Find all real solutions to the system of equations using the substitution method. -$\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 169 \\ x + y = 17 \end{array}$

A) (-12, -5), (-5, -12) B) (12, -5), (5, -12) C) (12, 5), (5, 12) D) (-12, 5), (-5, 12) A) (-12, -5), (-5, -12) B) (12, -5), (5, -12) C) (12, 5), (5, 12) D) (-12, 5), (-5, 12)

A) parabola B) ellipse C) circle D) hyperbola A) parabola B) ellipse C) circle D) hyperbola

Find all real solutions to the system of equations using the addition method. -$\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 27 \\ x ^ { 2 } + y ^ { 2 } = 39 \end{array}$

A) $( - \sqrt { 33 } , - \sqrt { 6 } )$ B) $( \sqrt { 33 } , \sqrt { 6 } ) , ( - \sqrt { 33 } , \sqrt { 6 } ) , ( \sqrt { 33 } , - \sqrt { 6 } ) , ( - \sqrt { 33 } , - \sqrt { 6 } )$ C) (0, 0) D) $( \sqrt { 33 } , \sqrt { 6 } ) , ( - \sqrt { 33 } , \sqrt { 6 } )$ A) $( - \sqrt { 33 } , - \sqrt { 6 } )$ B) $( \sqrt { 33 } , \sqrt { 6 } ) , ( - \sqrt { 33 } , \sqrt { 6 } ) , ( \sqrt { 33 } , - \sqrt { 6 } ) , ( - \sqrt { 33 } , - \sqrt { 6 } )$ C) (0, 0) D) $( \sqrt { 33 } , \sqrt { 6 } ) , ( - \sqrt { 33 } , \sqrt { 6 } )$

Find all real solutions to the system of equations using the addition method. -$\begin{aligned} x ^ { 2 } - 2 y ^ { 2 } & = 2 \\ 3 x ^ { 2 } + 2 y ^ { 2 } & = 14 \end{aligned}$

A) (2, 1), (2, -1), (-2, 1), (-2, -1) B) (-1, 2), (1, -2) C) (1, 2), (-1, 2), (1, -2), (-1, -2) D) (2, 1), (-2, -1) A) (2, 1), (2, -1), (-2, 1), (-2, -1) B) (-1, 2), (1, -2) C) (1, 2), (-1, 2), (1, -2), (-1, -2) D) (2, 1), (-2, -1)

Exam 11: Conic Sections

Determine the midpoint of the line segment between the pair of points. - $\left( - \frac { 8 } { 5 } , - \frac { 3 } { 2 } \right) \text { and } \left( - \frac { 7 } { 5 } , - \frac { 5 } { 2 } \right)$

(Multiple Choice)

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Question 21

Indicate whether the equation represents an ellipse, hyperbola, circle, or parabola. In equations that contain bothth $x ^ { 2 }$ 2 and $y ^ { 2 }$ terms, divide both terms, divide bothsides of the equation by the constant term to put the equation in a more recognizable form. - $3 x ^ { 2 } + 8 x - y = 72$

(Multiple Choice)

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Question 22

Graph the equation. - $9 ( x - 2 ) ^ { 2 } + 16 ( y + 2 ) ^ { 2 } = 144$ $Graph the equation. - 9 ( x - 2 ) ^ { 2 } + 16 ( y + 2 ) ^ { 2 } = 144$

(Multiple Choice)

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Question 23

Graph the equation. - $x = - 2 ( y + 4 ) ^ { 2 } - 1$ $Graph the equation. - x = - 2 ( y + 4 ) ^ { 2 } - 1$

(Multiple Choice)

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Question 24

Find all real solutions to the system of equations using the substitution method. - +=169 x+y=17

(Multiple Choice)

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Question 25

Determine the distance between the pair of points. -(0, -2)and (5, -2)

(Multiple Choice)

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Question 26

Write the equation of the circle. Assume the radius is a whole number. -

(Multiple Choice)

