intermediate algebra name () 7 - math tv · 2010-08-20 · title: microsoft word -...

Intermediate Algebra Problem Set 2.2 Solutions to Every Odd-Numbered Problem

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2.2 Formulas 1. Substituting x = 0: 3. Substituting x = 4:

3 0( ) ! 4y = 12

!4y = 12

y = !3

3 4( ) ! 4y = 12

12 ! 4y = 12

!4y = 0

y = 0

5. Substituting y = 0: 7. Substituting y = 5:

2x ! 3 = 0

2x = 3

x =3

2

2x ! 3 = 5

2x = 8

x = 4

9. Substituting y = !6

5: 11. Substituting x = 160 and y = 0:

x ! 2 !6

5

"#$

%&'= 4

x +12

5= 4

x =8

5

0 = a 160 ! 80( )2+ 70

!70 = a 80( )2

6,400a = !70

a = !70

6,400== !

7

640

13. Substituting p = 1.5: R = 900 ! 300 •1.5( ) 1.5( ) = 450( ) 1.5( ) = 675

15. a. Substituting x = 100: P = !0.1 100( )2+ 27 100( ) +1,700 = !1,000 + 2,700 +1,700 = 3,400

b. Substituting x = 170: P = !0.1 170( )2+ 27 170( ) !1,700 = !2,890 + 4,590 +1,700 = 3,400

17. a. Substituting t = 14

: h = 16 + 32 1

4

!"#

$%&'16

1

4

!"#

$%&2

= 16 + 8 '1 = 23

b. Substituting t = 74

: h = 16 + 32 7

4

!"#

$%&'16

7

4

!"#

$%&2

= 16 + 56 ' 49 = 23

19. Substituting d = 30, r = 12, and t = 3: 21. Substituting x = 5 and y = 15:

30 = 12 ! c( ) • 310 = 12 ! c

c = 2

15 = K 5( )K = 3


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23. Substituting P = 48 and V = 50: 25. Substituting x = 2:

50 =K

48K = 50 • 48 = 2,400

5 2( ) ! 3y = !15

10 ! 3y = !15

!3y = !25

y =25

3

27. Substituting x = !1

5: 29. Solving for r:

5 !1

5

"#$

%&'! 3y = !15

!1! 3y = !15!3y = !14

y =14

3

d = rt

r =d

t

31. Solving for t: 33. Solving for l:

d = r + c( )t

t =d

r + c

A = lw

l =A

w

35. Solving for t: 37. Solving for T:

I = prt

t =I

pr

PV = nRT

T =PV

nR

39. Solving for x: 41. Solving for F:

y = mx + b

y ! b = mx

x =y ! b

m

C =5

9(F ! 32)

9

5C = F ! 32

F =9

5C + 32

43. Solving for v: 45. Solving for d:

h = vt +16t

2

h !16t2= vt

v =h !16t

2

t

A = a + n !1( )d

A ! a = n !1( )d

d =A ! a

n !1


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47. Solving for y: 49. Solving for y:

2x + 3y = 6

3y = !2x + 6

y =!2x + 6

3

y = !2

3x + 2

!3x + 5y = 15

5y = 3x +15

y =3x +15

5

y =3

5x + 3

51. Solving for y: 53. Solving for x:

2x ! 6y +12 = 0

!6y = !2x !12

y =!2x !12

!6

y =1

3x + 2

ax + 4 = bx + 9

ax ! bx + 4 = 9

ax ! bx = 5

x a ! b( ) = 5

x =5

a ! b

55. Solving for h: 57. Solving for x:

S = !r

2+ 2!rh

S " !r2= 2!rh

h =S " !r

2

2!r

!3x + 4y = 12

!3x = !4y +12

x =!4y +12

!3

x =4

3y ! 4

59. Solving for x: 61. Solving for y:

ax + 3 = cx ! 7

ax ! cx + 3 = !7

ax ! cx = !10

x a ! c( ) = !10

x =!10

a ! c=10

c ! a

x = 2y ! 3

2y = x + 3

y =x + 3

2=1

2x +

3

2


y ! 3 = !2 x + 4( )y ! 3 = !2x ! 8

y = !2x ! 5

y ! 3 = !2

3x + 3( )

y ! 3 = !2

3x ! 2

y = !2

3x +1


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67. Solving for y:

y ! 4 = !1

2x +1( )

y ! 4 = !1

2x !

