Solve the compound inequality. Other than , use interval notation to express the solution set and graph the solution set
on a number line.
51)
32x – 3 9
51)
A)
(3, 6)
B)
[3, 6]
C)
(–6, –3)
D)
[–6, –3]
Solve the problem.
52)
There is a relationship between the expected number of tickets sold for a raffle and the dollar value
of the prize for the raffle. The equation T –5P =150 describes this relationship, where T is the
expected number of tickets sold, and P is the dollar value of the raffle prize. Suppose the expected
ticket sales for a certain raffle are 2650. Substitute 2650 into the equation to determine the dollar
value of the raffle prize.
52)
A)
$500
B)
$2500
C)
$450
D)
$13,400
Find the x–intercepts of the graph of the equation.
53)
y =x + 6 +2 – x – 4
53)
A)
–2
B)
0
C)
31, –2
D)
2, –2
21
Solve the equation by the method of your choice.
54)
(x +7)(x –8) =5
54)
A)
1±7i 5
2
B)
1±7 5
2
C)
–1±7i 5
2
D)
–1±7 5
2
Solve the problem.
55)
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.
55)
A)
30°, 90°, 60°
B)
12°, 42°, 126°
C)
21°, 63°, 96°
D)
12°, 36°, 132°
Find all values of x satisfying the given conditions.
56)
y1= 5(5x – 1)–1, y2= 2(5x – 1)–2, and y1 exceeds y2 by 2
56)
A)
–1
5, –1
10
B)
–1
5, 0
C)
–2, –1
2
D)
3
5, 3
10
Solve the absolute value inequality. Other than , use interval notation to express the solution set and graph the solution
set on a number line.
57)
x<2
57)
A)
[–2, 2]
B)
(–, –2] [2, )
C)
(–2, 2)
D)
(–, –2) (2, )
Solve the radical equation, and check all proposed solutions.
58)
2x +10 = x + 6
58)
A)
{8}
B)
{–4}
C)
{2, 8}
D)
–4, 4
3
Solve the problem.
59)
The formula N =2x2+6x +3 represents the number of households N, in thousands, in a certain
city that have a computer x years after 1990. According to the formula, in what year were there 111
thousand households with computers in this city?
59)
A)
1995
B)
1997
C)
1996
D)
1994
Solve the formula for the specified variable.
60)
I = Prt for t
60)
A)
t=P– Ir
B)
t=P– 1
Ir
C)
t=P– I
1 +r
D)
t=I
Pr
Find the x–intercepts of the graph of the equation.
61)
y =2x + 5 –x – 2 – 3
61)
A)
2, 38
B)
2
C)
–2
D)
3, 8
Divide and express the result in standard form.
62)
9+ 3i
9+ 8i
62)
A)
21
17 –9
17 i
B)
57
17 –9
17 i
C)
57
29 –99
29 i
D)
21
29 –9
29 i
Find all values of x satisfying the given conditions.
63)
y1=x
x –3+8, y2=6x
x –3 , and y1=y2
63)
A)
16
5, 4
B)
–16
5, –4
C)
4, 6
D)
4, 2
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write
and factor the trinomial.
64)
x2– 18x
64)
A)
324; x2– 18x +324 =(x – 18)2
B)
–81; x2– 18x –81 =(x –9) 2
C)
–324; x2– 18x –324 =(x – 18)2
D)
81; x2– 18x +81 =(x –9) 2
Solve the problem.
65)
The formula v =2.5r can be used to estimate the maximum safe velocity v, in miles per hour, at
which a car can travel along a curved road with a radius of curvature r, in feet. To the nearest
whole number, find the radius of curvature if the maximum safe velocity is 35 miles per hour.
65)
A)
1225 ft
B)
490 ft
C)
196 ft
D)
3063 ft
Find all values of x satisfying the given conditions.
66)
y1=1
x +15 , y2=1
x, and y1+y2=1
5
66)
A)
5±513
2
B)
25 ±513
2
C)
–25 ±513
2
D)
–5±513
2
Solve the problem.
67)
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.
67)
A)
70 sophomores; 34 juniors
B)
52 sophomores; 34 juniors
C)
35 sophomores; 17 juniors
D)
17 sophomores; 35 juniors
Solve the equation using the quadratic formula.
68)
3x2+ x –5= 0
68)
A)
1 –61
6, 1 +61
6
B)
–1 –61
2, –1 +61
2
C)
D)
–1 –61
6, –1 +61
6
Solve and check the linear equation.
69)
–7x + 6 = – 10 – 3x
69)
A)
1
4
B)
–1
4
C)
4
D)
5
2
Solve the radical equation, and check all proposed solutions.
