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Intermediate Algebra

Chapter 7

Intermediate AlgebraChapter 7

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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Quadratic Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  14. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
  15. Index

Try It

7.1

x=0x=0 n=13n=13
a=−1,a=−3a=−1,a=−3

7.2

q=0q=0 y=23y=23
m=2,m=−3m=2,m=−3

7.3

x + 1 x 1 , x + 1 x 1 , x 2 , x 2 , x 1 x 1

7.4

x 5 x 1 , x 5 x 1 , x 2 , x 2 , x 1 x 1

7.5

2 ( x 3 y ) 3 ( x + 3 y ) 2 ( x 3 y ) 3 ( x + 3 y )

7.6

5 ( x y ) 2 ( x + 5 y ) 5 ( x y ) 2 ( x + 5 y )

7.7

x + 1 x + 5 x + 1 x + 5

7.8

x + 2 x + 1 x + 2 x + 1

7.9

x 2 2 ( x + 3 ) x 2 2 ( x + 3 )

7.10

3 ( x 6 ) x + 5 3 ( x 6 ) x + 5

7.11

x 4 x 5 x 4 x 5

7.12

( b + 2 ) ( b 1 ) ( 1 + b ) ( b + 4 ) ( b + 2 ) ( b 1 ) ( 1 + b ) ( b + 4 )

7.13

2 ( x 2 + 2 x + 4 ) ( x + 2 ) ( x 2 2 x + 4 ) 2 ( x 2 + 2 x + 4 ) ( x + 2 ) ( x 2 2 x + 4 )

7.14

2 z z 1 2 z z 1

7.15

x + 2 4 x + 2 4

7.16

2 y + 5 2 y + 5

7.17

2 ( m + 1 ) ( m + 2 ) 3 ( m + 4 ) ( m 3 ) 2 ( m + 1 ) ( m + 2 ) 3 ( m + 4 ) ( m 3 )

7.18

( n + 5 ) ( n + 9 ) 2 ( n + 6 ) ( 2 n + 3 ) ( n + 5 ) ( n + 9 ) 2 ( n + 6 ) ( 2 n + 3 )

7.19

The domain of R(x)R(x) is all real numbers where x5x5 and x1.x1.

7.20

The domain of R(x)R(x) is all real numbers where x4x4 and x2.x2.

7.21

R ( x ) = 2 R ( x ) = 2

7.22

R ( x ) = 1 3 R ( x ) = 1 3

7.23

R ( x ) = x 2 4 ( x 8 ) R ( x ) = x 2 4 ( x 8 )

7.24

R ( x ) = x ( x 2 ) x 1 R ( x ) = x ( x 2 ) x 1

7.25

x + 2 x + 2

7.26

x + 3 x + 3

7.27

x 11 x 2 x 11 x 2

7.28

x 3 x + 9 x 3 x + 9

7.29

y + 3 y + 2 y + 3 y + 2

7.30

3 n 2 n 1 3 n 2 n 1

7.31

(x4)(x+3)(x+4)(x4)(x+3)(x+4)
2x+8(x4)(x+3)(x+4)2x+8(x4)(x+3)(x+4),
x+3(x4)(x+3)(x+4)x+3(x4)(x+3)(x+4)

7.32

(x+2)(x5)(x+1)(x+2)(x5)(x+1)
3x2+3x(x+2)(x5)(x+1)3x2+3x(x+2)(x5)(x+1),
5x25(x+2)(x5)(x+1)5x25(x+2)(x5)(x+1)

7.33

7 x 4 ( x 2 ) ( x + 3 ) 7 x 4 ( x 2 ) ( x + 3 )

7.34

7 m + 25 ( m + 3 ) ( m + 4 ) 7 m + 25 ( m + 3 ) ( m + 4 )

7.35

5 m 2 9 m + 2 ( m + 1 ) ( m 2 ) ( m + 2 ) 5 m 2 9 m + 2 ( m + 1 ) ( m 2 ) ( m + 2 )

7.36

2 n 2 + 12 n 30 ( n + 2 ) ( n 5 ) ( n + 3 ) 2 n 2 + 12 n 30 ( n + 2 ) ( n 5 ) ( n + 3 )

7.37

1 x 2 1 x 2

7.38

−3 z 3 −3 z 3

7.39

5 x + 1 ( x 6 ) ( x + 1 ) 5 x + 1 ( x 6 ) ( x + 1 )

