AnswersEAP-Algebra Functions and Data Analysis A CRModeling with Systems of Linear Inequalities

Modeling with Systems of Linear Inequalities — Unit test Answers

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Ori needed at least $1.47 in postage to mail an envelope to his cousin overseas. If x represents the number of $0.44 cent stamps he has and y represents the number of $0.10 cent stamps he has, the inequality representing the number of stamps he can use to mail the envelope is 0.44x+0.10y≥1.47.

A
1
B
2
C
3
D
5
2
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On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded.

Question illustration
A
y > 2x + 3
B
y < 2x + 3
C
y > −2x + 3
D
y < −2x + 3
3

On a coordinate plane, 2 dashed straight lines are shown. The first line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything to the right of the line is shaded. The second line has a negative slope and goes through (negative 2, 0) and (2, negative 4). Everything to the right of the line is shaded.

Question illustration
y
y > x + 1
y
y < x – 1
y
y > x – 1
y
y < x + 1
4

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

Question illustration
(
(0, 0), (0, 2.5), (1.5, 2), (3, 0)
(
(0, 0), (0, 4), (1.5, 2), (7.5, 0)
(
(0, 2.5), (1.5, 2), (4, 3)
(
(0, 4), (1.5, 2), (7.5, 0)
5

The questions in the first section on a test are worth 3 points and the questions in the second section are worth 5 points. Let x represent the number of correct questions from the first section, and let y represent the number of correct questions from the second section. Sydney earned more than 80 points on the test. The inequality representing her score is 3x+5y>80.

A
1
B
2
C
7
D
8
6

During free play, there must be more than 4 campers in a group, and the number of boys must not exceed the number of girls by more than 5. Which graph represents this system of inequalities?

A
Option
B
Option
C
Option
D
Option
7

Which statements are true about the graph of the system of linear inequalities? Select two options.y > 3x – 4y 3x − 4 has shading above a dashed line.The graph of y < x + 1 has shading below a dashed line.The graphs of the inequalities will intersect.There are no solutions to the system.The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).

Question illustration
A
The graph of y > 3x − 4 has shading above a dashed line.
B
The graph of y < x + 1 has shading below a dashed line.
Option B
C
The graphs of the inequalities will intersect.
D
There are no solutions to the system.
E
The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).
8

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?

$
$1,400
$
$1,600
$
$1,700
$
$1,800
9

Before any dinner service, the manager confirms when the number of reservations at a restaurant is subtracted from twice the number of loaves of bread on hand must be greater than 5. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

A
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 5) and (3, 1). Everything to the right of the line is shaded.
Option A
B
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 5) and (3, 1). Everything to the left of the line is shaded.
Option B
C
On a coordinate plane, a dashed straight line has a negative slope and goes through (negative 3, 1) and (0, negative 5). Everything to the left of the line is shaded.
Option C
D
On a coordinate plane, a dashed straight line has a negative slope and goes through (negative 3, 1) and (0, negative 5). Everything to the right of the line is shaded.
Option D
10

The system of inequalities in the graph represents the change in an account, y, depending on the days delinquent, x.

Question illustration
A
≤
B
≥
C
<
D
>
11

Which is true about the solution to the system of inequalities shown?y > 3x + 1y < 3x – 3

Question illustration
O
Only values that satisfy y > 3x + 1 are solutions.
O
Only values that satisfy y < 3x – 3 are solutions.
V
Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.
T
There are no solutions.
12

Which ordered pairs are in the solution set of the system of linear inequalities?y > x + 2y < 2x + 3

Question illustration
A
(2, 2), (3, 1), (4, 2)
B
(2, 2), (3, –1), (4, 1)
C
(2, 2), (1, –2), (0, 2)
D
(2, 2), (1, 2), (2, 0)
13

Which description of the graph of the linear inequality y > 3x – 8 is correct?

A
The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below the line.
B
The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the line.
C
The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the line.
D
The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line.
14

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 3) and (3, 1). Everything below and to the right of the line is shaded.

Question illustration
A
y > x – 2
Option A
B
y < x + 2
Option B
C
y > x + 1
Option C
D
y < x – 1
Option D
15

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

Question illustration
3
32
4
42
4
46
6
64
16

The members of the drama club have 100 tickets to sell to the school play. Students pay $5 per ticket, and nonstudents pay $10 per ticket. The drama club needs to collect at least $800 in total ticket sales. The system of inequalities represents the number of student tickets, s, and the number of nonstudent tickets, n, the members must sell. s + n ≤ 1005s + 10n ≥ 800

4
40
6
60
8
80
1
100
17

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.

Question illustration
A
(2, 3)
B
(2, 1)
C
(3, –2)
D
(–1, 3)
18

A ride at an amusement park has two options for cars, one that holds 6 passengers and one that holds 3 passengers. If the ride designer wants to make sure that each run holds at least 12 passengers, which graph represents the overall equation and shows the possible combinations of the number of 6-passenger cars, x, and the number of 3-passenger cars y (not all points may apply to the scenario)?

A
Option
B
Option
C
Option
D
Option
19

Dwayne is selling hamburgers and cheeseburgers. He has 100 burger buns. Each hamburger sells for $3, and each cheeseburger sells for $3.50. Which system of inequalities represents the number of hamburgers, h, and the number of cheeseburgers, c, he must sell to have sales of at least $80?

h
h + c ≤ 803h + 3.5c ≤ 100
h
h + c ≤ 803h + 3.5c ≥ 100
h
h + c ≤ 1003h + 3.5c ≤ 80
h
h + c ≤ 1003h + 3.5c ≥ 80

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