 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 90 Holt Middle School Math All rights reserved. Name Date Class Graph each inequality. 1. y 3x 4 2. y 2x 5 3. x 3y 9 4. 3x y 1 5. Richard must buy clothes for his new job. He has a budget of $250. The shirts he plans on buying cost $15 and the slacks costs $30. Let x equal the number of shirts and y equal the number of pairs of slacks Richard can buy with his clothes allowance. Write an inequality for this information. 15x 30y 250 6. If Richard buys 4 pairs of slacks, what is the most number of shirts he can buy? The most number of shirts Richard can buy is 8. y x 4 2 O 2 4 2 24 4 y x 4 2 O 2 4 2 24 4 y x 4 2 O 2 4 2 24 4 y x 4 2 O 2 4 2 24 4 Homework and Practice 11-6 Graphing Inequalities in Two Variables LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 91 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 11-7 Lines of Best Fit LESSON Plot the data and find a line of best fit. 1. y x 10 2. y3x 150 3. Nuxhall Company wants to predict their payroll costs for the next two years based on the salary cost over the past six years. Use the information in the table below and a line of best fit to estimate the payroll costs for the next two years. Sample: yr 7—$160,731; yr 8—$173,590 160 140 120 100 80 60 40 2000 10 20 30 40 50 30 25 20 15 10500 5 10 15 20 x 2 4 6 8 10 12 14 16 y 12 14 18 16 20 21 25 26 x 5 10 18 20 25 30 35 40 y 135 120 105 90 94 56 50 30 x Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 y $96,750 $104,490 $112,925 $125,150 $131,650 $148,825 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 92 Holt Middle School Math All rights reserved. Name Date Class Determine if each sequence could be arithmetic. If so, give the common difference. 1. 19, 16, 13, 10, 2. 7, 14, 28, 56, 112, … 3. 8, 1, 6, 13, 20, … 7, … 4. 1, 2.2, 4.84, 10.648, 5. 110 , 35, 1110, 85, 2110, ... 6. 10.4, 8.7, 7.1, 23.4256 … 5.4, 3.7, … 7. 18, 14, 38, 12, 58, ... 8. 91, 42, 7, 56, 9. 25.3, 18.5, 11.7, 105, … 4.9, 1.9, … Find the given term in each arithmetic sequence. 10. 15th term: 35, 42, 49, 56, 63, … 11. 28th term: 41, 29, 17, 5, 7, … 12. 32nd term: 204, 158, 112, 66, 20, … 13. 97th term: 8, 22, 36, 50, 64, … 14. 45th term: 3, 5.9, 8.8, 11.7, 14.6, … 15. 61st term: 49, 31, 13, 5, 23, … 16. 74th term: 84, 62, 40, 18, 4, … 17. 37th term: 19, 49, 79, 119, 149, ... 18. Write the first six terms in an arithmetic sequence that begins with 8.7 and has a common difference of 3.9. 8.7, 12.6, 16.5, 20.4, 24.3, 28.2, … 20. Corrine starts a book collection by purchasing seven books. Each week she adds two new books. How many weeks before Corrine has 75 books in her collection? 35 weeks 12191,522 130.6 1,031 1,222 1,352 133 283 49 6.8 18not 12not 3 not 7 Homework and Practice 12-1 Arithmetic Sequences LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 93 Holt Middle School Math All rights reserved. Name Date Class Determine if each sequence could be geometric. If so give the common ratio. 1. 3, 15, 75, 375, 1,875, … 2. 36, 30, 24, 18, 3. 3, 32, 34, 38, 136 , ... 12, … 4. 850, 170, 34, 6.8, 1.36, … 5. 6, 33, 171, 861, 6. 14, 98, 686, 4,802, 4,311, … 33,614, … 7. 999, 333, 111, 99, 33, … 8. 95, 38, 1515, 6225 , 9. 4, 22, 121, 665.5, 215245, … 3,660.25, … Find the given term in each geometric sequence. If necessary, round to the nearest hundredth. 