College Algebra Essentials
1st Edition
ISBN: 9780078035616
Author: Julie Miller
Publisher: MCG
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Question
Chapter R.1, Problem 74PE
To determine
The simplest form without absolute bars.
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Scientific Notation. In Exercises 9–12, the given expressions are designed to yield results expressed in a form of scientific notation. For example, the calculator-displayed result of 1.23E5 can be expressed as 123,000, and the result of 1.23E-4 can be expressed as 0.000123. Perform the indicated operation and express the result as an ordinary number that is not in scientific notation.
614
For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples.
• In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2).
• Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5).
To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that
x + 4 = (x + 2i)(x – 2i).
115. а. х
- 9
116. а. х?
- 100
117. а. х
- 64
b. x + 9
b. + 100
b. x + 64
118. а. х — 25
119. а. х— 3
120. а. х — 11
b. x + 25
b. x + 3
b. x + 11
In Exercises 102–103, perform the indicated operations. Assume
that exponents represent whole numbers.
102. (x2n – 3x" + 5) + (4x2" – 3x" – 4) – (2x2 – 5x" – 3)
103. (y3n – 7y2n + 3) – (-3y3n – 2y2" – 1) + (6y3n – yn + 1)
104. From what polynomial must 4x? + 2x – 3 be subtracted to
obtain 5x? – 5x + 8?
Chapter R Solutions
College Algebra Essentials
Ch. R.1 - Practice Exercises Concept Connections A ________...Ch. R.1 - Practice Exercises Concept Connections = {0, 1, 2,...Ch. R.1 - Practice Exercises Concept Connections N = {1, 2,...Ch. R.1 - Practice Exercises Concept Connections Z = {...,...Ch. R.1 - Practice Exercises Concept Connections A set can...Ch. R.1 - Prob. 6PECh. R.1 - Prob. 7PECh. R.1 - Prob. 8PECh. R.1 - Practice Exercises Concept Connections The...Ch. R.1 - Practice Exercises Concept Connections The...
Ch. R.1 - Prob. 11PECh. R.1 - Prob. 12PECh. R.1 - Practice Exercises Concept Connections The symbol...Ch. R.1 - Practice Exercises Concept Connections The...Ch. R.1 - Prob. 15PECh. R.1 - Prob. 16PECh. R.1 - Objective 1: Identify Subsets of the Set of Real...Ch. R.1 - Objective 1: Identify Subsets of the Set of Real...Ch. R.1 - Prob. 19PECh. R.1 - Prob. 20PECh. R.1 - Prob. 21PECh. R.1 - Prob. 22PECh. R.1 - Prob. 23PECh. R.1 - Prob. 24PECh. R.1 - Prob. 25PECh. R.1 - Prob. 26PECh. R.1 - Prob. 27PECh. R.1 - Prob. 28PECh. R.1 - Prob. 29PECh. R.1 - Prob. 30PECh. R.1 - Prob. 31PECh. R.1 - Prob. 32PECh. R.1 - Prob. 33PECh. R.1 - Prob. 34PECh. R.1 - Prob. 35PECh. R.1 - Prob. 36PECh. R.1 - Prob. 37PECh. R.1 - Prob. 38PECh. R.1 - Prob. 39PECh. R.1 - Prob. 40PECh. R.1 - Prob. 41PECh. R.1 - Prob. 42PECh. R.1 - Prob. 43PECh. R.1 - Prob. 44PECh. R.1 - Objective 2: Use Inequality Symbols and Interval...Ch. R.1 - Prob. 46PECh. R.1 - Prob. 47PECh. R.1 - Prob. 48PECh. R.1 - Prob. 49PECh. R.1 - Prob. 50PECh. R.1 - Prob. 51PECh. R.1 - Prob. 52PECh. R.1 - Prob. 53PECh. R.1 - Prob. 54PECh. R.1 - Prob. 55PECh. R.1 - Prob. 56PECh. R.1 - Prob. 57PECh. R.1 - Prob. 58PECh. R.1 - Prob. 59PECh. R.1 - Prob. 60PECh. R.1 - Prob. 61PECh. R.1 - Prob. 62PECh. R.1 - Prob. 63PECh. R.1 - Prob. 64PECh. R.1 - Prob. 65PECh. R.1 - Prob. 66PECh. R.1 - Prob. 67PECh. R.1 - Prob. 68PECh. R.1 - Prob. 69PECh. R.1 - Prob. 70PECh. R.1 - Prob. 71PECh. R.1 - Prob. 72PECh. R.1 - Prob. 73PECh. R.1 - Prob. 74PECh. R.1 - Prob. 75PECh. R.1 - Prob. 76PECh. R.1 - Prob. 77PECh. R.1 - Prob. 78PECh. R.1 - Prob. 79PECh. R.1 - Prob. 80PECh. R.1 - Prob. 81PECh. R.1 - Prob. 82PECh. R.1 - Prob. 83PECh. R.1 - Prob. 84PECh. R.1 - Prob. 85PECh. R.1 - Prob. 86PECh. R.1 - Prob. 87PECh. R.1 - Prob. 88PECh. R.1 - Prob. 89PECh. R.1 - Prob. 90PECh. R.1 - Prob. 91PECh. R.1 - Prob. 92PECh. R.1 - Prob. 93PECh. R.1 - Prob. 94PECh. R.1 - Prob. 95PECh. R.1 - Prob. 96PECh. R.1 - Objective 5: Evaluate Exponential Expressions,...Ch. R.1 - Prob. 98PECh. R.1 - Prob. 99PECh. R.1 - Prob. 100PECh. R.1 - Prob. 101PECh. R.1 - Prob. 102PECh. R.1 - Prob. 103PECh. R.1 - Prob. 104PECh. R.1 - Prob. 105PECh. R.1 - Prob. 106PECh. R.1 - Prob. 107PECh. R.1 - Prob. 108PECh. R.1 - Prob. 109PECh. R.1 - Prob. 110PECh. R.1 - Prob. 111PECh. R.1 - Prob. 112PECh. R.1 - Prob. 113PECh. R.1 - Prob. 114PECh. R.1 - Prob. 115PECh. R.1 - Prob. 116PECh. R.1 - Prob. 117PECh. R.1 - Prob. 118PECh. R.1 - Prob. 119PECh. R.1 - Prob. 120PECh. R.1 - Prob. 121PECh. R.1 - Explain why all integers are rational numbers.Ch. R.1 - Prob. 123PECh. R.1 - Prob. 124PECh. R.1 - Prob. 125PECh. R.1 - Prob. 126PECh. R.1 - Prob. 127PECh. R.1 - If n 0, then n - |n| = __________.Ch. R.1 - Prob. 129PECh. R.1 - Prob. 130PECh. R.1 - Prob. 131PECh. R.1 - Prob. 132PECh. R.1 - Prob. 133PECh. R.1 - Prob. 134PECh. R.1 - Prob. 135PECh. R.1 - Prob. 136PECh. R.1 - Prob. 137PECh. R.1 - Prob. 138PECh. R.1 - Prob. 139PECh. R.1 - Prob. 140PECh. R.1 - Prob. 141PECh. R.1 - Prob. 142PECh. R.1 - Prob. 143PECh. R.1 - Prob. 144PECh. R.1 - Prob. 145PECh. R.2 - For Exercises 1-2, write the interval notation and...Ch. R.2 - For Exercises 1-2, write the interval notation and...Ch. R.2 - For Exercises 3-4, write an absolute value...Ch. R.2 - For Exercises 3-4, write an absolute value...Ch. R.2 - For Exercises 5-8, determine whether the statement...Ch. R.2 - For Exercises 5-8, determine whether the statement...Ch. R.2 - For Exercises 5-8, determine whether the statement...Ch. R.2 - For Exercises 5-8, determine whether the statement...Ch. R.2 - For Exercises 9-10, simplify. 12(99)2(2)37+1Ch. R.2 - For Exercises 9-10, simplify. 10282(164)2Ch. R.2 - One type of mathematical model is a formula that...Ch. R.2 - Model _______ is a term used to describe a...Ch. R.2 - A _____ is a product of factors that may include...Ch. R.2 - The numerical _________ of a term is the constant...Ch. R.2 - The _______ properties of addition and...Ch. R.2 - The sum of a number and its additive inverse is...Ch. R.2 - The number _______ is the identity element of...Ch. R.2 - Zero is the _______ element of addition.Ch. R.2 - The additive inverse of a real number x is ______.Ch. R.2 - The statement a(b + c) = ab + ac represents the...Ch. R.2 - The multiplicative inverse of a nonzero real...Ch. R.2 - The ________ property of addition indicates that a...Ch. R.2 - The associative property of multiplication...Ch. R.2 - The number _________ is the only real number that...Ch. R.2 - Gas mileage depends in part on the speed of the...Ch. R.2 - The bacterium Pseudomonas aeruginosa is cultured...Ch. R.2 - Data from the Bureau of Labor Statistics Consumer...Ch. R.2 - Selena started a new diet and exercise program,...Ch. R.2 - The temperature at noon in Orlando, Florida, in...Ch. R.2 - Scientists often use the Kelvin scale to measure...Ch. R.2 - The retail price P for a sofa is the sum of the...Ch. R.2 - The sale price S for a tractor is the difference...Ch. R.2 - Jake is 1 yr younger than Charlotte. a. Write a...Ch. R.2 - For a recent NFL season, Aaron Rogers had 9 more...Ch. R.2 - At the end of the summer, a home store discounts...Ch. R.2 - When Ms. Tibbets has excellent service at a...Ch. R.2 - Suppose that an object is dropped from a height h....Ch. R.2 - The height of a sunflower plant can be determined...Ch. R.2 - A power company charges one household $0.12 per...Ch. R.2 - A utility company charges a base rate for water...Ch. R.2 - The cost C (in $) to rent an apartment is $640 per...Ch. R.2 - For a certain college, the cost C (in $) for...Ch. R.2 - A hotel charges $159 per night plus an 11% nightly...Ch. R.2 - A hotel charges $149 per night plus a 16% nightly...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 51-56, apply the commutative...Ch. R.2 - For Exercises 51-56, apply the commutative...Ch. R.2 - For Exercises 51-56, apply the commutative...Ch. R.2 - For Exercises 51-56, apply the commutative...Ch. R.2 - For Exercises 51-56, apply the commutative...Ch. R.2 - For Exercises 5156, apply the commutative property...Ch. R.2 - For Exercises 5760, apply the associative property...Ch. R.2 - For Exercises 5760, apply the associative property...Ch. R.2 - For Exercises 5760, apply the associative property...Ch. R.2 - For Exercises 5760, apply the associative property...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - The width of a rectangle is 3 ft less than twice...Ch. R.2 - The longest side of a triangle is 5 ft less than...Ch. R.2 - Total college enrollment in the United States...Ch. R.2 - The average cost per kilowatt-hour for residential...Ch. R.2 - Under selected conditions, a sports car gets 15...Ch. R.2 - Under selected conditions, a sedan gets 22 mpg in...Ch. R.2 - Explain the difference between the commutative...Ch. R.2 - Explain why 0 has no multiplicative inverse.Ch. R.2 - For Exercises 105106, use a calculator to evaluate...Ch. R.2 - For Exercises 105106, use a calculator to evaluate...Ch. R.3 - Prob. 1PECh. R.3 - Prob. 2PECh. R.3 - Prob. 3PECh. R.3 - Prob. 4PECh. R.3 - Prob. 5PECh. R.3 - Prob. 6PECh. R.3 - Prob. 7PECh. R.3 - Prob. 8PECh. R.3 - Prob. 9PECh. R.3 - Prob. 10PECh. R.3 - Prob. 11PECh. R.3 - Prob. 12PECh. R.3 - Prob. 13PECh. R.3 - Prob. 14PECh. R.3 - Prob. 15PECh. R.3 - Prob. 16PECh. R.3 - Prob. 17PECh. R.3 - Prob. 18PECh. R.3 - Prob. 19PECh. R.3 - Prob. 20PECh. R.3 - Prob. 21PECh. R.3 - Prob. 22PECh. R.3 - Prob. 23PECh. R.3 - Prob. 24PECh. R.3 - Prob. 25PECh. R.3 - Prob. 26PECh. 