Question 1

Identify the center and radius of the circle.

Accepted Answer

To find the center and radius of the circle given by the equation $x^2 - 8x + y^2 = 20$, we need to complete the square for the x-terms. The equation can be rewritten as $x^2 - 8x + 16 + y^2 = 20 + 16$ by adding 16 to both sides to complete the square, resulting in $(x-4)^2 + y^2 = 36$. This shows the circle has a center at $(4, 0)$ and a radius $r = \sqrt{36} = 6$.

Question 2

Write the word or phrase that best completes each statement or answers the question.&#10;Find all values of k so that the distance from (-10, 6) to (-7, k) is 5 units.

Accepted Answer

k = 2 or 10

Question 3

Determine if the three points define the vertices of a right triangle. (-1, -2), (-5, 6), (7, 2)&#10;A) Yes&#10;B) No

Accepted Answer

To determine if the three points define the vertices of a right triangle, we can use the distance formula to calculate the lengths of the sides formed by these points and then apply the Pythagorean theorem. The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.1. Distance between (-1, -2) and (-5, 6):$$d_1 = \sqrt{(-5 + 1)^2 + (6 + 2)^2} = \sqrt{(-4)^2 + (8)^2} = \sqrt{16 + 64} = \sqrt{80}$$2. Distance between (-1, -2) and (7, 2):$$d_2 = \sqrt{(7 + 1)^2 + (2 + 2)^2} = \sqrt{(8)^2 + (4)^2} = \sqrt{64 + 16} = \sqrt{80}$$3. Distance between (-5, 6) and (7, 2):$$d_3 = \sqrt{(7 + 5)^2 + (2 - 6)^2} = \sqrt{(12)^2 + (-4)^2} = \sqrt{144 + 16} = \sqrt{160}$$We see that $d_1^2 + d_2^2 = 80 + 80 = 160$, which equals $d_3^2$. This satisfies the Pythagorean theorem ($a^2 + b^2 = c^2$), indicating that the points form a right triangle.

Question 4

Write the word or phrase that best completes each statement or answers the question.&#10;Write an equation of a circle whose center is (20, 4) and that passes through the point (21, -5).

Accepted Answer

The answer of Write the word or phrase that best...

Question 5

Use the distance formula to find the distance between the two points. (4, 0) and (0, -7)&#10;A) 65&#10;B) 11&#10;C)  &#10;D) 3

Accepted Answer

The answer of Use the distance formula to find the...

Question 6

Use the distance formula to find the distance between the two points. (-3, 18) and (-3, -6)&#10;A) -12&#10;B) 24&#10;C) 12&#10;D) -24

Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For the points (-3, 18) and (-3, -6), the distance is $\sqrt{(-3 - (-3))^2 + (-6 - 18)^2} = \sqrt{0 + (-24)^2} = \sqrt{576} = 24$.

Question 7

Write the word or phrase that best completes each statement or answers the question.&#10;Write an equation of a circle centered at (10, -2) with a radius of 10.

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

Identify the center and radius of the circle.

Accepted Answer

The equation of a circle in the form $(x - h)^2 + (y - k)^2 = r^2$ has a center at $(h, k)$ and a radius $r$. Here, $h = \frac{5}{7}$, $k = 0$, and $r^2 = 8$, so $r = \sqrt{8} = 2\sqrt{2}$.

Question 9

Identify the center and radius of the circle.

Accepted Answer

To find the center and radius of the circle given by the equation $x^2 + 9x + y^2 - \frac{3}{2}y = 10$, we need to complete the square for both $x$ and $y$ terms. For $x^2 + 9x$, we add and subtract $\left(\frac{9}{2}\right)^2 = \frac{81}{4}$. For $y^2 - \frac{3}{2}y$, we add and subtract $\left(\frac{3}{4}\right)^2 = \frac{9}{16}$. Adding these to both sides, we get: $$x^2 + 9x + \frac{81}{4} + y^2 - \frac{3}{2}y + \frac{9}{16} = 10 + \frac{81}{4} + \frac{9}{16}$$Simplifying, we get:$$\left(x + \frac{9}{2}\right)^2 + \left(y - \frac{3}{4}\right)^2 = \frac{493}{16}$$Thus, the center is $\left(-\frac{9}{2}, \frac{3}{4}\right)$ and the radius $r = \sqrt{\frac{493}{16}} = \frac{\sqrt{493}}{4}$.

