Solve the radical equation, and check all proposed solutions.
56)
2x + 3 =4x – 5
56)
A)
11
2
B)
11 –69
8, 11 +69
8
C)
11 +69
8
D)
Solve the problem.
57)
The formula C =0.5x +15 represents the estimated future cost of yearly attendance at State
University, where C is the cost in thousands of dollars x years after 2002. Use a compound
inequality to determine when the attendance costs will range from 18.5 to 20.5 thousand dollars.
57)
A)
From 2008 to 2012
B)
From 2010 to 2012
C)
From 2010 to 2014
D)
From 2009 to 2013
58)
When making a long distance call from a certain pay phone, the first three minutes of a call cost
$2.40. After that, each additional minute or portion of a minute of that call costs $0.30. Use an
inequality to find the number of minutes one can call long distance for $4.20.
58)
A)
6 minutes or fewer
B)
14 minutes or fewer
C)
9 minutes or fewer
D)
2 minutes or fewer
Solve the equation by the square root property.
59)
(3x + 4)2=10
59)
A)
–4–10
3 , –4+10
3
B)
–14
3 , 2
C)
4–10
3 , 4+10
3
D)
10 –4
3 , 10 +4
3
21
Find all values of x satisfying the given conditions.
60)
y1=1
x + 3 , y2=4
x – 3 , y3=9
x2– 9 , and y1–y2=y3
60)
A)
{24}
B)
{2}
C)
{–8}
D)
{8}
Solve the problem.
61)
The algebraic expression 0.07d3/2 describes the duration of a storm, in hours, whose diameter is d
miles. Use a calculator to determine the duration of a storm with a diameter of 7 miles. Round to
the nearest hundredth.
61)
A)
18.52 hr
B)
0.34 hr
C)
0.19 hr
D)
1.3 hr
Find the x–intercept(s) of the graph of the equation. Graph the equation.
62)
y = – x2– 2x + 3
62)
A)
x–intercepts: –1 and 3
B)
x–intercepts: –1 and 3
22
C)
x–intercepts: –3 and 1
D)
x–intercepts: –3 and 1
Perform the indicated operations and write the result in standard form.
63)
–10 + – 12
2
63)
A)
5+ i 3
B)
–5+ i 2
C)
–5– i 3
D)
–5+ i 3
Solve the equation by making an appropriate substitution.
64)
(8x + 8)2+ 12(8x + 8) + 32 = 0
64)
A)
2, 11
2
B)
– 2, – 1 1
2
C)
{–8, –4}
D)
0, 1
2
23
Solve the compound inequality. Other than , use interval notation to express the solution set and graph the solution set
on a number line.
65)
–2< x + 2 1
65)
A)
[–4, –1)
B)
[0, 3)
C)
(–4, –1]
D)
(0, 3]
Solve the equation by the square root property.
66)
(x –3)2= – 6
66)
A)
{–3, 9}
B)
{–3±6i}
C)
{3 ± i 6}
D)
{3 ±6}
Express the interval in set–builder notation and graph the interval on a number line.
67)
–, 7
4
67)
A)
x x >7
4
B)
x x <7
4
C)
x x 7
4
D)
{x 4 x 7}
Solve the equation using the quadratic formula.
68)
x2– 6x + 25 = 0
68)
A)
{3 – 16i, 3+ 16i}
B)
{3 – 4i, 3+ 4i}
C)
{3 +4i}
D)
{–1, 7}
Solve the equation by factoring.
69)
2x2– 15x =8
69)
A)
–1
2, 2
B)
–1
2, 8
C)
1
15 , –1
2
D)
{–2, 8}
Solve the problem.
70)
It takes 23 minutes to set up a candy making machine. Once the machine is set up, it produces 20
candies per minute. Use an inequality to find the number of candies that can be produced in 5
hours if the machine has not yet been set up.
70)
A)
2300 candies or fewer
B)
5540 candies or fewer
C)
100 candies or fewer
D)
6440 candies or fewer
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write
and factor the trinomial.
71)
x2–2
5x
71)
A)
1
25 ; x2–2
5x +1
25 =x +1
5
2
B)
4
25 ; x2–2
5x +4
25 =x –2
5
2
C)
2
25 ; x2–2
5x +2
25 =x –1
5
2
D)
1
25 ; x2–2
5x +1
25 =x –1
5
2
First, write the value(s) that make the denominator(s) zero. Then solve the equation.
72)
x –8
2x +5=x +4
x
72)
A)
No restrictions; 6
5
B)
x 0; 16
9
C)
x 0, 2; 16
9
D)
x 0; – 11
Solve the formula for the specified variable.