70)
1 +8 x = 1 +x
70)
A)
{0, 100}
B)
{0, 36}
C)
{0, 64}
D)
0, 4
7
Graph the equation.
25
71)
y =1
x
71)
A)
B)
C)
D)
Solve the formula for the specified variable.
72)
A =1
2h(B + b) for B
72)
A)
B=A –bh
h
B)
B=2A +bh
h
C)
B=2A –bh
h
D)
B= 2A –bh
Solve the problem.
73)
A car rental agency charges $225 per week plus $0.20 per mile to rent a car. How many miles can
you travel in one week for $245?
73)
A)
1225 miles
B)
274 miles
C)
100 miles
D)
75 miles
Perform the indicated operations and write the result in standard form.
74)
(–10 + – 4)2
74)
A)
96 –40i
B)
100 +4i
C)
100 –4i
D)
104 + 40i
27
Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a
number line.
75)
5x + 6 >4x + 12
75)
A)
(18, )
B)
[6, )
C)
(6, )
D)
(–, 6]
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
76)
4(4x – 15) =16x – 60
76)
A)
Identity
B)
Conditional equation
C)
Inconsistent equation
A
Solve the polynomial equation by factoring and then using the zero product principle.
77)
3x –5=48x3–80x2
77)
A)
–1
4, 1
4, 3
5
B)
0, 5
3
C)
–1
4, 1
4, 5
3
D)
–1
16 , 1
16 , 5
3
C
C
Find all values of x satisfying the given conditions.
78)
y =x – 3 and y =9
78)
A)
12
B)
–12, 6
C)
–6, 12
D)
No solutions
Graph the equation.
79)
y =3|x|
79)
A)
B)
C)
D)
Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a
number line.
80)
x
5–1
5x
3+1
80)
A)
– 9,
B)
– 9,
C)
–, – 9
D)
–, – 9
Perform the indicated operations and write the result in standard form.
81)
(–9)( –4)
81)
A)
6
B)
–6
C)
6i2
D)
–6i
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
82)
–8x + 4(–2x – 4) = – 28 – 4x
82)
A)
Identity
B)
Conditional equation
C)
Inconsistent equation
Solve the equation.
83)
x
2x + 2 =–2x
4x + 4 +2x – 3
x + 1
83)
A)
{3}
B)
3
2
C)
–12
5
D)
{–3}
Solve the equation by making an appropriate substitution.
84)
7x–2– 8x–1+ 1 = 0
84)
A)
–1
7, –1
B)
{1, 7}
C)
{–1, –7}
D)
1
7, 1
Solve the radical equation, and check all proposed solutions.
85)
x + 6 +2 – x = 4
85)
A)
{2, –2}
B)
{31, –2}
C)
{–2}
D)
{0}
Find all values of x satisfying the given conditions.
86)
y =x –12
x
2– 3 x –12
x and y =4
86)
A)
– 4, – 2, 3, 6
B)
– 4, 3
C)
–1, 4
D)
No solution
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write
and factor the trinomial.
87)
x2–11x
87)
A)
11
2; x2–11x +11
2=x –11
2
2
B)
–121
4; x2–11x –121
4=x –11
2
2
C)
121; x2–11x +121 =(x –11)2
D)
121
4; x2–11x +121
4=x –11
2
2
Solve the absolute value inequality. Other than , use interval notation to express the solution set and graph the solution
set on a number line.
88)
|x + 7| + 5 7
88)
A)
[–9, –5]
B)
(–, –9] [–5, )
C)
[–9, 7]
D)
(–9, –5)
Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a
number line.
89)
5(4x +3) – 4x < 4(4+ 4x) – 6
89)
A)
( , 3)
B)
(3, )
C)
D)
( , )
32
Solve the equation by factoring.
90)
x2= x +30
90)
A)
{1, 30}
B)
{5, 6}
C)
{–5, 6}
D)
{–5, –6}
Express the interval in set–builder notation and graph the interval on a number line.
91)
(–, 6.5]
91)
A)
{x x 6.5}
B)
{x x <6.5}
C)
{x x >6.5}
D)
{x x 6.5}
Solve the radical equation, and check all proposed solutions.
92)
2x + 5 –x – 2 = 3
92)
A)
{–2}
B)
{3, 8}
C)
{2, 38}
D)
{2}
Solve the problem.
93)
A spinner has five regions numbered 1 through 5. If the spinner is spun 100 times, we would
expect about 20 of the outcomes to be Region 1. It can be determined that the spinner is unbalanced
if x, the number of outcomes that result in Region 1, satisfies x –20
4
1.645. Describe the number
of outcomes that determine an unbalanced spinner that is spun 100 times.
