Use the graph to determine the x– and y–intercepts.
175)
175)
A)
x–intercepts: –4, 4; y–intercepts: –5, 5
B)
x–intercepts: –5, 5; y–intercepts: –4, 4
C)
x–intercepts: –5, 5
D)
y–intercepts: –4, 4
Find the product and write the result in standard form.
176)
(–4+ i)(–4– i)
176)
A)
16
B)
–4
C)
–15
D)
17
D
Find all values of x satisfying the given conditions.
177)
y1=7–7x, y2= (4x + 9)(x – 1), and y1–y2= 0
177)
A)
1
B)
–4, 1
C)
1, –9
4
D)
–1, 4
B
61
B
Solve the problem.
178)
Greg is opening a car wash. He estimates his cost equation as C =9000 +0.09x and his revenue
equation as R =1.65x, where x is the number of cars washed in a six–month period. Find the
number of cars that must be washed in a six–month period for Greg to make a profit.
178)
A)
At least 4770 cars
B)
At least 577 cars
C)
At least 5770 cars
D)
At least 57,693 cars
Solve the equation by making an appropriate substitution.
179)
x2/5 –x1/5 –2= 0
179)
A)
{–2, 1}
B)
{2, –1}
C)
{32, –1}
D)
{–32, 1}
Solve the problem.
180)
A certain store has a fax machine available for use by its customers. The store charges $2.40 to send
the first page and $0.45 for each subsequent page. The total price, P, for the faxing x pages can be
modeled by the formula P =0.45(x – 1) +2.40. Determine the number of pages that can be faxed for
$6.45.
180)
A)
3 pages
B)
10 pages
C)
14 pages
D)
57 pages
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write
and factor the trinomial.
181)
x2–2
5x
181)
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
62
Solve the problem.
182)
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?
182)
A)
10 hours
B)
9 hours
C)
10.5 hours
D)
11 hours
Use interval notation to represent all values of x satisfying the given conditions.
183)
y1=x
3, y2=3+x
12 , and y1y2.
183)
A)
(–, 12]
B)
(12, )
C)
[–12, )
D)
[12, )
D
Use graphs to find the set.
184)
(–, 5)
[–3, 19)
184)
A)
(5, 19)
B)
(–, –3]
C)
[–3, 5)
D)
(–, 19)
C
Solve the problem.
185)
The U.S. Maritime Administration estimated that the cost per ton of building an oil tanker could be
represented by the model y =104,000
x +235 , where y is the cost in dollars per ton and x is the tons (in
thousands). What size of oil tanker (in thousands of tons) can be built for $350 per ton?
185)
A)
62 thousand tons
B)
532 thousand tons
C)
6 thousand tons
D)
178 thousand tons
A
63
A
Find all values of x such that y = 0.
186)
y =x +5
2+x –1
3–3
186)
A)
{18}
B)
7
C)
{0}
D)
{1}
Solve the equation using the quadratic formula.
187)
4x2= – 10x – 2
187)
A)
–5–17
8 , –5+17
8
B)
–10 –17
4 , –10 +17
4
C)
–5–33
4 , –5+33
4
D)
–5–17
4 , –5+17
4
D)
Find the product and write the result in standard form.
188)
–5i(3i – 3)
188)
A)
–15 + 15i
B)
15i – 15i2
C)
15i + 15i2
D)
15 + 15i
D)
Find all values of x satisfying the given conditions.
189)
y1= 8x + 4(4+ x), y2= 3(x –6) + 10x, and y1=y2
189)
A)
{–34}
B)
{10}
C)
{–10}
D)
{34}
D)
64
D)
Solve the problem.
190)
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.
190)
A)
From 2009 to 2013
B)
From 2010 to 2014
C)
From 2010 to 2012
D)
From 2008 to 2012
Solve the equation.
191)
x
3=x
8+6
191)
A)
{24}
B)
{48}
C)
{18}
D)
144
5
Solve the problem.
