Solve the problem.
113)
ABC phone company charges $23 per month plus 8¢ per minute of phone calls. XYZ phone
company charges $11 per month plus 11¢ per minute of phone calls. How many minutes of phone
calls in a month make XYZ phone company the better deal?
113)
A)
Less than 400 minutes
B)
Less than 40 minutes
C)
More than 40 minutes
D)
More than 400 minutes
Plot the given point in a rectangular coordinate system.
114)
(–4, –2)
114)
A)
B)
C)
D)
Solve the polynomial equation by factoring and then using the zero product principle.
115)
3x3+4x2=27x +36
115)
A)
–4
3, 3
B)
–4
3, 0
C)
–3, –4
3, 3
D)
{–3, 3}
Solve the absolute value equation or indicate that the equation has no solution.
116)
1
2x + 2 =3
4x – 2
116)
A)
{16, 12}
B)
{10, 10}
C)
{16, 0}
D)
Solve the absolute value inequality. Other than , use interval notation to express the solution set and graph the solution
set on a number line.
117)
x<2
117)
A)
(–, –2] [2, )
B)
(–, –2) (2, )
C)
(–2, 2)
D)
[–2, 2]
Solve the problem.
118)
A ladder that is 17 feet long is 8 feet from the base of a wall. How far up the wall does the ladder
reach?
118)
A)
225 ft
B)
15 ft
C)
353 ft
D)
3 ft
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write
and factor the trinomial.
119)
x2+ 18x
119)
A)
9; x2+ 18x +9= (x +81)2
B)
324; x2+ 18x +324 = (x +18)2
C)
18; x2+ 18x +18 = (x +324)2
D)
81; x2+ 18x +81 = (x +9)2
D
Add or subtract as indicated and write the result in standard form.
120)
(8 + 6i) – (–9+ i)
120)
A)
–1+ 7i
B)
17 + 5i
C)
17 – 5i
D)
–17 – 5i
B
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write
and factor the trinomial.
121)
x2+4
9x
121)
A)
8
81 ; x2+4
9x +8
81 =x +4
9
2
B)
2
81 ; x2+4
9x +2
81 =x +2
9
2
C)
4
81 ; x2+4
9x +4
81 =x +2
9
2
D)
4
9; x2+4
9x +4
9=x +2
9
2
C
43
B
Perform the indicated operations and write the result in standard form.
122)
3–12 +5–27
122)
A)
–21i 3
B)
21 3
C)
–21 3
D)
21i 3
Solve the problem.
123)
The length of a rectangular room is 6 feet longer than twice the width. If the room’s perimeter is
216 feet, what are the room’s dimensions?
123)
A)
Width =51 ft; length =57 ft
B)
Width =39 ft; length =84 ft
C)
Width =34 ft; length =74 ft
D)
Width =68 ft; length =148 ft
Solve the absolute value inequality. Other than , use interval notation to express the solution set and graph the solution
set on a number line.
124)
|3x – 4| + 1 > – 8
124)
A)
–5
3,
B)
–5
3, 13
3
C)
(–, )
D)
44
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.
125)
During which hour did the temperature increase the most?
125)
A)
9 a.m. to 10 a.m.
B)
1 p.m. to 2 p.m.
C)
12 p.m. to 1 p.m.
D)
10 a.m. to 11 a.m.
Solve the equation by factoring.
126)
x2+ 4x – 45 = 0
126)
A)
{–9, 1}
B)
{9, 5}
C)
{9, –5}
D)
{–9, 5}
Solve the problem.
127)
There are 18 more sophomores than juniors in an 8 AM algebra class. If there are 52 students in this
class, find the number of sophomores and the number of juniors in the class.
127)
A)
17 sophomores; 35 juniors
B)
70 sophomores; 34 juniors
C)
52 sophomores; 34 juniors
D)
35 sophomores; 17 juniors
First, write the value(s) that make the denominator(s) zero. Then solve the equation.
128)
16
8x –8+1
8=2
x – 1
128)
A)
x 1;
B)
x 8; {1}
C)
x –1, 8; {1, 8}
D)
x 1; {1}
Find the product and write the result in standard form.
