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Intermediate Algebra (11th edition)

(Marvins-Underground-K-12) #1

Section 5.3 (pages 290–292)



  1. (a) (b) 8 3. (a) 8 (b) 2 5. (a) 8 (b) 74

  2. (a) (b) 4 9. (a)4300 thousand lb (b)19,371 thousand lb


(c)64,449 thousand lb 11. (a)$28.2 billion (b)$79.1 billion
(c)$105.9 billion 13. (a) (b)



  1. (a) (b) 17.





      1. 6 25. 27. 0 29. 31.






33.For example, let and
For these functions,
and
Because the two differences are not equal, subtraction of functions is not


commutative. 35. 6 37. 83 39. 53 41. 13 43.







      1. 8 51. It computes






the number of inches in xmiles. 53. This is the
area of the circular layer as a function of time.






domain:

range: 1 - q,q 2

1 - q,q 2 ;

f(x) = –2x + 1

–2 0 2

y

x

1 ar 21 t 2 = 4 pt^2 ;

2 x- 2 974 1 ƒg 21 x 2 =63,360x;

2 x^2 + 11

12 x^2 - x+8, 1 g-ƒ 21 x 2 = 2 x^4 +x^3 - 12 x^2 +x-8.


3 x^3 - 9 x^2 + 2 x-4. 1 ƒ-g 21 x 2 =- 2 x^4 - x^3 +


ƒ 1 x 2 = 2 x^3 + 3 x^2 +x+ 4 g 1 x 2 = 2 x^4 +

6 x^2 - x- 6 - 33 - 49 -^92


  • x^2 + 12 x- 12 9 x^2 + 4 x+ 6 x^2 + 2 x- 9


8 x- 3 2 x- 17


  • 11

  • 10
    103. 105. 106.
    107. , or 108. 109.
    110. 111. (a)They must
    be equal to each other. (b)
    112. The large square is made up of two smaller
    squares and two congruent rectangles. The sum of
    the areas is. Since must
    represent the same quantity, they must be equal.
    Thus,
    113. 115. 117. 119.
    121. 123. 125. 36 127. 129. 131.
    133. 135.


Section 5.5 (pages 306–308)


1.quotient; exponents 3. 0 5. 7.






















































































  9. They are the same, which suggests that when is
    divided by the result is Here, 61.








































Chapter 5 Review Exercises (pages 311–314)



  1. 64 2. 3. 4. 18 5. 6. 7. 8. 9. 0














































22.In , the base is and the expression simplifies to 1. In ,

the base is 6 and the expression simplifies to 23.yes 24.No.

for all a,. For example, let and. Then

, while ;

. 25. 26.
27.1.38 10 -^1 28.3.0406 108 ;9.2 104 ; 1 102


121 Z 43 1.345*^104 7.65*^10 -^8

1 ab 2 -^1 = 13 # 42 -^1 = 12 -^1 = 121 ab-^1 = 3 # 4 -^1 = 3 # 41 = 43


1 ab 2 -^1 Zab-^1 bZ 0 a= 3 b= 4









1 - 620 - 6 - 60

10 p^8

q^7


  • 2 n
    m^5

  • 12 x^2 y^8
    2025
    8 r^4


1

96 m^7

25

z^4

r^17

9

25

m^18

1

z^15

y^6

x^2

x^8

1

38

3

4

1

30

16

25

81


  • (^12516)
    1
    81
    8 p^2 + 4 p 712 x- 3 z 2
    0 -^354728 y- 40
    x- 3
    2 x
    , xZ 0


