Add. Simplify the result, if possible.
64)
x2– 6x
x – 4 +8
x – 4
64)
A)
x + 2
B)
x – 2
C)
x2– 6x + 8
x – 4
D)
x – 4
Divide.
65)
(25x3+ 25x2+ 26x + 8) ÷ (–5x – 2)
65)
A)
x2– 3x – 4
B)
x2+ 3x + 4
C)
–5x2– 3x – 4
D)
–5x2– 4
C
Solve the problem.
66)
A cyclist bikes at a constant speed for 16 miles. He then returns home at the same speed but takes a
different route. His return trip takes one hour longer and is 21 miles. Find his speed.
66)
A)
6 mph
B)
5 mph
C)
4 mph
D)
7 mph
B
Divide as indicated.
67)
x2–7x + xy –7y
10x2–10y2÷x –7
3x –3y
67)
A)
3(x2–7x + xy –7y)
10(x + y)(x –7)
B)
1
C)
3
10
D)
(x –7)2
30(x – y)2
C
B
Use synthetic division and the Remainder Theorem to find the indicated function value.
68)
f(x) =x4– 5x3– 4x2+ 2x + 5; f –1
3
68)
A)
–331
81
B)
331
81
C)
110
27
D)
–331
243
The rational function f(x) =120x
100 – x models the cost, f(x), in millions of dollars, to remove x% of the trash from American
highways. The graph is shown. Use the equation to solve the problem.
69)
What value of x must be excluded from the rational function‘s domain?
69)
A)
100
B)
1
C)
1000
D)
10
Solve the equation for the specified variable.
70)
PV
T=pv
t for V
70)
A)
V =tvT
pP
B)
V =pvT
tP
C)
V =pv
tTP
D)
V =pvP
tT
If y varies inversely as x, find the inverse variation equation for the situation.
71)
y =9 when x =7
71)
A)
y =1
63x
B)
y =x
63
C)
y =9
7x
D)
y =63
x
Solve the problem.
72)
A drug is injected into a patient and the concentration of the drug is monitored. The drug’s
concentration, C(t), in milligrams after t hours is modeled by C(t) =5t
3t2+1. Estimate the drug’s
concentration after 4 hours. (Round to the nearest hundredth.)
72)
A)
1.60 mg
B)
0.47 mg
C)
0.41 mg
D)
1.54 mg
73)
A company that produces scooters has costs given by the function C(x) =25x + 30,000, where x is
the number of scooters manufactured and C(x) is measured in dollars. The average cost to
manufacture each scooter is given by C(x) =25x + 30,000
x. Find C(50). (Round to the nearest dollar,
if necessary.)
73)
A)
$88
B)
$595
C)
$625
D)
$85
Multiply as indicated.
74)
8x4·x2y
96x3y2
74)
A)
x6y
12x3y2
B)
x5
12y
C)
1
96xy
D)
x3
12y
Write an equation to describe the variation. Use k for the constant of proportionality.
75)
s varies directly as t and inversely as the square of u.
75)
A)
s+t–u2= k
B)
s=ku2
C)
stu2= k
D)
s=kt
Divide.
76)
(–20x8+ 35x6) ÷(–5x4)
76)
A)
–3x10
B)
4x4+ 35x6
C)
–20x8– 7x2
D)
4x4– 7x2
D
Find the least common denominator of the rational expressions.
77)
x – 5
x2+ 5x – 6 and x + 5
x2– 5x + 4
77)
A)
(x – 1)(x – 4)
B)
(x + 6)(x – 1)(x – 4)
C)
(x + 6)(x – 1)
D)
(x – 6)(x + 1)(x – 4)
B
Multiply as indicated.
78)
x2+ 10x + 24
x2+ 13x + 36
·x2+ 9x
x2+ 4x– 12
78)
A)
x
x – 2
B)
x2+ 9x
x – 2
C)
1
x – 2
D)
x
x2+ 13x + 36
A
24
D
Solve the problem.
79)
A taxi company charges riders a fixed charge of $2.50 plus $1.70 per mile. How many miles must a
rider go to have an average cost per mile of $1.90?
79)
A)
21 miles
B)
12.5 miles
C)
8.5 miles
D)
14.7 miles
Find the least common denominator of the rational expressions.
80)
6
x and –4
x – 5
80)
A)
–5
B)
5
C)
x – 5
D)
x(x – 5)
Divide.
81)
(–12x9+ 42x8– 12x6– 18x4) ÷(–6x6)
81)
A)
2x3– 7x2+ 2 +3
x2
B)
–2x3+ 7x2– 2 –3
x2
C)
2x3– 7x2+ 2
D)
2x3– 4x2+ 2
Use synthetic division to divide.
