Lesson 2 Menu : Lesson 2 Menu Five-Minute Check (over Lesson 11-1)
Main Ideas and Vocabulary
California Standards
Example 1: Excluded Values
Example 2: Use Rational Expressions
Example 3: Standards Example: Expression Involving Monomials
Example 4: Excluded Values
Lesson 2 MI/Vocab : Lesson 2 MI/Vocab rational expression excluded values Identify values excluded from the domain of a rational expression. Simplify rational expressions.
Lesson 2 CA : Lesson 2 CA Standard 12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. (Key)
Lesson 2 Ex1 : Lesson 2 Ex1 Excluded Values Exclude the values for which b + 7 = 0, because the denominator cannot equal 0. Answer: b cannot equal –7. Subtract 7 from each side. b + 7 = 0 b = –7
Lesson 2 Ex1 : Lesson 2 Ex1 Excluded Values Exclude the values for which a2 – a – 12 = 0. Answer: a cannot equal –3 or 4. Factor. a2 – a – 12 = 0 (a + 3)(a – 4) = 0 The denominator cannot equal zero. a = 4 a + 3 = 0 or a = –3 a – 4 = 0
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D A. 0, 2
B. 0, 2, 3
C. 2, 3
D. x is all real numbers.
Lesson 2 Ex2 : Lesson 2 Ex2 Use Rational Expressions A. HISTORY Refer toExample 2 of your textbook. Suppose the Egyptian worker finds a rock that he cannot move with a 6-foot bar, so he gets an 8-foot bar. But this time, he places the fulcrum so that the effort arm is 6 feet long,and the resistance arm in 2 feet long. Explain whether he has more or less mechanicaladvantage with his new setup. The original mechanical advantage was 5.
Lesson 2 Ex2 : Lesson 2 Ex2 Use Rational Expressions Use the expression for mechanical advantage to write an expression for the mechanical advantage in the new situation. Answer: Even though the bar is longer, because he moved the fulcrum he has a mechanical advantage of 3, so his mechanical advantage is less than before. Simplify. = 3 LE = 6, LR = 2
Lesson 2 Ex2 : Lesson 2 Ex2 Use Rational Expressions B. If the worker can apply a force of 180 pounds, what is the greatest weight he can lift with the longer bar? Answer: Since the mechanical advantage is 3, the worker can lift 3 ● 180 or 540 pounds with the longer bar.
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D A. 4
B. 2
C. 3
D. 16
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D A. 200 lb
B. 50 lb
C. 800 lb
D. 400 lb B. If they can apply a force of 200 pounds, what is the greatest weight they can lift?
Lesson 2 Ex3 : Lesson 2 Ex3 Read the Item Expression Involving Monomials
Lesson 2 Ex3 : Lesson 2 Ex3 Solve the Item Answer: The correct answer is C. Expression Involving Monomials Step 2 Divide the numerator and denominator by 4xy2. Step 1 The GCF of the numerator and denominator is 4xy2. Step 3 Simplify.
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Lesson 2 Ex4 : Lesson 2 Ex4 Excluded Values Divide the numerator and denominator by the GCF, x + 4. Factor. Simplify.
Lesson 2 Ex4 : Lesson 2 Ex4 Exclude the values for which x2 – 5x – 36 equals 0. Excluded Values Factor. The denominator cannot equal zero. Zero Product Property x2 – 5x – 36 = 0 (x – 9)(x + 4) = 0 x = 9 or x = –4
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End of Lesson 2 : End of Lesson 2