10. 8th term; 4, 12, 36, 108, 324, … 11. 5th term; a1 155, r 0.6 12. 7th term; 4, 14, 49, 171.5, 600.25, … 13. 12th term; a1 0.05, r 9 14. 16th term;31125 , 6125 , 1125 , 215 , 15, ... 15. 9th term; 79, 213, 7, 21, 63, ... 16. Nicholas has a picture that is 3 in. 5 in. If he enlarges the photo by 25% five times, what are the dimensions of the new photo? Round to the nearest tenth of an inch? 9.2 in. by 15.3 in. 9,765,625 5,103 7353.0625 1,569,052,980 8,748 20.09 5.5 25not 0.2 not 7125 not Homework and Practice 12-2 Geometric Sequences LESSON Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 94 Holt Middle School Math All rights reserved. Name Date Class Use first and second differences to find the next three terms in each sequence. 1. 12, 13, 16, 21, 28, … 2. 4, 6, 10, 16, 24, … 3. 34, 234, 514, 814, 1134, ... 4. 3.6, 4.1, 6.1, 9.6, 14.6, … Give the next three terms in each sequence using the simplest rule you can find. 5. 1, 2, 4, 7, 11, … 6. 6, 7, 10, 15, 22, … 7. 2, 5, 10, 17, 26, … 8. 32, 50, 72, 98, 128, … 9. 400, 361, 324, 289, 256, … 10. 2.5, 10, 22.5, 40, 62.5, … Find the first five terms of each sequence defined by the given rule. 11. an n 2n2 12. an n22n 513. an 6 nn21214. Suppose a, b, and c are three consecutive numbers in the Fibonacci sequence. Complete the following table and guess the pattern. The result of b 2 is one less than the product of a and c. 2, 2, 135, 1157, 1113 3, 214, 213, 258, 3 12, 1, 112, 2, 212225, 196, 169 90, 122.5, 160 37, 50, 65 162, 200, 242 16, 22, 29 31, 42, 55 1521.1, 29.1, 38.6 34, 2014, 251437, 48, 61 34, 46, 60 Homework and Practice 12-3 Other Sequences LESSON a, b, c ac b 2 1, 1, 2 2 1 2, 3, 5 10 9 5, 8, 13 65 64 13, 21, 34 442 441 34, 55, 89 3,026 3,025 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 95 Holt Middle School Math All rights reserved. Name Date Class 1. y 3x 4 2. y 2x 2 1 Complete the table and graph each function. Homework and Practice 12-4 Functions LESSON y x 4 2 O 2 4 6 2 246 4 6 y x 4 2 O 2 6 2 246 4 6 x 3x 4 y 3 3(3) 4 5 2 3(2) 4 2 1 3(1) 4 1 0 3(0) 4 4 1 3(1) 4 7 x 2x 2 1 y 2 2(2)2 1 7 1 2(1)2 1 1 0 2(0)2 1 1 1 2(1)2 1 1 2 2(2)2 1 7 Determine if each relationship represents a function. 3. y 2 4x 3 4. 5. For each function, find f (0), f (1), and f (2). 6. Given the function f (x)4x 2 5 and the domain { 3, 2, 1, 0, 1, 2, 3}. Find the range of the function. range is {41, 21, 9, 5} no yes Function f (0) f (1) f (2) y5x 2 2 7 8 y 3x 2 8 8 5 4 x 2 4 6 8 y 1 2 3 4 Holt Pre-AlgebraWrite a rule for each linear function. 1. 2. 3. 4. 5. A salesperson is paid a base salary of $300 plus 8% of their sales.Write a function rule for the salary. Graph the function. f (x) 0.08x 300 6. If a salesperson has $900 in sales, what is the salesperson’s salary? $372 f (x) 12 f (x) 3x 1 x 7 f (x) 13f (x) 2x 5 x 4 y x 4 2 O 2 4 6 6 2 246 4 6 y x 4 2 O 2 4 6 6 2 246 4 6 Homework and Practice 12-5 Linear Functions LESSON Copyright © by Holt, Rinehart and Winston. 96 Holt Middle School Math All rights reserved. Name Date Class x 4 2 3 5 f (x) 13 7 8 14 x 6 4 2 8 f (x) 10 9 6 3 1000 800 600 400 2000 2000 4000 6000 8000 y x Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 97 Holt Middle School Math All rights reserved. Name Date Class 1. f (x) 0.25 • 5 x 2. f (x) 14• 6 x 3. A lawyer opens a new office with 28 clients. She intends to increase her clientele 30% each year for the next 4 years. How many clients can she expect to have at the end of 4 years? Round the answer to the nearest whole number? 