AnswersEAP-Algebra Functions and Data Analysis A CRSolving Linear Systems by Substitution

Solving Linear Systems by Substitution — Unit test Answers

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Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. When Sharon jumps, Megan throws a beach ball up to Sharon with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. To the nearest hundredth of a second, how long after she jumps does the ball reach Sharon?

A
0.65 seconds
B
0.92 seconds
C
1.08 seconds
D
1.15 seconds
2
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Which system of equations is consistent and dependent?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

A picture frame has a perimeter of 100 cm. Its width is 4 cm less than twice its length. What is the width of the picture frame?

A
18 cm
B
32 cm
C
48 cm
D
50 cm
4

Evan washes two types of vehicles. It takes him 30 minutes to wash a car and 40 minutes to wash a truck. He charges $12 to wash a car and $15 to wash a truck. In 270 minutes, Evan made $105 washing cars and trucks. How many trucks did Evan wash?

A
2 trucks
B
3 trucks
C
4 trucks
D
5 trucks
5

A school district needs to arrange transportation for at least 360 students for a field trip. The district can use large buses or small buses. The large buses hold 60 students each and have an operating expense of $300 for the day. The small buses hold 45 students each and have an operating expense of $200 for the day. The district only has chaperones for, at most, seven buses. What is the minimum cost for the transportation for the field trip if each bus has chaperones?

A
$1,400
B
$1,600
C
$1,700
D
$1,800
6

Brandi is downloading music for her MP3 player. Albums cost $10 each, and singles cost $1 each. She wants to purchase at least 5 singles but wants to spend no more than $25 total. If Brandi purchases x albums and y singles, which of the following is a possible combination of albums and singles that Brandi could purchase and stay within her guidelines?

Question illustration
A
5 albums and 2 singles
B
2 albums and 5 singles
C
2 albums and 10 singles
D
10 albums and 2 singles
7

What is the value of y in the solution to the following system of linear equations?

Question illustration
A
3
B
5
C
8
D
12
8

Which graph represents the solution of x2 + (y – 2)2 8x?

A
On a coordinate plane, a circle has center (0, 2) and radius 3. A parabola opens to the right and goes through (8, 8), has vertex (0, 0), and goes through (4, negative 6). Everything inside of the circle and inside of the parabola is shaded.
Option A
B
On a coordinate plane, a circle has center (0, 2) and radius 3. A parabola opens to the right and goes through (8, 8), has vertex (0, 0), and goes through (4, negative 6). Everything inside of the circle and outside of the parabola is shaded.
Option B
C
On a coordinate plane, a circle has center (2, 0) and radius 6. A parabola opens to the right and goes through (8, 8), has vertex (0, 0), and goes through (4, negative 6). Everything inside of the circle and outside of the parabola is shaded.
Option C
D
Option
Option D
9

A pair of weak earthquakes is modeled by a system of inequalities. One earthquake occurred roughly 20 km east and 14 km north of the center of Columbia, NC. The quake could be felt from 25 km away. A couple days later, another earthquake occurred 8 km west and 3 km north of the center of Columbia and could be felt from 14 km away. If Columbia is located at (0, 0) on a coordinate grid, the system of inequalities represents this scenario.

Question illustration
A
4 km west and 12 km south
B
6 km west and 4 km north
C
2 km east and 10 km north
D
6 km east and 8 km north
10

Review the graph.

Question illustration
A
y ≤ x2 – 8 and x > y2 + 1
B
y ≥ x2 – 8 and x < y2 + 1
C
y ≤ x2 + 1 and x > y2 – 8
D
y ≥ x2 + 1 and x < y2 – 8
11

What is the minimum value of C = 7x + 8y, given the constraints on x and y listed below?

Question illustration
A
32
B
42
C
46
D
64
12

The constraints of a problem are listed below. What are the vertices of the feasible region?

Question illustration
A
(0, 0), (0, 3), (2, 3), (5, 0)
B
(0, 0), (0, 5), (2, 3), (5, 0)
C
(0, 0), (2, 3), (5, 0)
D
(0, 3), (0, 5), (2, 3)
13

The constraints of a problem are listed below. What are the vertices of the feasible region?

Question illustration
A
(0, 0), (0, 2.5), (1.5, 2), (3, 0)
B
(0, 0), (0, 4), (1.5, 2), (7.5, 0)
C
(0, 2.5), (1.5, 2), (4, 3)
D
(0, 4), (1.5, 2), (7.5, 0)
14

Raj tried to solve the system below. Raj’s Work What error did Raj make?

Question illustration
A
Raj forgot to multiply the value of x by 9 when solving for the value of y.
B
Raj subtracted 120 from both sides when he solved for the value of x.
C
Raj forgot the negative sign when substituting –15 + 9x for y.
D
Raj found the value of –y instead of y.
15

Which statement describes the system of equations?

Question illustration
A
The system has infinitely many solutions.
B
The system has no solution.
C
The system has one solution .
Option C
D
The system has one solution .
Option D
16

Organizers of the town fair make a total of $706 from selling 164 hot dogs and 74 hamburgers at one of their concession stands. At their other concession stand, they make $884 by selling 256 hot dogs and 61 hamburgers. If the prices are the same at both concession stands, what is the price of a hot dog?

A
$0.40
B
$2.50
C
$3.75
D
$4.00
17

A cell phone carrier offers two plans for text messaging. Plan A costs $20 per month plus $0.05 per text. Plan B costs $10 per month plus $0.10 per text. For how many text messages per month are the plans the same cost?

A
20
B
30
C
200
D
300
18

Which graph represents the solution to the system of inequalities?

Question illustration
A
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 8), (negative 4, 0), and (0, 8). Everything inside of the ellipse and below the curve is shaded.
Option A
B
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 8), (negative 4, 0), and (0, 8). Everything inside of the ellipse and above the curve is shaded.
Option B
C
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (8, 0), (0, negative 4), (negative 8, 0) and (0, 4). Everything inside of the ellipse and below the curve is shaded.
Option C
D
Option
Option D
19

A school choir has 36 members. This year, there are three times as many returning members as new members. How many new members are in the choir this year?

A
9 new members
B
12 new members
C
24 new members
D
27 new members
20

What is the point of intersection when the system of equations below is graphed on the coordinate plane?

Question illustration
A
(1, –3)
B
(–1, 3)
C
(1, 3)
D
(–1, –3)

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