82)
(x2– 64) ÷ (x – 8)
82)
A)
8x + 8
B)
64x + 8
C)
x + 64
D)
x + 8
Divide as indicated.
83)
5x – 5
x÷8x – 8
4x2
83)
A)
5x
2
B)
20x3– 20x2
8x2– 8x
C)
40x2+ 80x + 40
4x3
D)
2
5x
Solve the problem.
84)
Suppose a cost–benefit model is given by y =5.1x
100 – x , where y is the cost in thousands of dollars for
removing x percent of a given pollutant. Find the cost for removing 60% of the pollutant.
84)
A)
$7.7 thousands
B)
$9.2 thousands
C)
$76.5 thousands
D)
$1.9 thousands
Add. Simplify the result, if possible.
85)
8x + 5
x2– 5x – 6
+
–4– 7x
x2– 5x – 6
85)
A)
1
x + 1
B)
x – 1
x2– 5x – 6
C)
1
x – 6
D)
1
x2– 5x – 6
Use synthetic division and the Remainder Theorem to find the indicated function value.
86)
f(x) =6x4 + 12x3+ 6x2– 5x + 19; f(3)
86)
A)
1632
B)
868
C)
104
D)
2272
26
Solve the rational equation.
87)
1 +1
x=20
x2
87)
A)
–1
5, 1
4
B)
{–5, 4}
C)
{5, 4}
D)
{5, –4}
Find the domain of the rational function.
88)
f(x) =2
x – 5
88)
A)
domain of f: ( , –5) (–5, )
B)
domain of f: ( , 0) (0, )
C)
domain of f: ( , 5) (5, )
D)
domain of f: ( , )
Divide.
89)
(x2+ 11x + 10) ÷ (x + 10)
89)
A)
x2+ 11
B)
x + 11
C)
x2+ 1
D)
x + 1
Find the least common denominator of the rational expressions.
90)
–36
x2– 12x + 36 and 3x + 18
–3x + 18
90)
A)
–3(x + 6)(x + 6)
B)
–3(x + 6)(x – 6)
C)
–3(x – 6)(x + 6)
D)
–3(x – 6)(x – 6)
Use the graph or table to determine a solution of the equation. Use synthetic division to verify that this number is a
solution of the equation. Then solve the polynomial equation.
91)
x3+ 6x2+ 11x + 6 = 0
6
–1 3
–6
[–1, 3, 1] by [–6, 6, 1]
91)
A)
6; The remainder is zero; {–1, 6}
B)
–1; The remainder is zero; {–3, –1}
C)
–1; The remainder is zero; {–3, –2, –1}
D)
6; The remainder is zero; {–3, –2, –1, 6}
Divide.
92)
–64x8+ 56x7+ 24x5– 24x3
–8x5
92)
A)
8x3– 7x2– 3
B)
–8x3+ 7x2+ 3 –3
x2
C)
8x3– 7x2– 3 +3
x2
D)
8x3– 4x2– 3
Solve the problem.
93)
Write the average of 5
x3 and 4
x as a simplified rational expression. (Hint: To find the average of two
numbers, find their sum and divide by 2.)
93)
A)
5+4x2
2x3
B)
9
2x3+ 2x
C)
5+4x3
2x4
D)
10 +8x2
x3
Divide as indicated.
94)
30x –30
3÷10x –10
21
94)
A)
300(x – 1)2
63
B)
21
C)
1
21
D)
7(30x –30)
10x –10
Simplify the rational expression. If the rational expression cannot be simplified, so state.
95)
8x2+24x3
5x +15x2
95)
A)
8
5
B)
8x
5
C)
8+24x3
5x +15
D)
Cannot be simplified
Solve the problem.
96)
In calculus, the sum of an infinite geometric series whose first term is 1
3 is given by the complex
fraction
1
3
1 – r , where r is the common ratio between the terms. Simplify this expression.
96)
A)
1
3–3r
B)
1
3– r
C)
3
1 –3r
D)
3
3– r
Solve the equation for the specified variable.
97)
The gas law: PV
T=pv
t for P
97)
A)
P =pvT
tV
B)
P =tvT
pV
C)
P =pvV
tT
D)
P =pv
tTV
Solve the problem.
98)
One pump can drain a pool in 6 minutes. When a second pump is also used, the pool only takes 4
minutes to drain. How long would it take the second pump to drain the pool if it were the only
pump in use?
98)
A)
12 minutes
B)
22 minutes
C)
22
5 minutes
D)
1
12 minute
Solve.
99)
The power that a resistor must dissipate is jointly proportional to the square of the current flowing
through the resistor and the resistance of the resistor. If a resistor needs to dissipate 150 watts of
power when 5 amperes of current is flowing through the resistor whose resistance is 6 ohms, find
the power that a resistor needs to dissipate when 8 amperes of current are flowing through a
resistor whose resistance is 9 ohms.
