Systems of Inequalities Answers

1

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Which graph represents the solution of x2 + y2 < 25 and y2 < 6x?

A

On a coordinate plane, a circle has center (0, 0) and radius 5. A parabola open right and goes through (6, 6), has vertex (0, 0) and goes through (6, negative 6). Everything inside of the circle and inside of the parabola is shaded.

B

On a coordinate plane, a circle has center (0, 0) and radius 5. A parabola open right and goes through (6, 6), has vertex (0, 0) and goes through (6, negative 6). Everything outside of the circle and inside of the parabola is shaded.

C

On a coordinate plane, a circle has center (0, 0) and radius 5. A parabola open right and goes through (6, 6), has vertex (0, 0) and goes through (6, negative 6). Everything inside of the circle and outside of the parabola is shaded.

D

On a coordinate plane, a circle has center (0, 0) and radius 5. A parabola open right and goes through (6, 6), has vertex (0, 0) and goes through (6, negative 6). Everything outside of the circle and outside of the parabola is shaded.

2

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Which graph represents the solution of y ≤ x2 – 1 and x > y2 – 3?

A

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

B

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

C

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

D

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

3

Review the graph.

A

36 > (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2

B

36 > (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2

C

36 (x – 4)2 + y2

D

36 (x – 4)2 + y2

4

A large garden has a set of underground sprinklers. Suppose the center of the garden is located at the origin of a grid with intervals measured in feet. One sprinkler is positioned at (2, 4) and reaches a radius of 8 feet. The second sprinkler is positioned at (–6, –4) and reaches a radius of 6 feet. The system of inequalities represents this scenario.

A

(–3, –1)

B

(–7, 1)

C

(1, –5)

D

(2, 1)

5

Which graph represents the solution of x2 + 9y2 ≤ 81 and y2 + 2 < x?

A

On a coordinate plane, an ellipse has center (0, 0) and goes through (3, 0), (0, negative 9), (negative 3, 0), and (0, 9). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and outside of the parabola is shaded.

B

On a coordinate plane, an ellipse has center (0, 0) and goes through (3, 0), (0, negative 9), (negative 3, 0), and (0, 9). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and inside of the parabola is shaded.

C

On a coordinate plane, an ellipse has center (0, 0) and goes through (9, 0), (0, negative 3), (negative 9, 0) and (0, 3). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and inside of the parabola is shaded.

D

On a coordinate plane, an ellipse has center (0, 0) and goes through (9, 0), (0, negative 3), (negative 9, 0) and (0, 3). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and outside of the parabola is shaded.

6

Which graph shows the solution to the system of inequalities?

A

On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 3), and goes through (2, 7). An absolute value function opens up goes through (0, 10), has point (3, 1), and goes through (6, 10). Everything outside of the parabola and inside of the absolute value function is shaded.

B

On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 3), and goes through (2, 7). An absolute value function opens up goes through (0, 10), has point (3, 1), and goes through (6, 10). Everything outside of the absolute value function and parabola is shaded.

C

On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 3), and goes through (2, 7). An absolute value function opens up goes through (0, 10), has point (3, 1), and goes through (6, 10). Everything inside of the parabola and outside of the absolute value function is shaded.

D

On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 3), and goes through (2, 7). An absolute value function opens up goes through (0, 10), has point (3, 1), and goes through (6, 10). Everything inside of the parabola and inside the absolute value function is shaded.

7

The sum of the squares of two different numbers is less than or equal to 49. Twice one of the numbers squared is less than the other number. Which system of inequalities represents these criteria?

A

x2 + y2 ≤ 49 and 2x2 < y

B

x2 + y2 ≥ 49 and 2x2 < y

C

x2 + y2 ≤ 49 and x2 < 2y

D

x2 + y2 ≥ 49 and x2 < 2y

8

Review the graph.

A

x2 + y2 ≤ 9 and x ≥ –y2 + 1

B

x2 + y2 ≥ 9 and x ≥ –y2 + 1

C

x2 + y2 ≤ 9 and x ≥ y2 + 1

D

x2 + y2 ≥ 9 and x ≥ y2 + 1

9

Which point is a solution to the system of inequalities?

A

(–2, 6)

B

(1, 9)

C

(2, 8)

D

(0, 4)

10

A pair of fire towers uses technology to search for forest fires. Let the center of the forest be the origin on a coordinate grid. The first fire tower is located 5 km east and 8 km south of the center, and the second fire tower is located 7 km west and 4 km north of the center. The technology at the first tower can locate fires within a radius of 10 km and the second tower within a radius of 9 km. The system of inequalities represents this scenario.

A

2 km east and 3 km south

B

3 km east and 2 km north

C

2 km west and 1 km north

D

1 km west and 2 km south

11

Three times the square of a number is greater than a second number. The square of the second number increased by 6 is greater than the first number. Which system of inequalities represents these criteria?

A

x2 > y and y2 + 6 < x

B

x2 > y and y2 + 6 > x

C

3x2 > y and y2 + 6 > x

D

3x2 > y and y2 + 6 < x

12

Angela lives in a remote area serviced by only two cell phone towers. Tower 1 is located 5 miles west and 2 miles south of her home and transmits a signal for 12 miles. Tower 2 is located 8 miles east and 7 miles north of her home and transmits a signal for 10 miles. Consider the location of Angela’s house to be (0, 0) on a coordinate grid. The system of inequalities represents this scenario.

A

Angela will not have any cell phone service.

B

Angela will have cell phone service from tower 1 only.

C

Angela will have cell phone service from tower 2 only.

D

Angela will have cell phone service from both towers.

13

Which point is a solution to the system x2 + y2 ≤ 25 and x < y2 – 2?

A

(–5, 0)

B

(–2, 0)

C

(5, 0)

D

(2, 2)

14

Which graph represents the solution of < 1 and y ≤?

A

On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 0), (6, negative 2), (3, negative 4), and (0, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and below the curve is shaded.

B

On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 0), (6, negative 2), (3, negative 4), and (0, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and above the curve is shaded.

C

On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 1), (5.5, negative 2), (3, negative 5), and (0.5, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and below the curve is shaded.

D

On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 1), (5.5, negative 2), (3, negative 5), and (0.5, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and above the curve is shaded.

Systems of Inequalities Answers

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