80 clients 4. A company owns office cars worth a total of $587,000. The cars are depreciated by 12% a year for 10 years.What is the expected value of the cars at the end of 10 years? Round the answer to the nearest cent. $163,480.07 5. Clayton earns $725 a week at his job. He is given a 6% annual increase in pay. How much will Clayton earn per week after 3 years? Round the answer to the nearest cent. $863.49 Create a table for each exponential function, and use it to graph the function. Homework and Practice 12-6 Exponential Functions LESSON 1 0.5 0 0.5 1 1.5 2 y x 6543210 1 0.5 0 0.5 1 1.5 2 y x 109876543210 x y 1 y 0.25 • 51 0.05 0 y 0.25 • 50 0.25 1 y 0.25 • 51 1.25 2 y 0.25 • 52 6.25 x y 1 y 14• 61 2140 y 14• 60 141 y 14• 61 1122 y 14• 62 9 Holt Pre-AlgebraHomework and Practice 12-7 Quadratic Functions LESSON Copyright © by Holt, Rinehart and Winston. 98 Holt Middle School Math All rights reserved. Name Date Class Create a table for each quadratic function and use it to make a graph. 1. f (x) x 2 6 2. f (x) (x 5)(x 3) 3. f (x) x 2 3x 2 y x 4 2 O 2 4 2 24 4 y x 2 O 2 4 2 24 4 6 y x 4 2 O 2 4 2 24 4 x f (x) x 2 6 3 f (3) (3)2 6 3 1 f (1) (1)2 65 0 f (0) (0)2 66 2 f (2) (2)2 62 3 f (3) (3)2 6 3 x f (x) (x 5)(x 3) 6 f (5) (6 5)(6 3) 3 5 f (5) (5 5)(5 3) 0 4 f (4) (4 5)(4 3)1 3 f (3) (3 5)(3 3) 0 2 f (2) (2 5)(2 3) 3 x f (x) x 2 3x 2 3 f (3) (3)2 3(3) 22 2 f (2) (2)2 3(2) 24 1 f (1) (1)2 3(1) 24 0 f (0) (0)2 3(0) 22 1 f (1)(1)23(1)22 4. If the perimeter of a rectangle is 124 cm, find the dimensions of the rectangle with the greatest possible area? What is the greatest possible area? 31 cm 31 cm; area 961 cm2 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 99 Holt Middle School Math All rights reserved. Name Date Class Homework and Practice 12-8 Inverse Variation LESSON Tell whether each relationship is an inverse variation. 1. The table shows the length and width of a parallelogram. Length 4 8 10 12 36 Width 18 9 7.2 6 2 The relationship is an inverse variation. 2. The table shows the number of shelves and the number of books on each shelf in a library. Number of Shelves 3 4 6 12 16 Number of Books 32 24 16 8 6 The relationship is an inverse variation. 3. The table shows the number of guests at a party and the cost per guest. Number of Guests 66 75 96 100 150 Cost per Guest 9 8 6.25 6 4 The relationship is not an inverse variation. Graph each inverse variation. 4. f (x) 6x5. f (x) x46. Hertz, abbreviated Hz, is a unit of frequency equal to 1 cycle per second. The pitch of a musical instrument is measured in vibrations per second or Hertz. If the pitch of a panpipe 2 feet long is 282 Hz, what is the length of pipe with a pitch of 376 Hz? 1.5 feet y x 4 2 O 2 4 2 24 4 O 64 22 6 4 2 24 4 6 x y 6 y 7 x2y 9 x6Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. 100 Holt Pre-Algebra All rights reserved. Name Date Class Homework and Practice 13-1 Polynomials LESSON Determine whether each expression is a monomial. 1. xyz 2. u 3 3. 8q 3 4. 35rs 2t 3 5. a 2.2 6. 79x 79 Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial. 7. 