129)
(9 + 8i)(6– 6i)
129)
A)
102 – 6i
B)
6+ 102i
C)
102 + 6i
D)
–48i2– 6i + 54
A
Solve the polynomial equation by factoring and then using the zero product principle.
130)
x3+ 8x2+ 15x = 0
130)
A)
{0, 5, 3}
B)
{–5, –3}
C)
{0, –5, –3}
D)
{5, 3}
C
Add or subtract as indicated and write the result in standard form.
131)
3i + (–5– i)
131)
A)
5– 4i
B)
–5+ 2i
C)
5– 2i
D)
–5+ 4i
B
Plot the given point in a rectangular coordinate system.
132)
(–2, 3)
132)
46
A
A)
B)
C)
D)
Solve the problem.
133)
The sum of the angles of a triangle is 180°. Find the three angles of the triangle if one angle is
three times the smallest angle and the third angle is 30° greater than the smallest angle.
133)
A)
12°, 42°, 126°
B)
12°, 36°, 132°
C)
21°, 63°, 96°
D)
30°, 90°, 60°
Solve the equation by making an appropriate substitution.
134)
(x – 3)2+ 3(x – 3) – 18 = 0
134)
A)
{0, 9}
B)
{–3, 6}
C)
{–9, 0}
D)
{–6, 3}
47
Solve the equation using the quadratic formula.
135)
x2+ 6x – 16 = 0
135)
A)
{–8, 2}
B)
{8, 2}
C)
{–2, 8}
D)
{–8, 1}
Solve the problem.
136)
Claire has received scores of 85, 88, 87, and 85 on her algebra tests. What score must she receive on
the fifth test to have an overall test score average of at least 88?
136)
A)
94 or greater
B)
95 or greater
C)
96 or greater
D)
93 or greater
Complex numbers are used in electronics to describe the current in an electric circuit. Ohm’s law relates the current in a
circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the formula
E = IR. Solve the problem using this formula.
137)
Find E, the voltage of a circuit, if I = (18 + i) amperes and R = (3+2i) ohms.
137)
A)
(18 +39i) volts
B)
(52 +39i) volts
C)
(52 –39i) volts
D)
(18 –39i) volts
Solve the problem.
138)
A formula for the length of a diagonal from the upper corner of a box to the opposite lower corner
is d =L2+W2+H2, where L, W, and H are the length, width, and height, respectively. Find the
length of the diagonal of the box if the length is 23 inches, width is 15 inches, and height is 7 inches.
Leave your answer in simplified radical form.
138)
A)
803 in.
B)
1606 in.
C)
3 5 in.
D)
310 in.
Find all values of x satisfying the given conditions.
139)
y = x –3x – 2 and y = 4
139)
A)
2, 9
B)
9
C)
1, 2
D)
–1
Use the five–step strategy for solving word problems to find the number or numbers described in the following exercise.
140)
When a number is decreased by 40% of itself, the result is 288. What is the number?
140)
A)
480
B)
1200
C)
8
D)
192
The table of values was generated by a graphing utility with a TABLE feature. Use the following table to solve.
141)
At which points do the graph of Y1 and Y2 intersect?
141)
A)
(0, 1) and (3, 9)
B)
(–1, 1) and (0, 3)
C)
(–1, 1) and (3, 9)
D)
(0, 3) and (0, 1)
Solve and check the equation.
142)
(x +6)3/2 =8
142)
A)
32–6
B)
{–2}
C)
{10}
D)
{–4}
49
Solve the equation by the method of your choice.
143)
5x2=65
143)
A)
{32.5}
B)
{–13, 13}
C)
{–13 , 13}
D)
{14}
Solve the absolute value equation or indicate that the equation has no solution.
144)
2(x + 1) +4=8
144)
A)
{–7, 1}
B)
{–5, 0}
C)
{–7, 0}
D)
{–5, 3}
Solve the equation by factoring.
145)
7–7x = (4x + 9)(x – 1)
145)
A)
{–4, 1}
B)
{–1, 4}
C)
1
D)
1, –9
4
Solve the problem.
146)
A square sheet of paper measures 28 centimeters on each side. What is the length of the diagonal of
this paper?
