Solution manual for college algebra 6th edition by blitzer

false; Changes to make the statement true will vary.. false; Changes to make the statement true will vary.. false; Changes to make the statement true will vary.. false; Changes to make t

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Fundamental Concepts of Algebra

If trends continue, the tuition and fees will be $9209

3. The elements common to {3, 4, 5, 6, 7} and

Because 2 1.4, the number inside the

absolute value bars is negative The absolute

value of x when x < 0 is –x Thus,

1 2   1 2  2 1

b. π 3Because π3.14, the number inside the absolute value bars is positive The absolute value of a positive number is the number itself Thus,

8 7(4x23 ) 2(5x  x2 x)

2. b to the nth power; base; exponent

3. formula; modeling; models

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Chapter P Prerequisites: Fundamental Concepts of Algebra

5 210

x x

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41 Answers will vary An example is 2.

42. Answers will vary An example is 2

43 true; –13 is to the left of –2 on the number line

44. false; –6 is to the left of 2 on the number line

45 true; 4 is to the right of –7 on the number line

46. true; –13 is to the left of –5 on the number line

47. true;   

48. true; –3 is to the right of –13 on the number line

49. true; 0 is to the right of –6 on the number line

50. true; 0 is to the right of –13 on the number line

51. 300300

52. 203203

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81. 2 (–8 + 6) = –16 + 12;

distributive property of multiplication over addition

82. 8(3 11)    24 ( 88); distributive property of multiplication over addition

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105 3

0.65

0.6 0.60.6 0.6 0.6 0.6



Since 0.6 0.6, 3 0.6

5

106 5

2.52

2.5 2.5.5 2.5 2.5 2.5

2



Since 2.5 2.5, 5 2.5

0 1

0 1Since 0 1, 30 3 14 15

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10 9111121

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220 2010

720010

The lower limit of the heart rate for a

20-year-old with this exercise goal is 140 beats per

220 205

42005160

 

122021

220 302

1190295

 

322053

220 305

31905114

The formula projects the cost to be $30,568 in

2013

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135 – 143. Answers will vary

144 does not make sense; Explanations will vary

Sample explanation: Models do not always

accurately predict future values

Sample explanation: To use the model, substitute 0

for x

146 makes sense

Sample explanation: The commutative property

changes order and the associative property changes

groupings

148 false; Changes to make the statement true will vary

A sample change is: Some rational numbers are not

integers

A sample change is: All whole numbers are integers

150 true

A sample change is: Some irrational numbers are negative

A sample change is: The term x has a coefficient of

1

A sample change is:

5 3( x  4) 5 3x123x 7

A sample change is:    x x 2 x

155 true

156 2 1.41.4 1.5

1.5712

1.57 1.5713.14

b b b b b b b b

b

b b b b

b b b b b b b b b

b

b b b

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x y y x

2 2 8 8

2 2 8 2

5

525

x y x y y x y x

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0.4 100.4 10





The cost was $8300 per citizen

Concept and Vocabulary Check P.2

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55

10

1010

222

b b

(4 ) (4 )( )

414116

x

x x

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3 6

3 6 6

(10 ) 10

1011011000

x

x x

432

3434

x y

x y y x

330

133

x y

x y y x

3 4 3 3 12

3

327

y x y x

30 9

10

3327

b a b a

80 579, 000, 000, 000, 000, 0005.79 10 17

81 5716 5.716 10 3

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6.4 106.4 10

4.2 104.2 10

12.2 1012.2 101.22 10

11 ( 4) 15

480, 000, 000, 000 4.8 10

4.8 101.2 10

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1340 10 7.90 1.34 10 7.9

1.34 7.9 1010.586 101.0586 10

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118 6 9

9 9

1380 10 6.40 1.38 10 6.4

1.38 6.4 108.832 10

18

5.3 10 20, 000 5.3 10 2 10

5.3 2 10 1010.6 101.06 10 101.06 10

19

1.67 10 80, 000 1.67 10 8 10

1.67 8 10 1013.36 101.336 10 101.336 10

Americans eat 4.064 10 9chickens per year

122 365 days equals 365 24 or 8760 hours.

8760 hours equals 8760 60 or 525,600 minutes.

525,600 min equals

525,600 60 or 31,536,000 seconds.

There are 3.1536 10 7 seconds in a year

Sample explanation: 36(x3 9) 36x27not 36x12

133 makes sense

Sample explanation: 4.6 10 12 represents over 4

trillion The entire world population is measured in

billions (109)

135 makes sense

A sample change is: 424 3

137 true

A sample change is: ( 2)4 24 because 16 1

16



A sample change is: 5 52 2 2 2 5 5

A sample change is: 534.75347

A sample change is:

30

30 ( 5) 35 5

A sample change is:

60 min

hr

24 hrs

day

365 days



yr 80 yrs

9 9

70 60 24 365 80 beats

2943360000 beats2.94336 10 beats2.94 10 beats

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75

x x x

6 a. If we multiply numerator and denominator by

3, the denominator becomes

3 3 9  Therefore, multiply by 1, 3.choosing 3

3 for 1

3

b. The smallest number that will produce a perfect

square in the denominator of 6

12 is 3 because 12 3 36 6. So multiply by

1, choosing 3

3 for 1

36

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b 3  

2 2

32

423232

2 5101010

x x x

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12

x x x

x

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3 2

33

3 1 4 4

1010

2020

4 52

x x

x x x x

5010

10

x x

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59. 4 is not a real number 16

60. 4 is not a real number 81

6 6

64  2  2

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16

90. 5/2 15/2 1 5 15 116

1414

x x

1212

x x

55

44

x x

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y

y y

3 12

22

6 2/4 6 1/3 62/4 1/3

5/4

4 1/2 4 2/4 41/2 2/4

2

2 2 2

x y

x y y

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This underestimates the difference projected by

the graph of 65.8 47.3 18.5  by 2.7 This

represents a difference of 2.7 million people

117 2 5 1 2( 5 1)

