Intermediate Algebra (11th edition)

49. 
    
    
    
    51. 
        
        
        
        53. 
            
        
        
        
        
    
    
    
    


50. 
    
    
    
    57. 
        
        
        
        59. 4 61. , or
        
        
        
        
    
    
    
    


51. , or 65. 67. 69.


52. 
    
    
    
    73. 
        
        
        
        75. 
            
            
            
            77. 
                
            
            
            
            
        
        
        
        
    
    
    
    


53. 
    
    
    
    81. 
        
    
    
    
    


54. 
    
    
    
    85. 
        
    
    
    
    


55. 
    
    
    
    89. 
        
    
    
    
    


56. (a) (b)approximately 3.23 thousand dollars


57. 
    
    
    
    95. 
        
    
    
    
    

Section 7.3 (pages 384–386)

1. 
   
   
   
   3. 
      
      
      
      5. 
         
         
         
         7. 
            
            
            
            9. 
               
               
               
               11. 
                   
               
               
               
               
            
            
            
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   15. 
       
       
       
       17. 
           
           
           
           19. 
               
               
               
               21. 23.xy
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


3. 
   
   
   
   27. 
       
       
       
       29. 
           
           
           
           30. 
               
           
           
           
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   32. 
       
       
       
       33. 
           
       
       
       
       
   
   
   
   

34.Answers will vary. 35. 37. , or

39. 
    
    
    
    41. (a) (b)In the denominator,
    
    
    
    

not and not (c) 43.

45. 47.0;

Connections ( page 391) 1. 2.

Section 7.4 (pages 391–394)

1. (a) 0 (b) 3. (a) (b)


2. (a) (b) 7. (a)

(b) 9. (a) (b)

11. (a)4, (b) 13.No, there is no possibility that the
    proposed solution will be rejected, because there are no variables in the

denominators in the original equation. 15. 17.

19. 
    
    
    
    21. 
        
        
        
        23. 
            
            
            
            25. 
                
                
                
                27. 
                    
                    
                    
                    29. 
                        
                    
                    
                    
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


20. 
    
    
    
    33. 
        
        
        
        35. 
            
            
            
            37. 
                
                
                
                39. 
                    
                    
                    
                    41. 
                        
                    
                    
                    
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


21. 
    
    
    
    45. 
        
        
        
        47. 
            
        
        
        
        
    
    
    
    


22. ; 51. ; 53.

x

y

0

2

2

f(x) =x – 2^1

–3

x

y

0

3

3

–3 g(x) = –^1 x

x

y

02

2

f(x) =^2 x

x= 0 y= 0 x= 0 y= 0 x=2;y= 0

5 - 16 5136 5 x|xZ 36

556 0 E 5627 F 5 - 3,- 16 0 5 - 106

5 - 7, 3 (^6) E- 127 F 0 5 - 36 506 0
516 5 - 6, 4 6
27 Ex|xZ4,^72 F
5 x|xZ0, 1, -3, 2 6 -^74 , 0,^136 Ex|xZ- 47 , 0,^136 F

• 4, 4 5 x|xZ 46 0, 1, -3, 2

5 x|xZ 06 - 1, 2 5 x|xZ-1, 2 6

5 - 16 5 0.5 6

5166 5 x|xZ 06

5 - 126

3 - 4 m+ 8 p

2 p- 3 m

1

3 p

3 p-^1 =^3.

p

(^1) ,
2 m
,
2 m-^1 =
2
m
,
3
mp-
4
p+
8
m
2
m-
3
p
1
2 xy
y^2 +x^2
xy 1 y+x 2
y^2 +x^2
xy^2 +x^2 y
x^2 y^2
y^2 +x^2
m^2 + 6 m- 4
m^2 - m- 2
m 1 m- 12
m^2 + 6 m- 4
m^2 - m- 2
m^2 - m- 2
m 1 m- 12
m^2 + 6 m- 4
m 1 m- 12
x^2 + 5 x+ 4
x^2 + 5 x+ 10
3 y
2
a+b
ab
y+ 4
2
4 x x+ 4 y
y+x
y-x
6 x+ 1
7 x- 3
5 x^2
9 z^3
21 k+ 12
3 k- 1
2 x
x- 1
7
17
4
15
9
5
1
6
c 1 x 2 =
10 x
491101 - x 2
10 x+ 23
1 x+ 2221 x+ 32
3 r- 2 s
12 r-s 213 r-s 2
2 x^2 + 21 xy- 10 y^2
1 x+ 2 y 21 x-y 21 x+ 6 y 2
2 x 1 x+ 12 y 2
1 x+ 2 y 21 x-y 21 x+ 6 y 2
x
1 x- 2221 x- 32
4 p^2 - 21 p+ 29
1 p- 222
2 x+ 1
x
4 x- 7
x^2 - x+ 1
3 x- 2
x- 1
6
x- 2
7
y
212 x- 12
x- 1