73)
d = rt for t
73)
A)
t= dr
B)
t= d –r
C)
t=d
r
D)
t=r
d
Divide and express the result in standard form.
74)
5i
3– i
74)
A)
–5
8+15
8i
B)
–1
2+3
2i
C)
1
2+3
2i
D)
–1
2–3
2i
Use the five–step strategy for solving word problems to find the number or numbers described in the following exercise.
75)
When 10% of a number is added to the number, the result is 165. What is the number?
75)
A)
150
B)
15
C)
110
D)
9
Solve the problem.
76)
A train ticket in a certain city is $1.50. People who use the train also have the option of purchasing
a frequent rider pass for $15.75 each month. With the pass, each ticket costs only $0.75. Determine
the number of times in a month the train must be used so that the total monthly cost without the
pass is the same as the total monthly cost with the pass.
76)
A)
22 times
B)
23 times
C)
20 times
D)
21 times
D)
Solve the compound inequality. Other than , use interval notation to express the solution set and graph the solution set
on a number line.
77)
–15
7x – 6 <4
77)
A)
(7, 14]
B)
(7, 8]
C)
[7, 14)
D)
[7, 8)
D)
Write the English sentence as an equation in two variables. Then graph the equation.
78)
The y–value is two more than three times the x–value.
78)
27
A)
y = – 3x +2
B)
y =3x +2
C)
y =3x –2
D)
y = – 3x –2
Plot the given point in a rectangular coordinate system.
79)
(4, –3)
79)
28
A)
B)
C)
D)
Solve the problem.
80)
The president of a certain university makes three times as much money as one of the department
heads. If the total of their salaries is $270,000, find each worker’s salary.
80)
A)
president’s salary =$202,500; department head’s salary =$67,500
B)
president’s salary =$20,250; department head’s salary =$6750
C)
president’s salary =$135,000; department head’s salary =$67,500
D)
president’s salary =$67,500; department head’s salary =$202,500
Graph the equation.
29
81)
y =x2+ 2
81)
A)
B)
C)
D)
30
Solve the absolute value equation or indicate that the equation has no solution.
82)
x=3
82)
A)
{–3, 3}
B)
{9}
C)
{3}
D)
{–3}
Solve the polynomial equation by factoring and then using the zero product principle.
83)
8x3+64x2+120x = 0
83)
A)
{–1
5, –3}
B)
{0, 5, 3}
C)
{–5, –3}
D)
{0, –5, –3}
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.
84)
What temperature was recorded at 6 p.m.?
84)
A)
73 ° F
B)
76 ° F
C)
75 ° F
D)
77 ° F
Use interval notation to represent all values of x satisfying the given conditions.
85)
y1=4x – 2, y2=3x + 3, and y1>y2.
85)
A)
(5, )
B)
(1, )
C)
(–, 5]
D)
[5, )
Solve and check the linear equation.
86)
–7x + 6 = – 10 – 3x
86)
A)
1
4
B)
5
2
C)
4
D)
–1
4
Find all values of x satisfying the given conditions.
87)
y1=7–7x, y2= (4x + 9)(x – 1), and y1–y2= 0
87)
A)
–1, 4
B)
1
C)
1, –9
4
D)
–4, 1
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write
and factor the trinomial.
88)
x2– 18x
88)
A)
81; x2– 18x +81 =(x –9) 2
B)
–324; x2– 18x –324 =(x – 18)2
C)
324; x2– 18x +324 =(x – 18)2
D)
–81; x2– 18x –81 =(x –9) 2
Solve the problem.
89)
After a 9% price reduction, a boat sold for $29,120. What was the boat’s price before the reduction?
(Round to the nearest cent, if necessary.)
89)
A)
$2620.80
B)
$31,740.80
C)
$323,555.56
D)
$32,000
Compute the discriminant. Then determine the number and type of solutions for the given equation.
90)
x2+ 2x + 1 = 0
90)
A)
0; one real solution
B)
–4; two complex imaginary solutions
C)
4; two unequal real solutions
Solve the problem.
91)
A machine produces open boxes using square sheets of plastic. The machine cuts equal–sized
squares measuring 4 inches on a side from each corner of the sheet, and then shapes the plastic into
an open box by turning up the sides. If each box must have a volume of 1600 cubic inches, find the
length of one side of the open box.
91)
A)
20 in.
B)
24 in.
C)
19 in.
D)
28 in.
Express the interval in set–builder notation and graph the interval on a number line.
92)
[8, )
92)
A)
{x x >8}
B)
{x x 8}
C)
{x x 8}
D)
{x x >8}
Graph the equation.
