Systems of Inequalities Answers
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1
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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.
2
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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.
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 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.
5
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.
6
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)7
Review the graph.
A
x2 + y2 ≤ 9 and x ≥ –y2 + 1B
x2 + y2 ≥ 9 and x ≥ –y2 + 1C
x2 + y2 ≤ 9 and x ≥ y2 + 1D
x2 + y2 ≥ 9 and x ≥ y2 + 18
Which point is a solution to the system of inequalities?
A
(–2, 6)B
(1, 9)C
(2, 8)D
(0, 4)9
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.
10
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.
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