192)
A standard train ticket in a certain city costs $2.50 per ride. People who use the train also have the
option of purchasing a frequent–rider pass for $15.75 each month. With the pass, a ticket costs only
$1.75 per ride. How many train rides in a month make the frequent–rider pass a better deal than
standard train tickets?
192)
A)
23 or more rides
B)
20 or more rides
C)
22 or more rides
D)
21 or more rides
Solve and check the linear equation.
193)
0.50x – 0.20(50 + x) =0.04(50)
193)
A)
{40}
B)
{20}
C)
{30}
D)
{50}
65
First, write the value(s) that make the denominator(s) zero. Then solve the equation.
194)
8
x+9=5
2x +15
4
194)
A)
No restrictions; –21
22
B)
x 0; –22
21
C)
x 0; –21
22
D)
x 0, 2, 4; –22
21
Solve the problem.
195)
Two cars leave an intersection. One car travels north; the other east. When the car traveling north
had gone 18 mi, the distance between the cars was 6 mi more than the distance traveled by the car
heading east. How far had the east bound car traveled?
195)
A)
24 mi
B)
30 mi
C)
36 mi
D)
18 mi
Use the five–step strategy for solving word problems to find the number or numbers described in the following exercise.
196)
When 10% of a number is added to the number, the result is 165. What is the number?
196)
A)
9
B)
15
C)
150
D)
110
Divide and express the result in standard form.
197)
6– 5i
6+ 3i
197)
A)
7
15 –16
15 i
B)
17
9–16
27 i
C)
7
27 –16
27 i
D)
17
5+4
5i
66
Solve the equation by factoring.
198)
x2+ 4x – 45 = 0
198)
A)
{9, 5}
B)
{–9, 1}
C)
{–9, 5}
D)
{9, –5}
Find all values of x satisfying the given conditions.
199)
y =x2+4x and y =40
199)
A)
–2± 2 11
B)
± 2 11
C)
211 ±2
D)
–2± 2 22
Solve the problem.
200)
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.
200)
A)
0.34 hr
B)
1.3 hr
C)
0.19 hr
D)
18.52 hr
Graph the equation.
201)
y =x2+ 2
201)
67
A)
B)
C)
D)
First, write the value(s) that make the denominator(s) zero. Then solve the equation.
202)
12
x –9+3=6
x –9
202)
A)
x 9; {7}
B)
x 9;
C)
x –9; {15}
D)
x –9; {7}
68
Solve the equation by completing the square.
203)
x2+ 3x – 9 = 0
203)
A)
3+ 3 5
2
B)
{–3–3 5 , –3+3 5}
C)
–3– 3 5
2
D)
–3–3 5
2 , –3+3 5
2
D)
Solve the problem.
204)
The formula for converting Fahrenheit temperature, F, to Celsius temperature, C, is
C =5
9(F – 32).
If Celsius temperature ranges from –85° to –10°, inclusive, what is the range for the Fahrenheit
temperature?
204)
A)
(–121°F, 14°F)
B)
(–27°F, –19°F)
C)
[–27°F, –19°F]
D)
[–121°F, 14°F]
D)
Graph the equation.
205)
y = – 1
3x + 4
205)
69
A)
B)
C)
D)
Find the product and write the result in standard form.
206)
(–9– 3i)(2+ i)
206)
A)
–21 – 15i
B)
–15 – 15i
C)
–15 – 3i
D)
–21 – 3i
B
70
D
Solve the compound inequality. Other than , use interval notation to express the solution set and graph the solution set
on a number line.
207)
–2< x + 2 1
207)
A)
(–4, –1]
B)
[0, 3)
C)
[–4, –1)
D)
(0, 3]
Find all values of x satisfying the given conditions.
208)
y1=1
x +5, y2=3
x +4, y3=–1
x2+9x +20 , and y1+y2=y3
208)
A)
{4}
B)
{–5}
C)
{0}
D)
71