99)
A)
360 watts
B)
72 watts
C)
576 watts
D)
648 watts
Write an equation to describe the variation. Use k for the constant of proportionality.
100)
w varies jointly as x and the square of y.
100)
A)
w= kxy2
B)
w+x+y2= k
C)
wxy2= k
D)
w= k +x+y2
Solve.
101)
The amount of water used to take a shower is directly proportional to the amount of time that the
shower is in use. A shower lasting 17 minutes requires 11.9 gallons of water. Find the amount of
water used in a shower lasting 8 minutes.
101)
A)
5.6 gallons
B)
6.3 gallons
C)
136 gallons
D)
4.9 gallons
Find the variation equation for the variation statement.
102)
z varies jointly as y and the cube of x; z =512 when x =4 and y = – 2
102)
A)
y =4xy3
B)
y = – 4xy3
C)
y =4x3y
D)
y = – 4x3y
Write an equation to describe the variation. Use k for the constant of proportionality.
103)
P varies jointly as the square of R and the square of S.
103)
A)
P= kR2S2
B)
P= k +R2+S2
C)
PR2S2= k
D)
P+R2+S2= k
Solve.
104)
The amount of gas that a helicopter uses is directly proportional to the number of hours spent
flying. The helicopter flies for 4 hours and uses 40 gallons of fuel. Find the number of gallons of
fuel that the helicopter uses to fly for 5 hours.
104)
A)
20 gallons
B)
55 gallons
C)
60 gallons
D)
50 gallons
The graph of a rational function, f, is shown in the figure. Use the graph to answer the question.
105)
Find f(8).
105)
A)
–8
B)
–10.8
C)
3
D)
8
Find the function value.
106)
f(x) =x + 3
3x – 4 ; f(4)
106)
A)
–7
8
B)
7
16
C)
7
8
D)
7
5
If y varies inversely as x, find the inverse variation equation for the situation.
107)
y =1
7 when x =42
107)
A)
y =1
294x
B)
y =1
6x
C)
y =6
x
D)
y =x
6
Solve the problem.
108)
A company has monthly fixed costs of $11,000 for its facilities and it costs $90 per unit for each unit
that it produces. How many units must the company produce to have an average cost per unit of
$140?
108)
A)
220 units
B)
122 units
C)
180 units
D)
222 units
Add. Simplify the result, if possible.
109)
5
15x+6
15x
109)
A)
11
30x
B)
11
15x
C)
1
D)
15x
11
Solve the equation for the specified variable.
110)
P =Fd
t for t
110)
A)
t = P – Fd
B)
t =P
Fd
C)
t =Fd
P
D)
t = Fd – P
Divide.
111)
15x9– 50x6
5x3
111)
A)
3x6– 10x3
B)
–7x12
C)
3x6– 50x6
D)
15x9– 10x3
If y varies inversely as x, find the inverse variation equation for the situation.
112)
y =100 when x =7
112)
A)
y =100
7x
B)
y =x
700
C)
y =1
700x
D)
y =700
x
Solve the problem.
113)
A painter can finish painting a house in 8 hours. Her assistant takes 10 hours to finish the same job.
How long would it take for them to complete the job if they were working together?
113)
A)
7 hours
B)
44
9 hours
C)
9
40 hours
D)
9 hours
Solve the rational equation.
114)
x
2x + 2 =
–2x
4x + 4 +2x – 3
x + 1
114)
A)
{–3}
B)
–12
5
C)
3
2
D)
{3}
Perform the indicated operations. Simplify the result, if possible.
115)
3
x2–7
x
115)
A)
3+ 7x
x2
B)
7x – 3
x
C)
3x + 7
x2
D)
3– 7x
x2
Solve the rational equation.
116)
7
y + 5 –9
y – 5 =10
y2– 25
116)
A)
{78}
B)
{45}
C)
{90}
D)
{–45}
Solve.
117)
If the force acting on an object stays the same, then the acceleration of the object is inversely
proportional to its mass. If an object with a mass of 35 kilograms accelerates at a rate of 6 meters
per second per second by a force, find the rate of acceleration of an object with a mass of
5 kilograms that is pulled by the same force.
117)
A)
6
7 meters per second per second
B)
36 meters per second per second
C)
35 meters per second per second
D)
42 meters per second per second
Simplify the rational expression. If the rational expression cannot be simplified, so state.
118)
y2+ 12y + 36
y2+ 15y + 54
118)
A)
12y + 36
15y + 54
B)
12y + 2
15y + 3
C)
Cannot be simplified
D)
y + 6
y + 9
Simplify the rational expression.
119)
x
16 –1
x
1 +4
x
119)
A)
x –4
16
B)
16
x –4
C)
x +4
16
D)
16
x +4
Find the least common denominator of the rational expressions.