146)
A)
28 cm
B)
28 2 cm
C)
1568 cm
D)
56 cm
Solve the equation by the method of your choice.
147)
(2x + 9)2=64
147)
A)
1
2, 17
2
B)
–1
2, 0
C)
55
2
D)
–17
2, –1
2
50
Solve the equation by making an appropriate substitution.
148)
(x2–3x)2–14(x2–3x) +40 = 0
148)
A)
{10, 4}
B)
{– 2, – 1, 10, 4, 5, 4}
C)
{5, 4}
D)
{– 2, – 1, 5, 4}
Solve the problem.
149)
When an object is dropped to the ground from a height of h meters, the time it takes for the object
to reach the ground is given by the equation t =h
4.9 , where t is measured in seconds. Solve the
equation for h. Use the result to determine the height from which an object was dropped if it hits
the ground after falling for 5 seconds.
149)
A)
h = 4.9t2; 122.5 m
B)
h = 24.01t2; 600.3 m
C)
h = 4.9t; 24.5 m
D)
h = 24.01t; 120.1 m
A
Explanation:
Solve the radical equation, and check all proposed solutions.
150)
6x +55 = x
150)
A)
B)
{11}
C)
– 11
D)
{–5, 11}
B
Explanation:
Solve the equation by making an appropriate substitution.
151)
x4– 2x2–8= 0
151)
A)
{–4, 2}
B)
{2, i 2}
C)
{–2, 2, –2i, 2i}
D)
{–2, 2, –i 2, i 2}
D
Explanation:
D
Explanation:
Solve the equation.
152)
4x
5– x =x
45 –2
9
152)
A)
–5
4
B)
1
C)
5
4
D)
– 1
Solve the absolute value inequality. Other than , use interval notation to express the solution set and graph the solution
set on a number line.
153)
|x – 5| 0
153)
A)
{5}
B)
(–5, 5)
C)
(5, )
D)
(–, )
D
Find the product and write the result in standard form.
154)
(8 – 6i)(–5– 4i)
154)
A)
–16 – 62i
B)
–64 – 62i
C)
–16 – 2i
D)
–64 – 2i
D
B
Perform the indicated operations and write the result in standard form.
155)
–2– – 100
155)
A)
i( 2+ 10)
B)
2i – 10
C)
2i – 10i
D)
i( 2– 10)
Solve the formula for the specified variable.
156)
P =A
1 + rt for r
156)
A)
r= P – At
B)
r=P – 1
At
C)
r=A – P
Pt
D)
r=P – A
1 +t
Solve the equation by the method of your choice.
157)
7x2–13x –3= 0
157)
A)
13 ±253
14
B)
–13 ±97
14
C)
13 ±i71
14
D)
13 ±97
14
Find all values of x satisfying the given conditions.
158)
y =3x + 6 and y =8
158)
A)
–2
3, 14
3
B)
1
3, –7
3
C)
2
3, –14
3
D)
No solutions
Perform the indicated operations and write the result in standard form.
159)
–18 – – 180
6
159)
A)
–3+ i 5
B)
3+ i 5
C)
–3– i 5
D)
–3– i 6
Solve the problem.
160)
The formula P =0.61x2–0.041x +3 models the approximate population P, in thousands, for a
species of fish in a local pond, x years after 1997. During what year will the population reach 24,714
fish?
160)
A)
2005
B)
2004
C)
2002
D)
2003
Solve the formula for the specified variable.
161)
F =9
5C + 32 for C
161)
A)
C =9
5(F – 32)
B)
C =F – 32
9
C)
C =5
F – 32
D)
C =5
9(F – 32)
Solve the equation by the square root property.
162)
3x2=48
162)
A)
{0}
B)
{–4 3, 4 3}
C)
{–4, 4}
D)
{–3, 3}
Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a
number line.
163)
4x +5<33
163)
A)
(–, 7)
B)
(–, 7]
C)
(7, )
D)
[7, )
54
Use the five–step strategy for solving word problems to find the number or numbers described in the following exercise.
164)
When four times the number is added to 7 times the number, the result is 44. What is the number?
164)
A)
4
B)
–6.3
C)
0.7
D)
6.3
Solve the absolute value equation or indicate that the equation has no solution.
