Systems of Inequalities Answers
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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.
2
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Which point is a solution to the system of inequalities?
A
(–2, 6)B
(1, 9)C
(2, 8)D
(0, 4)3
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 < yB
x2 + y2 ≥ 49 and 2x2 < yC
x2 + y2 ≤ 49 and x2 < 2yD
x2 + y2 ≥ 49 and x2 < 2y4
Which graph represents the solution to the system of inequalities?
A
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). A parabola opens to the right and goes through (9, 4), has vertex (4, 0), and goes through (9, negative 4). Another parabola opens to the left and goes through (negative 9, 4), has vertex (negative 4, 0), and goes through (negative 9, negative 4). Everything outside of the parabola and above the curve is shaded.
B
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). A parabola opens to the right and goes through (9, 4), has vertex (4, 0), and goes through (9, negative 4). Another parabola opens to the left and goes through (negative 9, 4), has vertex (negative 4, 0), and goes through (negative 9, negative 4). Everything below the curve and inside both parabolas is shaded.
C
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 2), (negative 4, 0), and (0, 2). Everything above the curve and inside of the ellipse is shaded.
D
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 2), (negative 4, 0), and (0, 2). Everything below the curve and inside of the ellipse is shaded.
5
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 southB
3 km east and 2 km northC
2 km west and 1 km northD
1 km west and 2 km south6
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.
7
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.
8
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)9
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.
10
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 > xC
3x2 > y and y2 + 6 > xD
3x2 > y and y2 + 6 < xDid you find these answers helpful?
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