7.40

y + 3 y + 4 y + 3 y + 4

7.41

1 ( b + 1 ) ( b 1 ) 1 ( b + 1 ) ( b 1 )

7.42

1 ( x + 2 ) ( x + 1 ) 1 ( x + 2 ) ( x + 1 )

7.43

v + 3 v + 1 v + 3 v + 1

7.44

3 w w + 7 3 w w + 7

7.45

x 7 x 4 x 7 x 4

7.46

x 2 3 x + 18 ( x + 3 ) ( x 3 ) x 2 3 x + 18 ( x + 3 ) ( x 3 )

7.47

2 3 ( x 1 ) 2 3 ( x 1 )

7.48

1 2 ( x 3 ) 1 2 ( x 3 )

7.49

14 11 14 11

7.50

10 23 10 23

7.51

y + x y x y + x y x

7.52

a b b a a b b a

7.53

b ( b + 2 ) ( b 5 ) 3 b 5 b ( b + 2 ) ( b 5 ) 3 b 5

7.54

3 c + 3 3 c + 3

7.55

7 3 7 3

7.56

10 3 10 3

7.57

b + a a 2 + b 2 b + a a 2 + b 2

7.58

y x x y y x x y

7.59

3 ( x 2 ) 5 x + 7 3 ( x 2 ) 5 x + 7

7.60

x + 21 6 x 43 x + 21 6 x 43

7.61

3 5 x + 22 3 5 x + 22

7.62

2 ( 2 y 2 + 13 y + 5 ) 3 y 2 ( 2 y 2 + 13 y + 5 ) 3 y

7.63

x x + 4 x x + 4

7.64

x ( x + 1 ) 3 ( x 1 ) x ( x + 1 ) 3 ( x 1 )

7.65

y = 7 15 y = 7 15

7.66

x = 13 15 x = 13 15

7.67

x = −3 , x = 5 x = −3 , x = 5

7.68

y = −2 , y = 6 y = −2 , y = 6

7.69

x = 2 3 x = 2 3

7.70

y = 2 y = 2

7.71

There is no solution.

7.72

There is no solution.

7.73

x = 3 x = 3

7.74

y = 7 y = 7

7.75

There is no solution.

7.76

There is no solution.

7.77

There is no solution.

7.78

There is no solution.

7.79

The domain is all real numbers except x3x3 and x4.x4. x=2,x=143x=2,x=143
(2,3),(143,3)(2,3),(143,3)

7.80

The domain is all real numbers except x1x1 and x5.x5. x=214x=214 (214,4)(214,4)

7.81

y = m x 4 m + 5 y = m x 4 m + 5

7.82

y = m x + 5 m + 1 y = m x + 5 m + 1

7.83

a = b c b 1 a = b c b 1

7.84

y = 3 x x + 6 y = 3 x x + 6

7.85

y = 33 y = 33

7.86

z = 14 z = 14

7.87

The pediatrician will prescribe 12 ml of acetaminophen to Emilia.

7.88

The pediatrician will prescribe 180 mg of fever reducer to Isabella.

7.89

The distance is 150 miles.

7.90

The distance is 350 miles.

7.91

The telephone pole is 40 feet tall.

7.92

The pine tree is 60 feet tall.

7.93

Link’s biking speed is 15 mph.

7.94

The speed of Danica’s boat is 17 mph.

7.95

Dennis’s uphill speed was 10 mph and his downhill speed was 5 mph.

7.96

Joon’s rate on the country roads is 50 mph.

7.97

Kayla’s biking speed was 15 mph.

7.98

Victoria jogged 6 mph on the flat trail.

7.99

When the two gardeners work together it takes 2 hours and 24 minutes.

7.100

When Daria and her mother work together it takes 2 hours and 6 minutes.

7.101

Kristina can paint the room in 12 hours.

7.102

It will take Jordan 6 hours.

7.103

c=4.8tc=4.8t He would burn 432 calories.

7.104

d=50td=50t It would travel 250 miles.

7.105

h=130th=130t 123123 hours

7.106

x=3500px=3500p 500 units

7.107

( , −4 ) [ 2 , ) ( , −4 ) [ 2 , )

7.108

( , −2 ] ( 4 , ) ( , −2 ] ( 4 , )

7.109

( 3 2 , 3 ) ( 3 2 , 3 )

7.110

( −8 , 4 ) ( −8 , 4 )

7.111

( , −4 ) ( 2 , ) ( , −4 ) ( 2 , )

7.112

( , −4 ) ( 3 , ) ( , −4 ) ( 3 , )

7.113

( 2 , 4 ) ( 2 , 4 )

7.114

( 3 , 6 ) ( 3 , 6 )

7.115

( −4 , 2 ] ( −4 , 2 ]

7.116

[ −1 , 4 ) [ −1 , 4 )

7.117

c(x)=20x+6000xc(x)=20x+6000x
More than 150 items must be produced to keep the average cost below $60 per item.