• 2
  1 x+ 121 x- 12


• w-z
  z-w

w+z

w-z

• 3
  4 - x

3

x- 4

5 a 3

(^2) - 7 a
1 a+ 121 a- 32
1
x 1 x- 12
a^2 b^5 - 2 ab^6 + 3
a^5 b^7
4 pr+ 3 sq^3
14 p^4 q^4

55. (a) (b) (c) (d)The waiting time also increases.


56. (a)500 ft (b)It decreases. 59.four 61.


57. 
    

Summary Exercises on Rational Expressions and

Equations (page 395)

1.equation; 2.expression; 3.expression;

4.expression; 5.equation; 6.equation;

7.expression; 8.equation; 9.expression; ,

or 10.expression; 11.expression;

12.expression; 13.expression;

14.equation; 15.expression; 16.expression;

17.expression; 18.equation; 19.expression;

20.equation; 21.expression;

22.equation; 23.equation; 24.expression;

25.expression; , or 26.expression;

27.equation; 28.expression;

29.equation; 30.expression;

Section 7.5 (pages 402–406)

1.A 3.D 5. 24 7. 9. 11.

13. 
    
    
    
    15. , or 17. ,
    
    
    
    

or 19. 21.Multiply each side by

23.21 girls, 7 boys 25. job per hr 27.1.75 in. 29.5.4 in.

31.7.6 in. 33.56 teachers 35.210 deer 37.25,000 fish

39.6.6 more gallons 41. 43.2.4 mL

45.3 mph 47.1020 mi 49.1750 mi 51.190 mi 53. min

55.30 hr 57. 59.20 hr 61. hr 63. 65. 3

Section 7.6 (pages 412–415)

1.direct 3.direct 5.inverse 7.inverse 9.inverse 11.direct

13.joint 15.combined 17.increases; decreases 19.The perimeter

of a square varies directly as the length of its side. 21.The surface

area of a sphere varies directly as the square of its radius.

23.The area of a triangle varies jointly as the length of its base and

height. 25.4; 2; ; ; ; 27. 36 29. 31.0.625 33.

35. 37.$2.919, or 39.8 lb 41.about
    43.256 ft 45. 47.100 cycles per sec 49. foot-
    candles 51.$420 53.about 11.8 lb 55.about 448.1 lb

10623 mph (^2113)
22229 $2.91 109 450 cm^3
16
5
16
9
1
3 p
1
2
4
4 p 3 p
1
(^23)
4
(^25)
1
3 hr
(^623)
x= 27 ;AC=8;DF= 12
1
3
r= a-b.
eR
E-e
b=
2 a-hB
h
b=
2 a
h
r= -B
IR-nE

• In
  r=
  nE-IR
  In
  v=
  PVt
  pT

a=

bc

c+b

G=

Fd^2

Mm

25

4

k 12 k^2 - 2 k+ 52

1 k- 1213 k^2 - 22

0

13 x+ 28

2 x 1 x+ 421 x- 42

5 - 106

t- 2

8

1

3 - x

• 1
  x- 3

2 z- 3

2 z+ 3

E^54 F^0

3 y+ 2

y+ 3

5 - 136

• x
  3 x+ 5 y

526

2 x+ 10

x 1 x- 221 x+ 22

5

3 z

b+ 3

3

506

• 365

24 p

p+ 2

x^2 +xy+ 2 y^2

1 x+y 21 x-y 2

25

41 r+ 22

5 x- 1

• 21 x- 12

5 x- 1

(^516) - 2 x+ 2
43
24 x
E^12 F 576
y+x
y-x

• 22
  7 x

21 x+ 52

5

5206

c=P-a-b

t=

d

r

0 1.6 4.1

A-16 Answers to Selected Exercises