5a 4.9b 138. 9pq 1r 4 9. 9 r 2 2r 10. 1.077p 5r 11. 1.1q p 0.6 12. 7.55r 75 1 Find the degree of each polynomial. 13. z 0 y 9 x 14. 2k 7k 2 4k 3 15. 1p 2 2q p 3 8q 2 16. 2 17. 98ab 8c 2 d 11 18. 45c c 7 2 19. Look at the polynomial 2x 3 x 2 x.What is the degree? Is the polynomial a monomial, binomial, or trinomial? What is the value of the polynomial if x 2? degree 3; trinomial; 18 20. The volume of a box with width x, length x 2, and height 3x 2 is given by the trinomial 3x 3 4x 2 4x.What is the volume of the box if its width is 4 feet? 240 ft3 degree 0 degree 11 degree 7 degree 9 degree 3 degree 3 monomial not a polynomial binomial trinomial not a polynomial trinomial monomial not a monomial not a monomial monomial monomial monomialCopyright © by Holt, Rinehart and Winston. 101 Holt Pre-Algebra All rights reserved. Name Date Class Homework and Practice 13-2 Simplifying Polynomials CHAPTER Identify the like terms in each polynomial. 1. 6x x 5 2x 3 2x 2. 2c 2 d 3 4 3d 3 c 8 3. 3a 2 b a 2 4. 3x 2 2x x 2 9 x 5. c 2 2d 3 5d 3 9 2c 2 6. 2 9 x 2 3x 2 x 7. 5m 9m 2 3m 2 6 m 8. 6x x 5 2x 3 8x Simplify. 9. m 2(9mn 3n 2m) 10. 9(a 2 2ab b 2) 2(a 2 ab) 11. d 2e 3 2(d 2e 3 8d 3e 2) 12. 2v 3v 2 2(v 2 8 v 7) 13. xy 2xy 2x 3xy 14. 7(1 x) 5(2 2x) 3(x 4) 15. 2(c 3cd 9d) 4(9cd 3d 4c) 16. bc 3b 2 6c 2 2(b 2 3bc) 17. Mr. Rose wrote the following expression on the board: 3(8 9a) 2(9a a 2) 9a 2 a 3. Use the Distributive Property to simplify the expression. a 3 11a 2 45a 24 18c 30cd 6d 5b 2 5bc 6c 2 2x 14x 29 d 2e 3 16d 3e 2 5v 2 4v 2 5m 18mn 6n 7a 2 16ab 9b 2 5m and m; 9m2 and 3m2 6x and 8x c 2 and 2c 2; 2d 3 and 5d 3 2 and 9; x 2 and 3x 2 3a 2 and a 2 3x 2 and x 2; 2x and x 6x and 2x d 3 and 3d 3; 4 and 8Copyright © by Holt, Rinehart and Winston. 102 Holt Pre-Algebra All rights reserved. Name Date Class Homework and Practice 13-3 Adding Polynomials LESSON Add. 1. (2b 2 b 3) (5b 2 5b 7) 2. (3y 9y 2) (3y 12y 2) 3. (–a 2 9a – 6) (12a 2 a 2) 4. (6h 2 2h) (10h 2 11) 5. (2s 3t 8u) (s 4t 7u) (u – 3t) 3s 4t 16u 6. (4xw 2x 2w 9xw 2) (15x 2w 7xw 2) (3xw 2 15xw 6x 2w) 11xw 19x 2w 5xw 2 7. (3b 2c 2 3b 2c 3bc) (5b 2c 2 bc 2) (2b 2c 3bc 8) 8b 2c 2 b 2c bc 6 8. (7e 2 3e 2) (9 6e 4e 2) (9e 2 6e 2) (4e 2 7e 8) 9e 2 e 21 9. (f 4g fg 3 2fg 4) (3fg 3 3) (4f 4g 5fg) (3 12fg 3 f 4g) 6f 4g 10fg 3 3fg 2 10. Each side of an equilateral triangle has length 2m 3. Each side of a square has length 3m 2. Write an expression for the sum of the perimeter of the equilateral triangle and the perimeter of the square. 18m 1 11a 2 8a 4 16h 2 2h 11 7b 2 6b 10 6y 3y 2Copyright © by Holt, Rinehart and Winston. 103 Holt Pre-Algebra All rights reserved. Name Date Class Homework and Practice 13-4 Subtracting Polynomials LESSON Find the opposite of each polynomial. 1. 18xy 3 2. –9a 4 3. 6d 2 2d 8 Subtract. 4. (4n 3 4n + 4n 2) (6n 3 + 3n 8n 2) 5. (2b 2 4b + 6) (b 2 3b 5) 6. (9y 2 y 6) (4y 2 7y 2) 7. (17x 2 x 3) (14x 2 3x 5) 8. (9r 3s 3rs 4rs 3 5r 2s 2) (2rs 3 2r 2s 2 6rs 7r 3s) 2r 3s 9rs 2rs 3 7r 2s 2 9. w (3w 4 5w 3 2w 10) 3w 4 5w 3 w 10 10. (3qr 2 2q 3 14q 2r 2 9qr) (10qr 4q 3 5qr 2 6q 2r 2) 8qr 2 6q 3 8q 2r 2 qr 11. The volume of a rectangular prism, in cubic yards, is given by the expression x 4 3x 3 2x 2. The volume of a smaller rectangular prism is given by the expression x 4 3x 3 2x 2. How much greater is the volume of the larger rectangular prism? 