33
93)
y = – 1
3x + 4
93)
A)
B)
C)
D)
Solve the problem.
94)
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the
length of the ladder if the length is 2 ft more than its distance from the wall.
94)
A)
6 ft
B)
12 ft
C)
10 ft
D)
8 ft
Plot the given point in a rectangular coordinate system.
95)
(0, –4)
95)
A)
B)
C)
D)
D)
Solve the problem.
96)
On the first four exams, your grades are 76, 80, 71, and 77. You are hoping to earn a C in the course.
This will occur if the average of your five exam grades is greater than or equal to 70 and less than
80. What range of grades on the fifth exam will result in earning a C?
96)
A)
(46, 96]
B)
[36, 86)
C)
[46, 96)
D)
(36, 86]
Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a
number line.
97)
–6(5x + 7) < – 36x – 6
97)
A)
(–, 8]
B)
(–, 6)
C)
(–, 6]
D)
(6, )
D)
Solve the equation using the quadratic formula.
98)
3x2+ x –5= 0
98)
A)
–1 –61
2, –1 +61
2
B)
1 –61
6, 1 +61
6
C)
D)
–1 –61
6, –1 +61
6
D)
36
D)
First, write the value(s) that make the denominator(s) zero. Then solve the equation.
99)
8
x+9=5
2x +15
4
99)
A)
x 0, 2, 4; –22
21
B)
No restrictions; –21
22
C)
x 0; –22
21
D)
x 0; –21
22
Solve the equation by making an appropriate substitution.
100)
x4–30x2+125 = 0
100)
A)
{5, 5}
B)
{25, 5}
C)
{–5, 5, –5, 5}
D)
{–5, 5, –i 5, i 5}
C
101)
x–2– 11x–1+10 = 0
101)
A)
1
10 , 1
B)
{–1, –10}
C)
{1, 10}
D)
–1
10 , –1
A
Solve the formula for the specified variable.
102)
A = P(1 + nr) for n
102)
A)
n=A
r
B)
n=Pr
A – P
C)
n=A – P
Pr
D)
n=P – A
Pr
C
37
C
Solve the equation by completing the square.
103)
8x2–5x + 1 = 0
103)
A)
5±7
16
B)
–5± i 7
16
C)
5± i 7
16
D)
5– i 7
16 , –5+ i 7
16
Solve the problem.
104)
The number of centimeters, d, that a spring is compressed from its natural, uncompressed position
is given by the formula d =2W
k, where W is the number of joules of work done to move the
spring and k is the spring constant. Solve this equation for W. Use the result to determine the
work needed to move a spring 8 centimeters if it has a spring constant of 0.6.
104)
A)
W = 2d2k; 76.8 joules
B)
W =2d2
k; 213.3 joules
C)
W =d2k2
4; 5.8 joules
D)
W =d2k
2; 19.2 joules
Solve the equation.
105)
x +4
6=5
6–x –1
4
105)
A)
{0}
B)
17
2
C)
{20}
D)
{1}
38
Solve the compound inequality. Other than , use interval notation to express the solution set and graph the solution set
on a number line.
106)
–4 –4x – 12 < 4
106)
A)
(–, –4) or [–2, )
B)
(–4, –2]
C)
(–, –4]
D)
[–4, –2)
Solve the absolute value equation or indicate that the equation has no solution.
107)
x + 2 =5
107)
A)
{3}
B)
{–7, 3}
C)
{–3, 7}
D)
Solve the formula for the specified variable.
108)
I =nE
nr + R for n
108)
A)
n =IR
E – Ir
B)
n =–R
Ir – E
C)
n =IR
Ir + E
D)
n = IR(Ir – E)
Solve the absolute value equation or indicate that the equation has no solution.
109)
8x + 6 + 4 =7
109)
A)
{–3
2, –1
2}
B)
–9
8, –3
8
C)
3
8, 9
8
D)
39
Solve the formula for the specified variable.
110)
A =1
2bh for b
110)
A)
b=h
2A
B)
b=A
2h
C)
b=2A
h
D)
b=Ah
2
D)
Solve the compound inequality. Other than , use interval notation to express the solution set and graph the solution set
on a number line.
111)
–7–2x + 3 < – 1
111)
A)
(–5, –2]
B)
(2, 5]
C)
[–5, –2)
D)
[2, 5)
D)
Solve the equation by the method of your choice.
112)
(3x + 2)2=6
112)
A)
6±2
3
B)
2±6
3
C)
–8
3, 4
3
D)
–2±6
3
D)
40