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R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 1526, simplify the expression. (See...Ch. R.4 - For Exercises 2736, simplify each expression. (See...Ch. R.4 - For Exercises 2736, simplify each expression. (See...Ch. R.4 - For Exercises 2736, simplify each expression. (See...Ch. R.4 - For Exercises 2736, simplify each expression. (See...Ch. R.4 - For Exercises 2736, simplify each expression. (See...Ch. R.4 - For Exercises 2736, simplify each expression. (See...Ch. R.4 - For Exercises 2736, simplify each expression. (See...Ch. R.4 - For Exercises 2736, simplify each expression. (See...Ch. R.4 - For Exercises 2736, simplify each expression. (See...Ch. R.4 - For Exercises 2736, simplify each expression. (See...Ch. R.4 - For Exercises 3738, write the expression using...Ch. R.4 - For Exercises 3738, write the expression using...Ch. R.4 - For Exercises 3946, write the expression using...Ch. R.4 - For Exercises 3946, write the expression using...Ch. R.4 - For Exercises 3946, write the expression using...Ch. R.4 - For Exercises 3946, write the expression using...Ch. R.4 - For Exercises 3946, write the expression using...Ch. R.4 - For Exercises 3946, write the expression using...Ch. R.4 - For Exercises 3946, write the expression using...Ch. R.4 - For Exercises 3946, write the expression using...Ch. R.4 - For Exercises 4756, simplify each expression....Ch. R.4 - For Exercises 4756, simplify each expression....Ch. R.4 - For Exercises 4756, simplify each expression....Ch. R.4 - For Exercises 4756, simplify each expression....Ch. R.4 - For Exercises 4756, simplify each expression....Ch. R.4 - For Exercises 4756, simplify each expression....Ch. R.4 - For Exercises 4756, simplify each expression....Ch. R.4 - For Exercises 4756, simplify each expression....Ch. R.4 - For Exercises 4756, simplify each expression....Ch. R.4 - For Exercises 4756, simplify each expression....Ch. R.4 - a. For what values of t will the statement be...Ch. R.4 - a. For what values of c will the statement be...Ch. R.4 - For Exercises 5966, simplify each expression. (See...Ch. R.4 - For Exercises 5966, simplify each expression. (See...Ch. R.4 - For Exercises 5966, simplify each expression. (See...Ch. R.4 - For Exercises 5966, simplify each expression. (See...Ch. R.4 - For Exercises 5966, simplify each expression. (See...Ch. R.4 - For Exercises 5966, simplify each expression. (See...Ch. R.4 - For Exercises 5966, simplify each expression. (See...Ch. R.4 - For Exercises 5966, simplify each expression. (See...Ch. R.4 - For Exercises 6782, simplify each expression....Ch. R.4 - For Exercises 6782, simplify each expression....Ch. R.4 - For Exercises 6782, simplify each expression....Ch. R.4 - For Exercises 6782, simplify each expression....Ch. R.4 - Prob. 71PECh. R.4 - For Exercises 6782, simplify each expression....Ch. R.4 - For Exercises 6782, simplify each expression....Ch. R.4 - For Exercises 6782, simplify each expression....Ch. R.4 - For Exercises 6782, simplify each expression....Ch. R.4 - For Exercises 6782, simplify each expression....Ch. R.4 - Prob. 77PECh. R.4 - For Exercises 6782, simplify each expression....Ch. R.4 - Prob. 79PECh. R.4 - Prob. 80PECh. R.4 - Prob. 81PECh. R.4 - Prob. 82PECh. R.4 - Prob. 83PECh. R.4 - Prob. 84PECh. R.4 - Prob. 85PECh. R.4 - Prob. 86PECh. R.4 - Prob. 87PECh. 