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Question 27

Write the equation in the form $\mathbf { y = a ( x - h )} \mathbf {^ { 2 } + k.}$ - $y = x ^ { 2 } + 2 x - 7$

(Multiple Choice)

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Question 28

Name the conic. -

(Multiple Choice)

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Question 29

Find all real solutions to the system of equations using the addition method. - -=27 +=39

(Multiple Choice)

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Question 30

Solve the problem. -The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 38 feet and the height of the arch over the center of the roadway is 14 feet. Two trucks plan to use This road. They are both 12 feet wide. Truck 1 has an overall height of 13 feet and Truck 2 has an overall height Of 14 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

(Multiple Choice)

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Question 31

Write the equation of the circle with the given center and radius. -Center (7, 6), radius 5

(Multiple Choice)

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Question 32

Graph the equation. - $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$ $Graph the equation. - x ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$

(Multiple Choice)

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Question 33

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation. - $x=y^{2}-10 y+30$ $Write the equation in the form \mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h} h a nd then graph the equation. - x=y^{2}-10 y+30$

(Multiple Choice)

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Question 34

Graph the equation. - $y = 4 ( x + 1 ) ^ { 2 } + 5$ $Graph the equation. - y = 4 ( x + 1 ) ^ { 2 } + 5$

(Multiple Choice)

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Question 35

Find the equation of the ellipse satisfying the given conditions. -(4, 0), (-4, 0), (0, 3), (0, -3)are the endpoints of the major and minor axes.

(Multiple Choice)

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Question 36

Use the method of completing the square to write the equation in standard form. Then graph the equation. - $x ^ { 2 } + y ^ { 2 } + 4 x + 4 y + 4 = 0$ $Use the method of completing the square to write the equation in standard form. Then graph the equation. - x ^ { 2 } + y ^ { 2 } + 4 x + 4 y + 4 = 0$

(Multiple Choice)

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Question 37

Find all real solutions to the system of equations using the addition method. - -2 =2 3+2 =14

(Multiple Choice)

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Question 38

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation. - $x=-y^{2}-6 y-3$ $Write the equation in the form \mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h} h a nd then graph the equation. - x=-y^{2}-6 y-3$

(Multiple Choice)

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Question 39

Determine the distance between the pair of points. -(-7, -7)and (5, 3)

(Multiple Choice)

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Question 40

Showing 21 - 40 of 132

Determine the midpoint of the line segment between the pair of points. - $\left( - \frac { 8 } { 5 } , - \frac { 3 } { 2 } \right) \text { and } \left( - \frac { 7 } { 5 } , - \frac { 5 } { 2 } \right)$

Graph the equation. - $9 ( x - 2 ) ^ { 2 } + 16 ( y + 2 ) ^ { 2 } = 144$ $Graph the equation. - 9 ( x - 2 ) ^ { 2 } + 16 ( y + 2 ) ^ { 2 } = 144$

Graph the equation. - $x = - 2 ( y + 4 ) ^ { 2 } - 1$ $Graph the equation. - x = - 2 ( y + 4 ) ^ { 2 } - 1$

Find all real solutions to the system of equations using the substitution method. - +=169 x+y=17

Determine the distance between the pair of points. -(0, -2)and (5, -2)

Write the equation of the circle. Assume the radius is a whole number. -

Write the equation in the form $\mathbf { y = a ( x - h )} \mathbf {^ { 2 } + k.}$ - $y = x ^ { 2 } + 2 x - 7$

Name the conic. -

Find all real solutions to the system of equations using the addition method. - -=27 +=39

Write the equation of the circle with the given center and radius. -Center (7, 6), radius 5

Graph the equation. - $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$ $Graph the equation. - x ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$

Graph the equation. - $y = 4 ( x + 1 ) ^ { 2 } + 5$ $Graph the equation. - y = 4 ( x + 1 ) ^ { 2 } + 5$

Find the equation of the ellipse satisfying the given conditions. -(4, 0), (-4, 0), (0, 3), (0, -3)are the endpoints of the major and minor axes.