165)
6x + 5 =8
165)
A)
3
5, –13
5
B)
1
2, –13
6
C)
–1
2, 13
6
D)
Solve the equation by the square root property.
166)
(2x + 2)2=16
166)
A)
{0, 1}
B)
{–3, 1}
C)
{1, 3}
D)
{–9, 9}
Solve the equation by completing the square.
167)
x2+ 4x – 9 = 0
167)
A)
{–2–113 , –2+113}
B)
{–1–13 , –1+13}
C)
{2 +13}
D)
{–2–13 , –2+13}
Solve the equation.
168)
80 –x
9=x
7
168)
A)
640
B)
{315}
C)
1280
63
D)
{5}
Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a
number line.
169)
x
5–1
5x
3+1
169)
A)
– 9,
B)
– 9,
C)
–, – 9
D)
–, – 9
Solve the problem.
170)
A car rental agency charges $200 per week plus $0.25 per mile to rent a car. The total cost, C, for the
renting the car for one week and driving it x miles can be modeled by the formula C =0.25x +200.
How many miles can you travel in one week for $325?
170)
A)
1300 miles
B)
500 miles
C)
475 miles
D)
281.25 miles
Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a
number line.
171)
30x – 20 5(5x – 2)
171)
A)
[–, –6)
B)
[2, )
C)
(–, 2]
D)
(–, 2)
Find the x–intercept(s) of the graph of the equation. Graph the equation.
172)
y =x2+ 4x – 7
172)
57
A)
x–intercept: 4
B)
x–intercepts: –2 ±11
C)
x–intercepts: none
D)
x–intercepts: –4 and 3
Find all values of x satisfying the given conditions.
173)
y =x –12
x
2– 3 x –12
x and y =4
173)
A)
–1, 4
B)
– 4, – 2, 3, 6
C)
– 4, 3
D)
No solution
Solve the problem.
174)
For a cone, the formula r =3V
h describes the relationship between the radius r of the base, the
volume V, and the height h. Find the volume if the radius is 3 inches and the cone is 4 inches high.
(Use 3.14 as an approximation for , and round to the nearest tenth.)
174)
A)
37.7 cubic in.
B)
339.1 cubic in.
C)
12.6 cubic in.
D)
9.4 cubic in.
175)
An auto repair shop charged a customer $496 to repair a car. The bill listed $96 for parts and the
remainder for labor. If the cost of labor is $40 per hour, how many hours of labor did it take to
repair the car?
175)
A)
10.5 hours
B)
10 hours
C)
9 hours
D)
11 hours
Add or subtract as indicated and write the result in standard form.
176)
–7– (4– 5i) – (2– 4i)
176)
A)
–6– 9i
B)
–13 + 9i
C)
–6+ 9i
D)
–13 – 9i
Solve and check the equation.
177)
(4x – 5)1/3 – 6 = – 4
177)
A)
11
4
B)
9
4
C)
13
4
D)
Solve the equation by the method of your choice.
178)
2x
x – 5 –x
x – 8 =7
x2– 13x + 40
178)
A)
–11 ±93
2
B)
11 ±93
2
C)
11 ±149
2
D)
–11 ±149
2
Solve the problem.
179)
The equation V = – 3000t +25,000 describes the value in dollars of a certain model of car after it is t
years old. If a car is worth $13,000, substitute 13,000 into the equation to find the age of the car.
179)
A)
3 years
B)
6 years
C)
4 years
D)
5 years
180)
You inherit $56,000 from a very wealthy grandparent, with the stipulation that for the first year, the
money must be invested in two stocks paying 4% and 10% annual interest, respectively. How much
should be invested at each rate if the total interest earned for the year is to be $3200?
180)
A)
$30,000 invested at 4%; $26,000 invested at 10%
B)
$26,000 invested at 4%; $30,000 invested at 10%
C)
$16,000 invested at 4%; $40,000 invested at 10%
D)
$40,000 invested at 4%; $16,000 invested at 10%
Divide and express the result in standard form.
181)
2+ 7i
7– 2i
181)
A)
1
B)
i
C)
–1
D)
–i