6x 3 cubic yards 12. Alice has a closet with an area of 5y 2 10y 15 square feet. She has a piece of carpet with an area of 2y 2 2y 4 square feet. She wants the carpet to cover the closet floor.What is the expression that represents the number of square feet of additional carpet she needs to cover the closet floor? 3y 2 8y 11 square feet more 5y 2 8y 4 3x 2 4x 2 2n 3 7n 12n 2 3b 2 b 11 18xy 3 9a 4 6d 2 2d 8Copyright © by Holt, Rinehart and Winston. 104 Holt Pre-Algebra All rights reserved. Name Date Class Homework and Practice 13-5 Multiplying Polynomials LESSON Multiply. 1. (a)(9a) 2. (8bc 2)(d 2e 2) 3. (2ef 4)(2ef) 4. (2hk 2)(h 2k 2) 5. 6k(2m 3 2k) 6. p 2(2 n 2 10n) 7. 12q(2q 4q 2 8q 3 16q 4) 8. 6rs(3r 2 rs 2s 3) 9. 4u 5v 2(u 4v 7 14u 2v) 10. (w 2 (xyz) w 4)(w 8) 11. 34a 2b 2(4 16ab 8ab 3) 12. (d 8)(d 2 28e 17d 5e 2) 13. 4gh 2 (h 12gh 2g 2 4gh) 14. (2k )(7k 2 2k 3)(k ) 15. (12k 3m 2)13m 56k 5m 5 km16. (p)(3n)(np np 2 4n 4) 17. The volume of a rectangular prism is given by the expression (s 14)(s)(2s). Simplify the expression. 2s 3 28s 2 10k 8m7 12k 4m3 4k 3m3 3n 2p 3 3n 2p 2 12n 5p 4gh 3 8g 3h 2 14g 2h 3 14k 4 4k 3 6k 2 3a 2b 2 12a 3b 3 6a 3b 5 d 10 28d 8e 17d 9 5d 8e 2 4u 9v 9 u 6v 2 8u 5v 3 w 10 w 8xyz w 12 q 2 2q 3 4q 4 8q 5 18r 3s 6r 2s 2 12rs 4 12km3 12k 2 2p 2 n 2p 2 10np 2 4e 2f 5 2h 3k 4 9a 2 8bc 2d 2e 2Copyright © by Holt, Rinehart and Winston. 105 Holt Pre-Algebra All rights reserved. Name Date Class Homework and Practice 13-6 Multiplying Binomials LESSON Multiply. 1. (a 4)(a 2) 2. (7 b)(2 b) 3. (4c 1)(2c 1) 4. (d 1)(d 3) 5. (3e 1)(e 1) 6. (3g 2f )(2g 3f ) 7. A square garden is 6 meters across. The drainage strip that runs around the garden is h meters wide.What expression gives the combined area of the garden and the drainage strip? 4h 2 24h 36 square meters Multiply. 8. (x 5)2 9. (3 k)2 10. (k 8)(k 8) 11. (2m 6)(2m 6) 12. (n p)(n p) 13. (2q 3r )(2q 3r ) 14. (s 2t )2 15. (2u 4)(12u 1) 16. (20 w)2 17. (9y 2)(–2 9y) 18. (z 3 1)2 19. (a 2 b 2)(a 2 b 2) 20. A rectangular swimming pool is 30 feet long and 15 feet wide. It is surrounded by a deck of width c feet.What expression gives the total area of the pool and deck? 450 90c 4c 2 square feet 21. A circular pond with a radius of 21 ft is surrounded by a stone walkway with width b.What expression gives the total area of the pond and the walkway? Use 272for pi. 1,386 132b 2 72 b 2 ft 2 81y 2 36y 4 z 6 2z 3 1 a 4 2a 2b 2 b 4 s 2 4st 4t 2 24u 2 50u 4 400 40w w 2 4m2 36 n 2 p 2 4q 2 9r 2 x 2 10x 25 9 6k k 2 k 2 64 d 2 4d 3 3e 2 2e 1 6g 2 5gf 6f 2 a 2 6a 8 14 9b b 2 8c 2 2c 1Copyright © by Holt, Rinehart and Winston. 106 Holt Pre-Algebra All rights reserved. Insert the correct symbol to make each statement true. 1. {oak, pine} {tree types} 2. hair {appendages} 3. {parallelograms, rhombuses} 4. 17 {integer factors of 51} {rectangles} Determine whether the first set is a subset of the second set. Use the correct symbol. 5. M {2-digit whole numbers} 6. H {trees, walls, puddles} D {real numbers less than 90} N {naturally occurring structures} 7. W {water toys} 8. E {4x 2 2x 3, 7a 3b c} J {jet skis} T {trinomials} Tell whether each set is finite or infinite. 