7.118

c(x)=5x+900xc(x)=5x+900x More than 60 items must be produced to keep the average cost below $20 per item.

Section 7.1 Exercises

1.

z=0z=0 p=56p=56
n=−4,n=2n=−4,n=2

3.

y=0y=0, x=12x=12, u=−4,u=7u=−4,u=7

5.

4 5 4 5

7.

2 m 2 3 n 2 m 2 3 n

9.

8 3 8 3

11.

x + 5 x 1 x + 5 x 1

13.

a + 2 a + 8 a + 2 a + 8

15.

p 2 + 4 p 2 p 2 + 4 p 2

17.

4 b ( b 4 ) ( b + 5 ) ( b 8 ) 4 b ( b 4 ) ( b + 5 ) ( b 8 )

19.

3 ( m + 5 n ) 4 ( m 5 n ) 3 ( m + 5 n ) 4 ( m 5 n )

21.

−1 −1

23.

5 y + 4 5 y + 4

25.

w 2 6 w + 36 w 6 w 2 6 w + 36 w 6

27.

z 5 4 + z z 5 4 + z

29.

3 10 3 10

31.

x 3 8 y x 3 8 y

33.

p ( p 4 ) 2 ( p 9 ) p ( p 4 ) 2 ( p 9 )

35.

y 5 3 ( y + 5 ) y 5 3 ( y + 5 )

37.

4 ( b + 9 ) 3 ( b + 7 ) 4 ( b + 9 ) 3 ( b + 7 )

39.

c + 5 3 c + 1 c + 5 3 c + 1

41.

( m 3 ) ( m 2 ) ( m + 4 ) ( m + 3 ) ( m 3 ) ( m 2 ) ( m + 4 ) ( m + 3 )

43.

1 v + 5 1 v + 5

45.

3 s s + 4 3 s s + 4

47.

4 ( p 2 p q + q 2 ) ( p q ) ( p 2 + p q + q 2 ) 4 ( p 2 p q + q 2 ) ( p q ) ( p 2 + p q + q 2 )

49.

x 2 8 x ( x + 5 ) x 2 8 x ( x + 5 )

51.

2 a 7 5 2 a 7 5

53.

3 ( 3 c 5 ) 3 ( 3 c 5 )

55.

4 ( m + 8 ) ( m + 7 ) 3 ( m 4 ) ( m + 2 ) 4 ( m + 8 ) ( m + 7 ) 3 ( m 4 ) ( m + 2 )

57.

( 4 p + 1 ) ( p 4 ) 3 p ( p + 9 ) ( p 1 ) ( 4 p + 1 ) ( p 4 ) 3 p ( p + 9 ) ( p 1 )

59.

x5x5 and x5x5

61.

x2x2 and x3x3

63.

R ( x ) = 2 R ( x ) = 2

65.

R ( x ) = x + 5 2 x ( x + 2 ) R ( x ) = x + 5 2 x ( x + 2 )

67.

R ( x ) = 3 x ( x + 7 ) x 7 R ( x ) = 3 x ( x + 7 ) x 7

69.

R ( x ) = x ( x 5 ) x 6 R ( x ) = x ( x 5 ) x 6

71.

Answers will vary.

73.

Answers will vary.

Section 7.2 Exercises

75.

3 5 3 5

77.

3 c + 5 4 c 5 3 c + 5 4 c 5

79.

r + 8 r + 8

81.

2 w w 4 2 w w 4

83.

3 a + 7 3 a + 7

85.

m 2 2 m 2 2

87.

p + 3 p + 5 p + 3 p + 5

89.

r + 9 r + 7 r + 9 r + 7

91.

4 4

93.

x + 2 x + 2

95.

z + 4 z 5 z + 4 z 5

97.

4 b 3 b 7 4 b 3 b 7

99.

(x+2)(x4)(x+3)(x+2)(x4)(x+3)
5x+15(x+2)(x4)(x+3)5x+15(x+2)(x4)(x+3),
2x2+4x(x+2)(x4)(x+3)2x2+4x(x+2)(x4)(x+3)

101.