-^54
x^2 - 9
2 x
2 x-3;- 1 4 x^2 + 6 x+9;^32 , xZ 0


x-r, P 1 r 2. r=-1. 5 x-1; 0


  • 13;-13; P 1 x 2


2 p+ 7

3

4

a- 2 +

1

4 a+ 3

2

3

p^2 +p+ 1 x- 1

3

2 a-^10 +

77

p 2 a+ 6

(^2) +^5
2 p+^2 +



  • 1
    2 p+ 2


x^2 - 4 x+ 2 +

9 x- 4

x^2 + 3

2 k^2 + 3 k- 1 2 y^2 + 2

3 x^2 + 6 x+ 11 +

26

x- 2

x^2 +x+ 3 2 x^2 - x- 5

2 x- 5 +


  • 4 x+ 5
    3 x^2 - 2 x+ 4
    x^2 + 2 x- 3 +
    6
    4 x+ 1
    z^2 + 3


p- 4 + m^2 + 2 m- 1 m^2 +m+ 3

44

p+ 6

r^2 - 7 r+ 6 y- 4 q+ 8 t+ 5

2 y

x

+

3

4

+

3 w

x

2

7 n


  • 3
    2 m



  • 9
    7 mn
    3 +
    5
    m


  • 6
    m^2




3 y+ 4 -

5

y

3 x^3 - 2 x^2 + 1


  • 8 a^2 +a+ 4

  • 4 b^6
    3 a^2

  • 20 2 x^2 - 6 x^3541859642 p^4


10 x^2 - 2 x 2 x^2 - x- 3 8 x^3 - 27 2 x^3 - 18 x

1 a+b 22 =a^2 + 2 ab+b^2.

a^2 + 2 ab+b^21 a+b 22

Area:

a^2

Area:

b^2

Area:

ab

Area:

ab

ab

a

b

1 a-b 22 =a^2 - 2 ab+b^2

a^2 - 12 ab- 2 b^22 - b^2 =a^2 - 2 ab+b^2

1 a-b 2 b ab-b^2 ; 2 ab- 2 b^2 b^2 a^2 ;a

15 x^2 - 2 x- 24 a-b a=s^2 ; 1 a-b 22

A-12 Answers to Selected Exercises


57.

domain:

range: 1 - q, 0 4

1 - q,q 2 ;

x

y

–3

–2 2

0

f(x) = –3x^2

59.

domain:

range: 1 - q,q 2

1 - q,q 2 ;

x

y

–2 02

f(x) = x^3 + 1













Section 5.4 (pages 299–301)


1.C 3.D 5. 7. 9.















































  7. 41.The product of two binomials is the
    sum of the product of the first terms, the product of the outer terms,


the product of the inner terms, and the product of the last terms.






































63.Write 101 as and 99 as Then




















































97.49; 25; 49Z 25 99.2401; 337; 2401Z 337 101. 29 x^2 - 2 y^2


m^4 - 4 m^2 p^2 + 4 mp^3 - p^4 a^4 b- 7 a^2 b^3 - 6 ab^4

6 a^3 + 7 a^2 b+ 4 ab^2 +b^34 z^4 - 17 z^3 x+ 12 z^2 x^2 - 6 zx^3 +x^4

125 r^3 - 75 r^2 s+ 15 rs^2 - s^3 q^4 - 8 q^3 + 24 q^2 - 32 q+ 16

4 h^2 - 4 hk+k^2 - j^2 y^3 + 6 y^2 + 12 y+ 8

4 a^2 + 4 ab+b^2 - 12 a- 6 b+ 9 4 a^2 + 4 ab+b^2 - 9

25 x^2 + 10 x+ 1 + 60 xy+ 12 y+ 36 y^2

k^2 -^107 kp+ 4925 p^2 0.04x^2 - 0.56xy+1.96y^2

0.1x^2 +0.63x-0.13 3 w^2 -^234 wz- 21 z^216 x^2 - 94

1100 + 121100 - 12 = 1002 - 12 =10,000- 1 =9999.


100 + 1 100 - 1. 101 # 99 =


x^2 + 2 x+ 1 4 p^2 + 28 p+ 49 16 n^2 - 24 nm+ 9 m^2

16 m^2 - 49 n^475 y^7 - 12 y y^2 - 10 y+ 25

x^2 - 81 4 p^2 - 9 25 m^2 - 1 9 a^2 - 4 c^2

12 c^2 + 16 cd- 3 d^2

m^2 - 3 m- 40 12 k^2 +k- 6 3 z^2 +zw- 4 w^2

8 z^4 - 14 z^3 + 17 z^2 + 20 z- 3 6 p^4 +p^3 + 4 p^2 - 27 p- 6


  • 2 b^3 + 2 b^2 + 18 b+ 12 25 m^2 - 9 n^2


4 x^5 - 4 x^4 - 24 x^36 y^2 +y- 12

m^3 - 3 m^2 - 40 m 24 z^3 - 20 z^2 - 16 z


  • 2 q^3 - 3 q^418 k^4 + 12 k^3 + 6 k^26 t^3 +t^2 - 14 t- 3

    • 24 m^5 - 28 x^7 y^4 - 6 x^2 + 15 x




12 m^5 - 6 a^3 b^960 x^3 y^4
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