9. {laps driven in the Daytona 500} 10. {real numbers between 0 and 1} 11. {leaves on a tree} 12. {points on a coordinate plane} 13. Write a statement using one of the symbols , , , or to show the relationship between Mexico and the continents. Mexico {continents} 14. Write a statement using one of the symbols , , , or to show the relationship between Jupiter and the set of planets in the solar system. Jupiter {planets in the solar system} finite infinite finite infinite No, W J Yes, E T No, M D No, H N Name Date Class Homework and Practice 14-1 Sets LESSONCopyright © by Holt, Rinehart and Winston. 107 Holt Pre-Algebra All rights reserved. Name Date Class Homework and Practice 14-2 Intersection and Union LESSON Find the intersection of the sets. 1. S {2, 4, 6, 8, 10} 2. I {c 5 c 10} W {negative even integers} J {c 10 c 5} 3. X {negative odd integers} 4. K {g 9 g 9} Y {6, 5, 4, 0, 2, 3} E {g g 3} Find the union of the sets. 5. C 12, 23, 346. J {x 9 x 2} L 0, 12, 13, 14, 16I {x x 0} 7. A {multiples of 4 less than 30} 8. H {factors of 24} C {multiples of 6 less than 30} K {factors of 36} Find the intersection and union of the sets. 9. D {x 5 x 5} 10. P {5, 3, 1, 0, 2, 4, 6} E {x 2 x} Q {2, 1, 0, 1, 2} 11. T {factors of 2} 12. W {d d ≠ 0} U {factors of 10} Y {d –5 ≤ d ≤ 0} W Y {5 d 0} W Y {real numbers} T U {1, 2} T U {1, 2, 5, 10} P Q {1, 0, 2} P Q {5, 3, 2, 1, 0, 1, 2, 4, 6} D E {x 2 x 5} D E {x –5 x} H K {1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36} A C {4, 6, 8, 12, 16, 18, 20, 24, 28} C L 0,J I {x x 2} 12, 13, 14, 16, 23, 43X Y {5} K E {g 3 g 9} S W {10, 6, 2} I J {c 5 c 5}Copyright © by Holt, Rinehart and Winston. 108 Holt Pre-Algebra All rights reserved. Name Date Class Homework and Practice 14-3 Venn Diagrams CHAPTER Draw a Venn Diagram to show the relationship between the sets. 1. Use a Venn Diagram to identify intersections, unions, and subsets. 2. A B A C {2, 4, 6} B C {8, 10} A B {2, 4, 6, 8, 10, 12, 14, 16} A C {2, 4, 6, 8, 10, 12, 14, 16, 18} B C {2, 4, 6, 8, 10, 18} B C Use a Venn diagram to show the following logical argument. 3. All of Mike’s friends are on the 4. All whales are mammals. football team. No tuatara is a mammal. Charles is Mike’s friend. No tuatara is a whale. Charles is on the football team. Set Elements Forest animals bears, deer, included in snakes, frogs, Jenn’s research rabbits, elephants Carnivorous lions, snakes, animals included sharks, frogs, in Jenn’s vultures, research crocodiles Bears Deer Rabbits Snakes Frogs Elephants Lions Sharks Vultures Crocodiles Forest Animals Carnivores A 12 14 246 16 18 C 8 B 10 Football Team Mike’s Friends Charles Mammals Whales TuataraName Date Class Homework and Practice 14-4 Compound Statements LESSON Copyright © by Holt, Rinehart and Winston. 109 Holt Pre-Algebra All rights reserved. Make a truth table for the conjunction P and Q. 1. P: HJKL is a rhombus Q: HJKL is a rectangle Examples P Q P and Q HJKL is a square. True True True HJKL has all equal sides and True False False: only one of the an 80º angle. conditions in the conjunction is met. HJKL has a pair of opposite False True False: only one of the sides that measure 4 cm each conditions in the conjunction and a pair of opposite sides is met. that measure 5 cm each, and it has a right angle. HJKL is a trapezoid. False False False: neither condition is met. Make a truth table for the disjunction P or Q. 2. P: Tony is