(z2)(z+4)(z4)(z2)(z+4)(z4)
9z36(z2)(z+4)(z4)9z36(z2)(z+4)(z4),
4z28z(z2)(z+4)(z4)4z28z(z2)(z+4)(z4)

103.

(b+3)(b+3)(b5)(b+3)(b+3)(b5)
4b20(b+3)(b+3)(b5)4b20(b+3)(b+3)(b5),
2b2+6b(b+3)(b+3)(b5)2b2+6b(b+3)(b+3)(b5)

105.

(d+5)(3d1)(d6)(d+5)(3d1)(d6)
2d12(d+5)(3d1)(d6)2d12(d+5)(3d1)(d6),
5d2+25d(d+5)(3d1)(d6)5d2+25d(d+5)(3d1)(d6)

107.

21 y + 8 x 30 x 2 y 2 21 y + 8 x 30 x 2 y 2

109.

5 r 7 ( r + 4 ) ( r 5 ) 5 r 7 ( r + 4 ) ( r 5 )

111.

11 w + 1 ( 3 w 2 ) ( w + 1 ) 11 w + 1 ( 3 w 2 ) ( w + 1 )

113.

2 y 2 + y + 9 ( y + 3 ) ( y 1 ) 2 y 2 + y + 9 ( y + 3 ) ( y 1 )

115.

b ( 5 b + 10 + 2 a 2 ) a 2 ( b 2 ) ( b + 2 ) b ( 5 b + 10 + 2 a 2 ) a 2 ( b 2 ) ( b + 2 )

117.

m m + 4 m m + 4

119.

3 ( r 2 + 6 r + 18 ) ( r + 1 ) ( r + 6 ) ( r + 3 ) 3 ( r 2 + 6 r + 18 ) ( r + 1 ) ( r + 6 ) ( r + 3 )

121.

2 ( 7 t 6 ) ( t 6 ) ( t + 6 ) 2 ( 7 t 6 ) ( t 6 ) ( t + 6 )

123.

4 a 2 + 25 a 6 ( a + 3 ) ( a + 6 ) 4 a 2 + 25 a 6 ( a + 3 ) ( a + 6 )

125.

−6 m 6 −6 m 6

127.

p + 2 p + 3 p + 2 p + 3

129.

3 r 2 3 r 2

131.

4 ( 8 x + 1 ) 10 x 1 4 ( 8 x + 1 ) 10 x 1

133.

x 5 ( x 4 ) ( x + 1 ) ( x 1 ) x 5 ( x 4 ) ( x + 1 ) ( x 1 )

135.

1 ( x 1 ) ( x + 1 ) 1 ( x 1 ) ( x + 1 )

137.

5 a 2 + 7 a 36 a ( a 2 ) 5 a 2 + 7 a 36 a ( a 2 )

139.

c 5 c + 2 c 5 c + 2

141.

3 ( d + 1 ) d + 2 3 ( d + 1 ) d + 2

143.

R(x)=(x+8)(x+1)(x2)(x+3)R(x)=(x+8)(x+1)(x2)(x+3) R(x)=x+1x+3R(x)=x+1x+3

145.

3(3x+8)(x8)(x+8)3(3x+8)(x8)(x+8)
R(x)=3x+8R(x)=3x+8

147.

Answers will vary.

149.

Answers will vary.
Answers will vary.
Answers will vary.
x+yxyx+yxy

Section 7.3 Exercises

151.

a 4 2 a a 4 2 a

153.

1 2 ( c 2 ) 1 2 ( c 2 )

155.

12 13 12 13

157.

20 57 20 57

159.

n 2 + m m n 2 n 2 + m m n 2

161.

r t t r r t t r

163.

( x + 1 ) ( x 3 ) 2 ( x + 1 ) ( x 3 ) 2

165.

4 a + 1 4 a + 1

167.

11 8 11 8

169.

19 19

171.

c 2 + c c d 2 c 2 + c c d 2

173.

p q q p p q q p

175.

2 x 10 3 x + 16 2 x 10 3 x + 16

177.

3 z 19 3 z + 8 3 z 19 3 z + 8

179.

4 3 a 7 4 3 a 7

181.

2 c + 29 5 c 2 c + 29 5 c

183.

2 p 5 5 2 p 5 5

185.

m ( m 5 ) ( 4 m 19 ) ( m + 5 ) m ( m 5 ) ( 4 m 19 ) ( m + 5 )

187.