Find all real solutions to the system of equations using the addition method. - -2 =2 3+2 =14

Determine the distance between the pair of points. -(-7, -7)and (5, 3)

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Sequences, Series, and Probability

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Exam 11: Conic Sections

Determine the midpoint of the line segment between the pair of points. - (−85,−32) and (−75,−52)\left( - \frac { 8 } { 5 } , - \frac { 3 } { 2 } \right) \text { and } \left( - \frac { 7 } { 5 } , - \frac { 5 } { 2 } \right)(−58​,−23​) and (−57​,−25​)

Graph the equation. - 9(x−2)2+16(y+2)2=1449 ( x - 2 ) ^ { 2 } + 16 ( y + 2 ) ^ { 2 } = 1449(x−2)2+16(y+2)2=144

Graph the equation. - x=−2(y+4)2−1x = - 2 ( y + 4 ) ^ { 2 } - 1x=−2(y+4)2−1

Find all real solutions to the system of equations using the substitution method. - +=169 x+y=17

Determine the distance between the pair of points. -(0, -2)and (5, -2)

Write the equation of the circle. Assume the radius is a whole number. -

Write the equation in the form y=a(x−h)2+k.\mathbf { y = a ( x - h )} \mathbf {^ { 2 } + k.}y=a(x−h)2+k. - y=x2+2x−7y = x ^ { 2 } + 2 x - 7y=x2+2x−7

Name the conic. -

Find all real solutions to the system of equations using the addition method. - -=27 +=39

Write the equation of the circle with the given center and radius. -Center (7, 6), radius 5

Graph the equation. - x2+(y−5)2=9x ^ { 2 } + ( y - 5 ) ^ { 2 } = 9x2+(y−5)2=9

Write the equation in the form y=a(x−h)2+k or x=a(y−k)2+h\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}y=a(x−h)2+k or x=a(y−k)2+h h a nd then graph the equation. - x=y2−10y+30x=y^{2}-10 y+30x=y2−10y+30

Graph the equation. - y=4(x+1)2+5y = 4 ( x + 1 ) ^ { 2 } + 5y=4(x+1)2+5

Find the equation of the ellipse satisfying the given conditions. -(4, 0), (-4, 0), (0, 3), (0, -3)are the endpoints of the major and minor axes.

Use the method of completing the square to write the equation in standard form. Then graph the equation. - x2+y2+4x+4y+4=0x ^ { 2 } + y ^ { 2 } + 4 x + 4 y + 4 = 0x2+y2+4x+4y+4=0

Find all real solutions to the system of equations using the addition method. - -2 =2 3+2 =14

Write the equation in the form y=a(x−h)2+k or x=a(y−k)2+h\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}y=a(x−h)2+k or x=a(y−k)2+h h a nd then graph the equation. - x=−y2−6y−3x=-y^{2}-6 y-3x=−y2−6y−3

Determine the distance between the pair of points. -(-7, -7)and (5, 3)

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Sequences, Series, and Probability

Filters

Determine the midpoint of the line segment between the pair of points. - $\left( - \frac { 8 } { 5 } , - \frac { 3 } { 2 } \right) \text { and } \left( - \frac { 7 } { 5 } , - \frac { 5 } { 2 } \right)$

Graph the equation. - $9 ( x - 2 ) ^ { 2 } + 16 ( y + 2 ) ^ { 2 } = 144$ $Graph the equation. - 9 ( x - 2 ) ^ { 2 } + 16 ( y + 2 ) ^ { 2 } = 144$

Graph the equation. - $x = - 2 ( y + 4 ) ^ { 2 } - 1$ $Graph the equation. - x = - 2 ( y + 4 ) ^ { 2 } - 1$

Write the equation in the form $\mathbf { y = a ( x - h )} \mathbf {^ { 2 } + k.}$ - $y = x ^ { 2 } + 2 x - 7$

Graph the equation. - $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$ $Graph the equation. - x ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$

Graph the equation. - $y = 4 ( x + 1 ) ^ { 2 } + 5$ $Graph the equation. - y = 4 ( x + 1 ) ^ { 2 } + 5$