on the basketball team. Q: Tony is over six feet tall. Examples P Q P or Q Tony is on the basketball True True True team. Tony is 6' 2" tall. Tony is on the basketball True False True: only one of the team. Tony is 5' 11" tall. conditions in the disjunction must be met. The only sport that Tony False True True: only one of the plays is football. Tony is conditions in the disjunction 6' 1" tall. must be met. The only sport that Tony False False False: neither condition is plays is basketball. Tony is met. 5' 9" tall. Possible answers are given.Copyright © by Holt, Rinehart and Winston. 110 Holt Pre-Algebra All rights reserved. Name Date Class Homework and Practice 14-5 Deductive Reasoning LESSON Identify the hypothesis and the conclusion in each conditional. 1. Charles gets excited if he eats chocolate. Hypothesis: Charles eats chocolate. Conclusion: Charles gets excited. 2. You will get better if you practice. Hypothesis: You practice. Conclusion: You will get better. 3. If you study hard for a test, you will get a good grade. Hypothesis: You study hard for a test. Conclusion: You will get a good grade. 4. The teacher gives homework if he completes a section. Hypothesis: The teacher completes a section. Conclusion: He gives homework. Make a conclusion, if possible, from each deductive argument. 5. If Johnny makes it home by 6:00 P.M., he will eat very well tonight. Johnny walked into his house at 5:50 P.M. Conclusion: Johnny will eat well tonight. 6. If a polynomial has two terms, then it is binomial. The polynomial x 2 2 has two terms. Conclusion: x 2 2 is a binomial 7. If a polygon is regular, then it has all equal angles. PQRS has all equal sides. Possible answer: No conclusion can be made. PQRS is a rhombus, but not necessarily regular.Name Date Class Homework and Practice 14-6 Networks and Euler Circuits LESSON Copyright © by Holt, Rinehart and Winston. 111 Holt Pre-Algebra All rights reserved. Find the degree of each vertex, and determine whether the graph is connected. 1. 2. 3. 4. Determine whether the graph can be traversed through an Euler Circuit. If your answer is yes, describe an Euler Circuit in the graph. 5. 6. Yes, Possible answer: CNOTXENSZANHC No. H C ZN S E O A H X T A E B C I D FG E :1, F :1, K :3, L :3, O :3, P :3, X :1, Z :1; The graph is connected. L :2, M:3, N :2, O :3, P :2, Q :2, R :3, S :2, T :2, U :3; The graph is connected. E FZ LP KO X L U T RS PM N O Q F :2, G :2, H :2, I :2, J :4, K :0; The graph is not connected. A :2, B :2, C :4, D :2, E :4; The graph is connected. F GK H J I CDE A BCopyright © by Holt, Rinehart and Winston. 112 Holt Pre-Algebra All rights reserved. Name Date Class Homework and Practice 14-7 Hamiltonian Circuits LESSON Find a Hamiltonian Circuit in each graph. 1. 2. 3. 4. Determine the shortest Hamiltonian circuit beginning at G. 5. 6. 7. 8. Possible answer: G-K-L-D-O-N-G Possible answer: G-B-C-J-I-H-G G H J IC B 1 yd 1 yd 1 yd 1 yd 1 yd 1 yd 1 yd 2 yds 2 yds G N DK L O 10 in. 1 in. 4 in. 3 in. 3 in. 1 in. Possible answer: G-D-A-B-C-E-G Possible answer: G-T-U-V-G T G U 1 m V 2 m 3 m 4 m 3 m A B CE GD 3 cm 3 cm 2 cm 8 cm 2 cm 4 cm8 cm 2 cm Possible answer: B-D-H-G-I-F-B Possible answer: R-K-M-L-O-R K M L R O B D I H G F Possible answer: A-E-I-H-G-D-A Possible answer: Q-N-P-R-S-T-Q N P SQ T R A EI H G D