13 24 13 24

189.

2 ( a 4 ) 2 ( a 4 )

191.

3 m n n m 3 m n n m

193.

( x 1 ) ( x 2 ) 6 ( x 1 ) ( x 2 ) 6

195.

Answers will vary.

Section 7.4 Exercises

197.

a = 10 a = 10

199.

v = 40 21 v = 40 21

201.

m = −2 , m = 4 m = −2 , m = 4

203.

p = −5 , p = −4 p = −5 , p = −4

205.

v = 14 v = 14

207.

x = 4 5 x = 4 5

209.

z = −145 z = −145

211.

q = −18 , q = −1 q = −18 , q = −1

213.

no solution no solution

215.

no solution no solution

217.

b = −8 b = −8

219.

d = 2 d = 2

221.

m = 1 m = 1

223.

no solution no solution

225.

s = 5 4 s = 5 4

227.

x = 4 3 x = 4 3

229.

no solution

231.

> The domain is all real numbers except x2x2 and x4.x4. x=−3,x=145x=−3,x=145 (−3,5),(145,5)(−3,5),(145,5)

233.

The domain is all real numbers except x2x2 and x5.x5. x=92,x=92, (92,2)(92,2)

235.

r = C 2 π r = C 2 π

237.

w = 2 v + 7 w = 2 v + 7

239.

c = b + 3 + 2 a a c = b + 3 + 2 a a

241.

p = q 4 q 2 p = q 4 q 2

243.

w = 15 v 10 + v w = 15 v 10 + v

245.

n = 5 m + 23 4 n = 5 m + 23 4

247.

c = E m 2 c = E m 2

249.

y = 20 x 12 x y = 20 x 12 x

251.

Answers will vary.

Section 7.5 Exercises

253.

x = 49 x = 49

255.

p = −11 p = −11

257.

a = 16 a = 16

259.

m = 60 m = 60

261.

p = 30 p = 30

263.

162 beats per minute yes

265.

99 ml

267.

159159 calories

269.

325325 Canadian dollars

271.

33 cups

273.

4 bags

275.

6 1212

277.

950 miles

279.

680 miles

281.

2323 foot (88 in.)

283.

247.3247.3 feet

285.

160160 mph

287.

2929 mph

289.

3030 mph

291.

2020 mph

293.

44 mph

295.

6060 mph

297.

650650 mph

299.

5050 mph

301.

5050 mph

303.

4.2 mph

305.

22 hours

307.

22 hours and 4444 minutes

309.

77 hours and 3030 minutes

311.

1010 min

313.

y = 14 3 x y = 14 3 x

315.

p = 3.2 q p = 3.2 q

317.

P=2.5gP=2.5g $82.50$82.50

319.

m=8vm=8v 1616 liters

321.

L=3d2L=3d2 300300 pounds

323.

y = 20 x y = 20 x

325.

v = 3 w v = 3 w

327.

g=92,400wg=92,400w 16.8 mpg

329.

t=1000rt=1000r 2.52.5 hours

331.

c=2tc=2t 11 cavity

333.

c=2.5mc=2.5m $55

335.

Answers will vary.

337.

Answers will vary.

Section 7.6 Exercises

339.

( , −4 ) [ 3 , ) ( , −4 ) [ 3 , )

341.

[ −1 , 3 ) [ −1 , 3 )

343.

( , 1 ) ( 7 , ) ( , 1 ) ( 7 , )

345.

( −5 , 6 ) ( −5 , 6 )

347.

( 5 2 , 5 ) ( 5 2 , 5 )

349.

( , −3 ) ( 6 , ) ( , −3 ) ( 6 , )

351.

[ −9 , 6 ) [ −9 , 6 )

353.

( , −6 ] ( 4 , ) ( , −6 ] ( 4 , )

355.

( , −4 ) ( −3 , ) ( , −4 ) ( −3 , )

357.

( 1 , 4 ) ( 1 , 4 )

359.

( , −3 ) ( 5 2 , ) ( , −3 ) ( 5 2 , )

361.

( , 2 3 ) ( 3 2 , ) ( , 2 3 ) ( 3 2 , )

363.

( , 0 ) ( 0 , 4 ) ( 6 , ) ( , 0 ) ( 0 , 4 ) ( 6 , )

365.

[ −2 , 0 ) ( 0 , 4 ] [ −2 , 0 ) ( 0 , 4 ]

367.