5 1

2( 5 1)4

5 121.62

c R

f

R

R R



If you are gone for 44 weeks, then 100 weeks will

have passed for your friend

121 – 128 Answers will vary

129 does not make sense; Explanations will vary Sample explanation: The denominator is rationalized correctly

Sample explanation: Finding the nth root first often

gives smaller numbers on the middle step

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133 false; Changes to make the statement true will vary A sample change is: 12 12 1

7 7 7 7

134 false; Changes to make the statement true will vary A sample change is:  

 

1 3

135 false; Changes to make the statement true will vary The cube root of –8 is the real number –2

136 false; Changes to make the statement true will vary A sample change is: 20 5

3 2

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22

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6 a Use the special-product formula shown

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13. A22ABB2; minus; product of the terms; plus

14. n m

Exercise Set P.4

1. yes; 2x3x2 5 3x22x 5

2. no; The term 3x1 does not have a whole number exponent

3. no; The form of a polynomial involves addition and subtraction, not division

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The model estimates the median annual income for a woman with 18 years of education to be $50,082

The model underestimates the actual value of $50,576 shown in the bar graph by $494

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106 makes sense, although answers may vary

107 false; Changes to make the statement true will vary A sample change is: (3x32)(3x3 2) 9x6 4

108 false; Changes to make the statement true will vary A sample change is: (x5)2x210x 25

109 false; Changes to make the statement true will vary A sample change is: (x1)2x22x 1

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28. Since x  then x0   Thus x x x2  x x2   x3

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5. Find two First terms whose product is 6x2

Find two Last terms whose product is –7

The possible factors are 1(–7) and –1(7)

Try various combinations of these factors to find the factorization in which the sum of the Outside and Inside products is

19x

Possible Factors of

2

6x 19x 7

Sum of Outside and Inside

Products (Should Equal 19x)

Find two Last terms whose product is 4 y 2

The possible factors are (2 )(2 )y y , ( 2 )( 2 ) y  y , (4 )( )y y , and ( 4 )( y  y)

Try various combinations of these factors to find the factorization in which the sum of the Outside and Inside products is

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8. Express 81x4 as the difference of two squares and use the formula for factoring 16 A2B2.

b. Since 16x2(4 )x 2 and 497 ,2 check to see if the middle term can be expressed as twice the product of 4x and

7 Since 2 4  x 7 56 , 16x x256x49 is a perfect square trinomial Thus, 2 2 2

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72. 3 2 3 2

2 2

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2 2

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134 false; Changes to make the statement true will vary A sample change is:

4 16 ( 2 4)( 2 4) ( 2 4)( 2)( 2)

135 true

136 false; Changes to make the statement true will vary A sample change is: The binomial x236 is prime

137 false; Changes to make the statement true will vary A sample change is: 3   

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Section P.6

Check Point Exercises

1 a. The denominator would equal zero if x 5,

so –5 must be excluded from the domain

b. x236 (x 6)(x6)

The denominator would equal zero if x 6 or

x = 6, so –6 and 6 must both must be excluded

from the domain

c. x25x14 (x 2)(x7)

The denominator would equal zero if x 2 or

x = 7, so –2 and 7 must both must be excluded

from the domain

x x x

( 1)( 1)

( 1)( 1)2(4 1)

x x x The least common denominator is the product of all factors in the final list

2(x3)(x3)(x3) or (x3) (x3) is the least common denominator

8. Find the least common denominator

The least common denominator is 2(x – 5)(x – 5)

Write all rational expressions in terms of the least common denominator

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Add numerators, putting this sum over the least

6.

2

43

x  x

7. x and 3 x ; 2 x and 3 x ; 1(x3)(x2)(x 1)

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x

x x

34

x x

327

x x

x x x

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20,1, 1,5, 5

x x x

x x

3

x 

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35.

2 2

23

, 0, 33

x x x x x

, 3, 43

x x x

x x

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x x x

x x

5 5

x 

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x x

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x x

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b. For x = 100, the function is not defined

c. As x approaches 100, the value of the function increases rapidly So it costs an astronomical amount of money to inoculate almost all of the people, and it is impossible to inoculate 100% of the population

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If r1 = 40 and r2 = 30, the value of

this expression will be

2 40 30 2400

2

34 7





Your average speed will be 342

7 miles per hour

83 a. Substitute 4 for x in the model

2 2

66(4) 526(4) 10302078

120(4) 998(4) 5902662

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98 does not make sense; Explanations will vary Sample explanation: 3 3 3(1) 3 0

share a common factor

100 does not make sense; Explanations will vary Sample explanation: The first step is to invert the second fraction

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Chapter P Review Exercises

15. 3( 5 3) 15 3 ; distributive property of multiplication over addition

16. (6 9) 2     ; 2 (6 9)commutative property of multiplication

17. 3( 5 3)( 5 3) 3; commutative property of multiplication

18. (3 7) (4 7)       ; (4 7) (3 7)commutative property of addition

x x x

This is the same as the value displayed in the bar graph

24. ( 3) ( 2) 3  2 ( 27) (4)  108

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12

116

x x x

2828

144

x y

x y y x

3 10

2.3 100.023

22

x x x

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(5 )25

x x



72. 6 y3 (y3 1/6) y31/6  y1/2 y

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11

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3,

x x x

,4

3, 3

=+

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3 5

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27

2433

2727

In 2003, 43.08% of bachelor’s degrees were

awarded to men This overestimates the actual

percent shown by the bar graph by 0.08%

2

3

n R

Three women will receive bachelor’s degrees

for every two men This describes the

projections exactly

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