Linear Programming — Test Answers

1

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A system of inequalities, where x is the rate of a spaceship in a video game and y is where the ship travels on the screen in 3.5 seconds, is represented by the graph.

A

≤

B

≥

C

<

D

>

2

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Which point is a solution of x2 + y2 > 49 and y ≤ –x2 – 4?

A

(–8, –1)

B

(–3, 1)

C

(1, –9)

D

(0, –6)

3

The graph of a system of inequalities is shown.

A

y > 2xx + 2y ≤ –8

B

y ≥ 2xx + 2y < –8

C

y < 2xx + 2y ≥ –8

D

y ≤ 2xx + 2y > –8

4

Which ordered pair makes both inequalities true?y –x + 4

A

(4,0)

B

(1,2)

C

(0,4)

D

(2,1)

5

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 2, 3) and (0, negative 1). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (1, 0). Everything to the right of the line is shaded.

A

y<−2x+2

B

y>−2x+2

C

y<2x−2

D

y>2x−2

6

Review the graph.

A

x2 + y2 > 9 and y < –x2 + 2

B

x2 + y2 < 9 and y < –x2 + 2

C

x2 + y2 > 9 and x < –y2 + 2

D

x2 + y2 < 9 and x < –y2 + 2

7

Charlene is knitting a baby blanket. She wants its width, w, to be at least half its length, l. She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches. The system of inequalities shown represents the width of the blanket in inches, w, and the length in inches, l. w ≥ 0.5l2l + 2w ≤ 180

A

30 inches

B

45 inches

C

60 inches

D

90 inches

8

The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is the greater integer, which system of inequalities could represent the values of a and b?

A

a + b ≥ 30 b ≥ a + 10

B

a + b ≥ 30 b ≤ a – 10

C

a + b ≤ 30 b ≥ a + 10

D

a + b ≤ 30 b ≤ a – 10

9

A farm irrigation system waters a large field. Consider the center of the field as the origin and the rest of the field as a grid measured in yards. The first irrigation unit is located at the point (–400, –200) and waters 500 yards in every direction. The second is located at (200, 300) and waters 400 yards in every direction. The system of inequalities represents this scenario.

A

(100, 100)

B

(–100, 100)

C

(100, –100)

D

(–100, –100)

10

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

A

y > x – 2 and x – 2y < 4

B

y > x + 2 and x + 2y < 4

C

y > x – 2 and x + 2y < 4

D

y > x – 2 and x + 2y < –4

11

Which ordered pair is in the solution set of the system of linear inequalities?y > x – 1y < x – 1

A

(–5, 2)

B

(2, 2)

C

(5, 2)

D

no solution

12

Which ordered pairs make both inequalities true? Select two options. y x + 1

A

(–1, 3)

B

(0, 2)

C

(1, 2)

D

(2, –1)

E

(2, 2)

13

Which graph represents the solution of y ≤ x2 + 1 and x > y2 – 5?

A

On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 1) and goes through (2, 6). Another parabola opens to the right and goes through (4, 3), has vertex (negative 5, 0), and goes through (4, negative 3). Everything outside of the first parabola and inside of the second parabola is shaded.

B

On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 1) and goes through (2, 6). Another parabola opens to the right and goes through (4, 3), has vertex (negative 5, 0), and goes through (4, negative 3). Everything inside of both parabolas is shaded.

C

On a coordinate plane, a parabola opens up and goes through (negative 3, 4), has vertex (0, negative 5), and goes through (3, 4). Another parabola opens to the right and goes through (5, 2), has vertex (1, 0), and goes through (5, negative 2). Everything inside of both parabolas is shaded.

D

On a coordinate plane, a parabola opens up and goes through (negative 3, 4), has vertex (0, negative 5), and goes through (3, 4). Another parabola opens to the right and goes through (5, 2), has vertex (1, 0), and goes through (5, negative 2). Everything inside the first parabola and outside of the second parabola is shaded.

14

One winter day, the outside temperature, y, never dropped below −1°. The inside temperature, x, of a car was always at least 4° warmer than the outside temperature. Which graph represents the solution to the system of inequalities that models this situation?

A

Option

B

Option

C

Option

D

Option

15

One half the square of a number is less than a second number. The sum of 3 and the opposite of the second number is greater than the square of the first number.Which graph represents the solution set?

A

On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything outside of the first parabola and inside the second parabola is shaded.

B

On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything outside of both parabolas is shaded.

C

On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything inside of the first parabola and outside of the second parabola is shaded.

D

On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything inside the first parabola and inside the second parabola is shaded.

16

Consider the system of inequalities and its graph.y ≤ –0.75xy ≤ 3x – 2

A

1

B

2

C

3

D

4

17

A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and each pie, p, requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?

A

t ≤ 40 p ≤ 184

B

t ≤ 40 8p ≤ 184

C

t ≤ 40p + 8t ≤ 184

D

t ≤ 408p + t ≤ 184

18

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, 3) and (3, 4). Everything above the line is shaded. The second dashed line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the right of the line is shaded.

A

y > x + 3 and 3x – y > 2

B

y > x + 3 and 3x – y > 2

C

y > x + 3 and 3x + y > 2

D

y > x + 3 and 2x – y > 2

19

Which ordered pairs are in the solution set of the system of linear inequalities?y > xy < x + 1

A

(5, –2), (3, 1), (–4, 2)

B

(5, –2), (3, –1), (4, –3)

C

(5, –2), (3, 1), (4, 2)

D

(5, –2), (–3, 1), (4, 2)

20

Question text not available

A

y > x – 2 and y < x + 1

B

y x + 1

C

y x + 1

D

y > x – 2 and y < x + 1

Linear Programming — Test Answers

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