1

2

y = !1

2x +

7

2

69. a. Solving for y: b. Solving for y:

y +1

x ! 0= 4

y +1 = 4 x ! 0( )y +1 = 4 x

y = 4 x !1

y + 2

x ! 4= !

1

2

y + 2 = !1

2x ! 4( )

y + 2 = !1

2x + 2

y = !1

2x

c. Solving for y:

y + 3

x ! 7= 0

y + 3 = 0 x ! 7( )y + 3 = 0

y = !3


x

8+y

2= 1

8x

8+y

2

!"#

$%&= 8 1( )

x + 4y = 8

4y = 'x + 8

y = '1

4x + 2

x

5+y

!3= 1

15x

5+y

!3"#$

%&'= 15 1( )

3x ! 5y = 15!5y = !3x +15

y =3

5x ! 3


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75. a. Solving the equation:

!4 x + 5 = 20

!4 x = 15

x = !15

4= !3.75

b. Substituting x = 3: !4 x + 5 = !4 3( ) + 5 = !7 c. Solving for y: d. Solving for x:

!4 x + 5y = 20

5y = 4 x + 20

y =4

5x + 4

!4 x + 5y = 20

!4 x = !5y + 20

x =5

4y ! 5

77. Substituting A = 30, P = 30, and N = 4: W =APN

2000=

30( ) 30( )4

2000=

9

5= 1.8 tons

79. Substituting h = 192:

192 = 96 + 80t !16t2

0 = !16t2+ 80t ! 96

0 = !16 t2! 5t + 6( )

0 = !16 t ! 2( ) t ! 3( )

t = 2,3

The bullet will be 192 feet in the air after 2 sec and 3 sec. 81. Let c represent the rate of the current. The equation is:

2 15 ! c( ) = 1830 ! 2c = 18

!2c = !12

c = 6

The speed of the current is 6 mph. 83. Let w represent the rate of the wind. The equation is:

4 258 ! w( ) = 8641032 ! 4w = 864

!4w = !168

w = 42

The speed of the wind is 42 mph. 85. The distance traveled by the rider is the circumference: C = ! 65( ) " 3.14( ) 65( ) " 204.1 feet

Finding the rate: 204.1 feet

30 seconds! 6.8 feet per second


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87. Substituting R = $7,000:

R = xp

7000 = 1700 !100p( ) p

7000 = 1700p !100p2

0 = !100p2+1700p ! 7000

0 = !100 p2!17p + 70( )

0 = !100 p ! 7( ) p !10( )

p = 7,10

The calculators should be sold for either $7 or $10.

89. Substituting the values: S =480 • 216 • 30 •150

35000=13,330 kilobytes

91. Substituting n = 1, y = 7, and z = 15:

x1 + 71 = 151

x + 7 = 15

x = 8

93. For Shar, M = 220 – 46 = 174 and R = 60: T = R + 0.6 M ! R( ) = 60 + 0.6 174 ! 60( ) = 128.4 beats per minute For Sara, M = 220 – 26 = 194 and R = 60: T = R + 0.6 M ! R( ) = 60 + 0.6 194 ! 60( ) = 140.4 beats per minute 95. Translating into symbols: 2x ! 3 97. Translating into symbols: x + y = 180 99. Solving the equation: 101. Solving the equation:

x + 2x = 90

3x = 90

x = 30

2 2x ! 3( ) + 2x = 454 x ! 6 + 2x = 45

6x ! 6 = 45

6x = 51

x =51

6= 8.5

103. Solving the equation:

6x + 5 10,000 ! x( ) = 56,0006x + 50,000 ! 5x = 56,000

x + 50,000 = 56,000

x = 6,000

intermediate algebra name () 7 - math tv · 2010-08-20 · title: microsoft word -...

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