( −4 , 4 ) ( −4 , 4 )

369.

[ −10 , −1 ) ( 2 , ) [ −10 , −1 ) ( 2 , )

371.

( 2 , 5 ] ( 2 , 5 ]

373.

( , −2 ) [ 6 , ) ( , −2 ) [ 6 , )

375.

Answers will vary.

Review Exercises

377.

a 2 3 a 2 3

379.

y 0 y 0

381.

3 4 3 4

383.

x + 3 x + 4 x + 3 x + 4

385.

1 6 1 6

387.

−3 x 2 −3 x 2

389.

3 x ( x + 6 ) ( x + 6 ) 3 x ( x + 6 ) ( x + 6 )

391.

1 11 + w 1 11 + w

393.

5 c + 4 5 c + 4

395.

R ( x ) = 3 R ( x ) = 3

397.

1 1

399.

y + 5 y + 5

401.

x + 4 x + 4

403.

q 3 q + 5 q 3 q + 5

405.

15 w + 2 6 w 1 15 w + 2 6 w 1

407.

3 b 2 b + 7 3 b 2 b + 7

409.

( a + 2 ) ( a 5 ) ( a + 4 ) ( a + 2 ) ( a 5 ) ( a + 4 )

411.

( 3 p + 1 ) ( p + 6 ) ( p + 8 ) ( 3 p + 1 ) ( p + 6 ) ( p + 8 )

413.

11 c 12 ( c 2 ) ( c + 3 ) 11 c 12 ( c 2 ) ( c + 3 )

415.

5 x 2 + 26 x ( x + 4 ) ( x + 4 ) ( x + 6 ) 5 x 2 + 26 x ( x + 4 ) ( x + 4 ) ( x + 6 )

417.

2 ( y 2 + 10 y 2 ) ( y + 2 ) ( y + 8 ) 2 ( y 2 + 10 y 2 ) ( y + 2 ) ( y + 8 )

419.

2 m 7 m + 2 2 m 7 m + 2

421.

4 a 8 4 a 8

423.

R ( x ) = x + 8 x + 5 R ( x ) = x + 8 x + 5

425.

R ( x ) = 2 x + 11 R ( x ) = 2 x + 11

427.

x 2 2 x x 2 2 x

429.

( x 8 ) ( x 5 ) 2 ( x 8 ) ( x 5 ) 2

431.

11 8 11 8

433.

z 5 21 z + 21 z 5 21 z + 21

435.

x = 6 7 x = 6 7

437.

b = 3 2 b = 3 2

439.

no solution

441.

The domain is all real numbers except x2x2 and x4.x4. x=1,x=6x=1,x=6
(1,1),(6,1)(1,1),(6,1)

443.

l = V h w l = V h w

445.

z = y + 5 + 7 x x z = y + 5 + 7 x x

447.

12 5 12 5

449.

15 15

451.

11611161 calories

453.

b = 9 ; x = 2 1 3 b = 9 ; x = 2 1 3

455.

23 feet

457.

4545 mph

459.

1616 mph

461.

4545 hour

463.

1212 days

465.

7 7

467.

301301 mph

469.

288288 feet

471.

9797 tickets

473.

( −4 , 3 ] ( −4 , 3 ]

475.

[ −6 , 4 ) [ −6 , 4 )

477.

( , −2 ] [ 4 , ) ( , −2 ] [ 4 , )

479.

( , 2 ) [ 5 , ) ( , 2 ) [ 5 , )

481.


c(x)=150x+100000xc(x)=150x+100000x
More than 10,000 items must be produced to keep the average cost below $160$160 per item.

Practice Test

483.

a 3 b a 3 b

485.

x + 3 3 x x + 3 3 x

487.

x 3 x + 9 x 3 x + 9

489.

3 n 2 n 1 3 n 2 n 1

491.

n m m + n n m m + n

493.

z = 1 2 z = 1 2

495.

[ −3 , 6 ) [ −3 , 6 )

497.

( , 0 ) ( 0 , 4 ] [ 6 , ) ( , 0 ) ( 0 , 4 ] [ 6 , )

499.

R ( x ) = 1 ( x + 2 ) ( x + 2 ) R ( x ) = 1 ( x + 2 ) ( x + 2 )

501.

( 2 , 5 ] ( 2 , 5 ]

503.

y = 81 16 y = 81 16

505.

Oliver’s dad would take 445445 hours to split the logs himself.

507.

The distance between Dayton and Columbus is 64 miles.

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