AnswersAlgebra 2Systems of Inequalities

Systems of Inequalities — Quiz Answers

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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 open paren 0 comma 0 close paren on a coordinate grid, the system of inequalities represents this scenario. open parenthesis x minus 20 close parenthesis squared plus open parenthesis y minus 14 close parenthesis squared is less than or equal to 625; open parenthesis x plus 8 close parenthesis squared plus open parenthesis y minus 3 close parenthesis squared is less than or equal to 196 Which location relative to Columbia felt both earthquakes?

A
2 km east and 10 km north
B
6 km west and 4 km north
C
6 km east and 8 km north
D
4 km west and 12 km south
2
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Which graph represents the solution of x squared plus y squared is less than 25 and y squared is less than 6 x ?

A
Image with description 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.
B
Image with description 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
Image with description 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
Image with description 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.
3

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 open paren 2 comma 4 close paren and reaches a radius of 8 feet. The second sprinkler is positioned at open paren negative 6 comma negative 4 close paren and reaches a radius of 6 feet. The system of inequalities represents this scenario. open parenthesis x minus 2 close parenthesis squared plus open parenthesis y minus 4 close parenthesis squared is less than or equal to 64; open parenthesis x plus 6 close parenthesis squared plus open parenthesis y plus 4 close parenthesis squared is less than or equal to 36 Which location is in the region for plants receiving the maximum amount of water?

A
open paren negative 7 comma 1 close paren
B
open paren 1 comma negative 5 close paren
C
open paren negative 3 comma negative 1 close paren
D
open paren 2 comma 1 close paren
4

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. open parenthesis x minus 5 close parenthesis squared plus open parenthesis y plus 8 close parenthesis squared is less than or equal to 100; open parenthesis x plus 7 close parenthesis squared plus open parenthesis y minus 4 close parenthesis squared is less than or equal to 81 At which location, from the origin, would a fire be detected by both towers?

A
1 km west and 2 km south
B
2 km west and 1 km north
C
2 km east and 3 km south
D
3 km east and 2 km north
5

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 open paren 0 comma 0 close paren on a coordinate grid. The system of inequalities represents this scenario. open parenthesis x plus 5 close parenthesis squared plus open parenthesis y plus 2 close parenthesis squared is less than or equal to 144; open parenthesis x minus 8 close parenthesis squared plus open parenthesis y minus 7 close parenthesis squared is less than or equal to 100 Angela travels to a friend’s house, which is 4 miles east and 8 miles north of her house. Will Angela have cell phone service at her friend’s house?

A
Angela will not have any cell phone service.
B
Angela will have cell phone service from both towers.
C
Angela will have cell phone service from tower 2 only.
D
Angela will have cell phone service from tower 1 only.
6

Which graph represents the solution of y is less than or equal to x squared minus 1 and x is greater than y squared minus 3 ?

A
Image with description 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.
B
Image with description 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.
C
Image with description 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.
D
Image with description 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.
7

Which graph represents the solution of x squared plus 9 y squared is less than or equal to 81 and y squared plus 2 is less than x ?

A
Image with description 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.
B
Image with description 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
Image with description 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.
D
Image with description 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.
8

Which point is a solution to the system x squared plus y squared is less than or equal to 25 and x is less than y squared minus 2 ?

A
open paren 5 comma 0 close paren
B
open paren 2 comma 2 close paren
C
open paren negative 2 comma 0 close paren
D
open paren negative 5 comma 0 close paren
9

Which system of inequalities is shown in the graph?

A
36 is greater than open paren x minus 2 close paren squared plus open paren y plus 3 close paren squared and 16 is greater than open paren x minus 4 close paren squared plus y squared
B
36 is greater than open paren x plus 3 close paren squared plus open paren y minus 2 close paren squared and 16 is greater than open paren x minus 4 close paren squared plus y squared
C
36 is less than open paren x minus 2 close paren squared plus open paren y plus 3 close paren squared and 16 is greater than open paren x minus 4 close paren squared plus y squared
D
36 is less than open paren x plus 3 close paren squared plus open paren y minus 2 close paren squared and 16 is greater than open paren x minus 4 close paren squared plus y squared
10

Which system of inequalities is shown in the graph?

A
x squared plus y squared is greater than or equal to 9 and x is greater than or equal to y squared plus 1
B
x squared plus y squared is less than or equal to 9 and x is greater than or equal to y squared plus 1
C
x squared plus y squared is greater than or equal to 9 and x is greater than or equal to negative y squared plus 1
D
x squared plus y squared is less than or equal to 9 and x is greater than or equal to negative y squared plus 1

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