93)
A)
Between 17 and 29 outcomes
B)
Fewer than 14 or more than 26 outcomes
C)
Between 14 and 26 outcomes
D)
Fewer than 17 or more than 29 outcomes
Use interval notation to represent all values of x satisfying the given conditions.
94)
y1=4x – 2, y2=3x + 3, and y1>y2.
94)
A)
(–, 5]
B)
(1, )
C)
[5, )
D)
(5, )
Solve the equation by completing the square.
95)
8x2–5x + 1 = 0
95)
A)
5– i 7
16 , –5+ i 7
16
B)
5± i 7
16
C)
–5± i 7
16
D)
5±7
16
96)
x2– 2x – 3 = 0
96)
A)
{–3, 1}
B)
{–1, –2}
C)
{–1, 3}
D)
{–3, 3}
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.
97)
At what time was the temperature its lowest?
97)
A)
1 p.m.
B)
4 p.m.
C)
6 p.m.
D)
9 a.m.
Solve and check the linear equation.
98)
32– 2(12 –9)2=54x
98)
A)
{0}
B)
7
6
C)
–1
6
D)
{6}
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
99)
11x
x=11
99)
A)
Identity
B)
Conditional equation
C)
Inconsistent equation
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.
100)
At what time was the temperature the highest?
100)
A)
5 p.m.
B)
11 a.m.
C)
2 p.m.
D)
1 p.m.
Solve the equation by factoring.
101)
2x2– 15x =8
101)
A)
{–2, 8}
B)
–1
2, 2
C)
1
15 , –1
2
D)
–1
2, 8
Solve and check the equation.
102)
x3/2 =8
102)
A)
32
B)
{2}
C)
{16 2}
D)
{4}
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
103)
7x + 7 – 8x – 9 =6x – 7x – 5
103)
A)
Identity
B)
Conditional equation
C)
Inconsistent equation
Add or subtract as indicated and write the result in standard form.
104)
3i + (–5– i)
104)
A)
–5+ 4i
B)
5– 2i
C)
5– 4i
D)
–5+ 2i
D
Solve the equation by factoring.
105)
7–7x = (4x + 9)(x – 1)
105)
A)
{–4, 1}
B)
1, –9
4
C)
1
D)
{–1, 4}
A
Solve the radical equation, and check all proposed solutions.
106)
x –3x – 2 = 4
106)
A)
{9}
B)
{–1}
C)
{2, 9}
D)
{1, 2}
A
Use graphs to find the set.
107)
(–10, 0) [–1, 5]
107)
A)
(0, 5]
B)
[–1, 0)
C)
(–10, 5]
D)
(–10, –1]
C
C
Divide and express the result in standard form.
108)
8
7– i
108)
A)
7
6–1
6i
B)
28
25 +4
25 i
C)
7
6+1
6i
D)
28
25 –4
25 i
Solve the radical equation, and check all proposed solutions.
109)
x + 5 =7
109)
A)
{44}
B)
{49}
C)
{144}
D)
{54}
Solve the absolute value inequality. Other than , use interval notation to express the solution set and graph the solution
set on a number line.
110)
|x – 5| 0
110)
A)
(5, )
B)
(–5, 5)
C)
{5}
D)
(–, )
Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a
number line.
111)
–6(5x + 7) < – 36x – 6
111)
A)
(–, 6]
B)
(–, 6)
C)
(6, )
D)
(–, 8]
Solve the equation by the square root property.
112)
(2x – 5)2=49
112)
A)
{–1, 6}
B)
{–6, 1}
C)
{–12, 2}
D)
{–2, 12}
Perform the indicated operations and write the result in standard form.
113)
5–16 +4–4
113)
A)
28
B)
28i
C)
–28
D)
–28i
114)
( 3 – – 36)( 3+ – 36)
114)
A)
3–36i
B)
39
C)
–33
D)
3– 6i
39
Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a
number line.
115)
4x +5<33
115)
A)
(–, 7)
B)
(–, 7]
C)
[7, )
D)
(7, )
Solve the equation by the method of your choice.
116)
1
x +5+1
x=1
15
116)
A)
–35 ±537
2
B)
25 ±537
2
C)
–25 ±537
2
D)
35 ±537
2
Solve the equation using the quadratic formula.
117)
4x2+ 12x + 2 = 0
117)
A)
–3–7
2, –3+7
2
B)
–12 –7
2 , –12 +7
2
C)
–3–7
8 , –3+7
8
D)
–3–11
2 , –3+11
2
Solve the absolute value equation or indicate that the equation has no solution.
118)
x + 2 =5
118)
A)
{3}
B)
{–7, 3}
C)
{–3, 7}
D)
40