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R.5 - Prob. 54PECh. R.5 - Prob. 55PECh. R.5 - Prob. 56PECh. R.5 - The total national expenditure for health care has...Ch. R.5 - Prob. 58PECh. R.5 - Prob. 59PECh. R.5 - Prob. 60PECh. R.5 - Prob. 61PECh. R.5 - Prob. 62PECh. R.5 - Prob. 63PECh. R.5 - Prob. 64PECh. R.5 - Prob. 65PECh. R.5 - Prob. 66PECh. R.5 - Prob. 67PECh. R.5 - Prob. 68PECh. R.5 - Suppose that x represents the smaller of two...Ch. R.5 - Prob. 70PECh. R.5 - Prob. 71PECh. R.5 - Prob. 72PECh. R.5 - Prob. 73PECh. R.5 - Prob. 74PECh. R.5 - Prob. 75PECh. R.5 - Prob. 76PECh. R.5 - Prob. 77PECh. R.5 - Prob. 78PECh. R.5 - Prob. 79PECh. R.5 - Prob. 80PECh. R.5 - Prob. 81PECh. R.5 - Prob. 82PECh. R.5 - Prob. 83PECh. R.5 - Prob. 84PECh. R.5 - Prob. 85PECh. R.5 - Prob. 86PECh. R.5 - Prob. 87PECh. R.5 - Prob. 88PECh. R.5 - Prob. 89PECh. R.5 - Prob. 90PECh. R.5 - Prob. 91PECh. R.5 - Prob. 92PECh. R.5 - Prob. 93PECh. R.5 - Prob. 94PECh. R.5 - Prob. 95PECh. R.5 - Prob. 96PECh. R.5 - Prob. 97PECh. R.5 - Prob. 98PECh. R.5 - Prob. 99PECh. 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R.6 - Prob. 116PECh. R.6 - Prob. 117PECh. R.6 - Prob. 118PECh. R.6 - Prob. 119PECh. R.6 - Prob. 120PECh. R.7 - For Exercises 18, factor completely. 30x365x225xCh. R.7 - Prob. 2PECh. R.7 - Prob. 3PECh. R.7 - Prob. 4PECh. R.7 - Prob. 5PECh. R.7 - Prob. 6PECh. R.7 - Prob. 7PECh. R.7 - Prob. 8PECh. R.7 - Prob. 9PECh. R.7 - Prob. 10PECh. R.7 - Prob. 11PECh. R.7 - Prob. 12PECh. R.7 - Prob. 13PECh. R.7 - Prob. 14PECh. R.7 - Prob. 15PECh. R.7 - Prob. 16PECh. R.7 - Prob. 17PECh. R.7 - Prob. 18PECh. R.7 - Prob. 19PECh. R.7 - Prob. 20PECh. R.7 - Prob. 21PECh. R.7 - Prob. 22PECh. R.7 - Prob. 23PECh. R.7 - Prob. 24PECh. R.7 - Prob. 25PECh. R.7 - Prob. 26PECh. R.7 - Prob. 27PECh. R.7 - Prob. 28PECh. R.7 - Prob. 29PECh. R.7 - Prob. 30PECh. R.7 - Prob. 31PECh. R.7 - Prob. 32PECh. R.7 - Prob. 33PECh. R.7 - Prob. 34PECh. R.7 - Prob. 35PECh. R.7 - Prob. 36PECh. R.7 - Prob. 37PECh. R.7 - Prob. 38PECh. R.7 - Prob. 39PECh. R.7 - Prob. 40PECh. R.7 - Prob. 41PECh. R.7 - Prob. 42PECh. R.7 - Prob. 43PECh. 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R.7 - The concentration C (in ng/mL) of a drug in the...Ch. R.7 - An object that is originally 35C is placed in a...Ch. R.7 - Prob. 95PECh. R.7 - Prob. 96PECh. R.7 - Prob. 97PECh. R.7 - Prob. 98PECh. R.7 - Prob. 99PECh. R.7 - Prob. 100PECh. R.7 - Prob. 101PECh. R.7 - Prob. 102PECh. R.7 - Prob. 103PECh. R.7 - Prob. 104PECh. R.7 - Prob. 105PECh. R.7 - Prob. 106PECh. R.7 - Prob. 107PECh. R.7 - Prob. 108PECh. R.7 - Prob. 109PECh. R.7 - Prob. 110PECh. R.7 - Prob. 