120)
1
30x, 1
6x2, and 1
5x3
120)
A)
30x5
B)
30x2
C)
30x3
D)
5x3
The graph of a rational function, f, is shown in the figure. Use the graph to answer the question.
121)
What is the domain of f?
121)
A)
domain of f: ( , –4)
(–4, )
B)
domain of f: ( , 4) (4, )
C)
domain of f: ( , –4)
(–4, 4)
(4, )
D)
domain of f: ( , –6)
(–6, )
Multiply as indicated.
122)
2x – 2
x·8x2
3x – 3
122)
A)
16x
3
B)
3
16x
C)
6x2+ 12x + 6
8x3
D)
16x3– 16x2
3x2– 3x
Use synthetic division to divide.
123)
(x2– 13x + 40) ÷ (x – 8)
123)
A)
x – 5
B)
x – 8
C)
x + 5
D)
x + 40
Find the domain of the rational function.
124)
f(x) =x2– 16
x2+ 5x + 6
124)
A)
domain of f: ( , 0) (0, )
B)
domain of f: ( , 2) (2, 3)
(3, )
C)
domain of f: ( , –3) (–3, –2) (–2, )
D)
domain of f: ( , –4) (–4, 4) (4, )
Solve.
125)
The amount of simple interest earned on an investment over a fixed amount of time is jointly
proportional to the principle invested and the interest rate. A principle investment of $1900.00 with
an interest rate of 4% earned $304.00 in simple interest. Find the amount of simple interest earned if
the principle is $2100.00 and the interest rate is 1%.
125)
A)
$76.00
B)
$8400.00
C)
$84.00
D)
$336.00
126)
The amount of time it takes a swimmer to swim a race is inversely proportional to the average
speed of the swimmer. A swimmer finishes a race in 37.5 seconds with an average speed of 4 feet
per second. Find the average speed of the swimmer if it takes 25 seconds to finish the race.
126)
A)
7 feet per second
B)
8 feet per second
C)
5 feet per second
D)
6 feet per second
Provide an appropriate response.
127)
Find the domain of f(x) =x2–7x
x2+ 2x – 63 . Then simplify the right side of the function’s equation.
127)
A)
domain of f: ( , –7) (–7, 9) (9, ); x
x +9
B)
domain of f: ( , 0) (0, ); 0
C)
domain of f: ( , –9) (–9, 7) (7, ); x
x +9
D)
domain of f: ( , –6) (–6, 6) (6, ); x
x +6
If y varies directly as x, find the direct variation equation for the situation.
128)
y =3 when x =1
4
128)
A)
y =1
12 x
B)
y = x +11
4
C)
y =1
3x
D)
y =12x
Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve
the polynomial equation.
129)
3x3– 7x2– 22x + 8 = 0; 4
129)
A)
The remainder is zero; –2
3, 1, 4
B)
The remainder is zero; 1
3, 2, 4
C)
The remainder is zero; 1
3, –2, 4
D)
The remainder is zero; –1
3, –2, 4
Find the domain of the rational function.
130)
f(x) =4
x + 5
130)
A)
domain of f: ( , 5) (5, )
B)
domain of f: ( , )
C)
domain of f: ( , 0) (0, )
D)
domain of f: ( , –5) (–5, )
Solve the problem.
131)
If the formula for the area of a triangle, A =1
2bh, is solved for h, then h =2A
b. Use this formula to
find h if area A is 2y + 1
4 square feet and base b is 3y – 5
11 feet. Write h in simplified form.
131)
A)
11(2y + 1)
4(3y – 5) ft
B)
(2y + 1)(3y – 5)
22 ft
C)
11(2y + 1)
2(3y – 5) ft
D)
2(3y – 5)
11(2y + 1) ft
Simplify the complex fraction.
132)
x
5
3
x + 7
132)
A)
15x(x + 7)
B)
3x
5(x + 7)
C)
x(x + 7)
15
D)
x + 7
15x
133)
f(x) =x – 3
2
133)
A)
domain of f: ( , 0) (0, )
B)
domain of f: ( , 3) (3, )
C)
domain of f: ( , )
D)
domain of f: ( , –3) (–3, )
Multiply as indicated.
134)
x2+ 15x + 54
x2+ 10x + 24
·x2+ 10x + 24
x2+ 15x + 54
134)
A)
x + 4
x + 6
B)
x + 9
x + 4
C)
1
x + 6
D)
1
Perform the indicated operations. Simplify where possible.
135)
4x2– 12x – 4
x2– 6x + 9
–3x2– 8x – 7
x2– 6x + 9
135)
A)
x + 1
x – 3
B)
x – 1
x + 3
C)
x – 1
x – 3
D)
x2– 4x + 3
x2– 6x + 9