111PECh. R.7 - Prob. 112PECh. R.7 - Prob. 113PECh. R.7 - Prob. 114PECh. R.7 - Prob. 115PECh. R.7 - Prob. 116PECh. R.7 - Prob. 117PECh. R.7 - Prob. 118PECh. R.7 - Prob. 119PECh. R.7 - Prob. 120PECh. R.7 - Prob. 121PECh. R.7 - Prob. 122PECh. R.7 - Prob. 123PECh. R.7 - Prob. 124PECh. R.7 - Prob. 125PECh. R.7 - Prob. 126PECh. R.7 - Prob. 127PECh. R.7 - Prob. 128PECh. R.7 - Prob. 129PECh. R.7 - Prob. 130PECh. R.7 - Prob. 131PECh. R.7 - Prob. 132PECh. R.7 - Prob. 133PECh. R.7 - Prob. 134PECh. R - Prob. 1RECh. R - Prob. 2RECh. 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- Exercises 38–40 will help you prepare for the material covered in the first section of the next chapter. In Exercises 38-39, simplify each algebraic expression. 38. (-9x³ + 7x? - 5x + 3) + (13x + 2r? – &x – 6) 39. (7x3 – 8x? + 9x – 6) – (2x – 6x? – 3x + 9) 40. The figures show the graphs of two functions. y y 201 10- .... -20- flx) = x³ glx) = -0.3x + 4x + 2arrow_forwardIn Exercises 101–103, perform the indicated operations. 1 1 1 101. x" – 1 x" + 1 x2" – 1 (1-X- -X ) (1 – (1 – 102. (1 - x + 1) x + 2 x + 3 103. (x – y)-1 + (x – y)-2arrow_forwardIn Exercises 33–37, simplify each exponential expression. 33. (-2r)(7x-10) 34. (-&rSy)(-5x?y*) -10xty 35. -40x-2y6 36. (4x-Sy?)-3 -6xy 37. -2 2x*y 3,,-4arrow_forward
- In Exercises 126–129, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 126. Once a GCF is factored from 6y – 19y + 10y“, the remaining trinomial factor is prime. 127. One factor of 8y² – 51y + 18 is 8y – 3. 128. We can immediately tell that 6x? – 11xy – 10y? is prime because 11 is a prime number and the polynomial contains two variables. 129. A factor of 12x2 – 19xy + 5y² is 4x – y.arrow_forwardSection #3: Key methods and concepts: →Use the exponent rules to simplify each expression below. 2) For n an 3 1) 2x7 (4x²)żarrow_forwardMake Sense? In Exercises 135–138, determine whether each statement makes sense or does not make sense, and explain your reasoning. 135. I use the same ideas to multiply (V2 + 5) (V2 + 4) that I did to find the binomial product (x + 5)(x + 4). 136. I used a special-product formula and simplified as follows: (V2 + V5)? = 2 + 5 = 7. 137. In some cases when I multiply a square root expression and its conjugate, the simplified product contains a radical. 138. I use the fact that 1 is the multiplicative identity to both rationalize denominators and rewrite rational expressions with a common denominator.arrow_forward
- In Exercises 83–90, perform the indicated operation or operations. 83. (3x + 4y)? - (3x – 4y) 84. (5x + 2y) - (5x – 2y) 85. (5x – 7)(3x – 2) – (4x – 5)(6x – 1) 86. (3x + 5)(2x - 9) - (7x – 2)(x – 1) 87. (2x + 5)(2r - 5)(4x? + 25) 88. (3x + 4)(3x – 4)(9x² + 16) (2x – 7)5 89. (2x – 7) (5x – 3)6 90. (5x – 3)4arrow_forwardIn Exercises 133–136, factor each polynomial completely. Assume that any variable exponents represent whole numbers. 133. y + x + x + y 134. 36x2" – y2n 135. x* 3n 12n 136. 4x2" + 20x"y" + 25y2marrow_forwardSimplify each express.arrow_forward
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