Question 10

11eb44e8_09cd_688a_b8e7_31c88366e8ef_TB7603_00

Accepted Answer

The equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. Here, the center is $(- \frac{2}{3}, \frac{1}{3})$ and the radius is $3\sqrt{5}$, so the equation is $(x + \frac{2}{3})^2 + (y - \frac{1}{3})^2 = (3\sqrt{5})^2 = 45$.

Question 11

Which of the following is the equation of a circle?

Accepted Answer

The answer of Which of the following is the equation...

Question 12

Write the word or phrase that best completes each statement or answers the question.&#10;Identify the center and radius of the circle and then graph the circle.

Accepted Answer

The answer of Write the word or phrase that best...

Question 13

Use the distance formula to find the distance between the two points. (-2, 18) and (4, 10)&#10;A) 10&#10;B) 14&#10;C) 100&#10;D)

Accepted Answer

The answer of Use the distance formula to find the...

Question 14

Identify the center and radius of the circle.

Accepted Answer

The answer of Identify the center and radius of the...

Question 15

Write the word or phrase that best completes each statement or answers the question.&#10;Write the distance formula.

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Write an equation that represents the graph of the circle.

Accepted Answer

The answer of Write an equation that represents the graph...

Question 17

Find the midpoint of the line segment. (You can check your answer by plotting the midpoint on the graph).

Accepted Answer

The answer of Find the midpoint of the line segment....

Question 18

Use the distance formula to find the distance between the two points. (2, 6) and (-2, 14)

Accepted Answer

The answer of Use the distance formula to find the...

Question 19

Write an equation of a circle centered at (-2, -8) with a diameter of 2.

Accepted Answer

The answer of Write an equation of a circle centered...

Question 20

Write the word or phrase that best completes each statement or answers the question.&#10;Identify the center and radius of the circle and then graph the circle.

Accepted Answer

The answer of Write the word or phrase that best...

Question 21

Determine the vertex by using the vertex formula.

Accepted Answer

The answer of Determine the vertex by using the vertex...

Question 22

Use the equation of the parabola in standard form y = a(x - h)2 + k to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph
The parabola.

Accepted Answer

The answer of Use the equation of the parabola in...

Question 23

Use the equation of the parabola in standard form y = a(x - h)2 + k to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph
The parabola.

Accepted Answer

The answer of Use the equation of the parabola in...

Question 24

Use the equation of the parabola in standard form   to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph&#10;The parabola.

Accepted Answer

The answer of Use the equation of the parabola in...

Question 25

Use the equation of the parabola in standard form   to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph&#10;The parabola.

Accepted Answer

The answer of Use the equation of the parabola in...

Question 26

The cross sections of a certain satellite dish are parabolic in shape. A cross section through the vertex can be described by the equation

where d(x) is the depth of the dish (in feet) at a distance of x ft from the edge of the dish. How deep
Is the satellite dish?

Accepted Answer

The answer of The cross sections of a certain satellite...

Question 27

Use the equation of the ellipse to identify the center (h, k).

Accepted Answer

The answer of Use the equation of the ellipse to...

Question 28

Write the word or phrase that best completes each statement or answers the question.&#10;Find the x- and y-intercepts of the ellipse

Accepted Answer

The answer of Write the word or phrase that best...

Question 29

Find the midpoint of the line segment between the two given points. (1, -2) and (-9, 2)&#10;A) (-8, 0)&#10;B) (-2, 5)&#10;C) (-3, 1)&#10;D) (-4, 0)

Accepted Answer

The answer of Find the midpoint of the line segment...

Question 30

Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right.  &#10;A) Vertical axis of symmetry;&#10;B) Horizontal axis of symmetry; opens downward opens right&#10;C) Vertical axis of symmetry;&#10;D) Horizontal axis of symmetry; opens upward opens left

Accepted Answer

The answer of Use the equation of the parabola first...

Question 31

Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right.  &#10;A) Horizontal axis of symmetry;&#10;B) Vertical axis of symmetry; opens left opens downward&#10;C) Vertical axis of symmetry;&#10;D) Horizontal axis of symmetry; opens upward opens right

Accepted Answer

The answer of Use the equation of the parabola first...

Question 32

Use the equation of the parabola in standard form   to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph&#10;The parabola.

Accepted Answer

The answer of Use the equation of the parabola in...

Question 33

Find the center of a circle if a diameter of the circle has endpoints (-5, -4) and (-11, -2).&#10;A) (-8, -3)&#10;B) (3, -1)&#10;C) (3, -3)&#10;D) (-8, -1)

Accepted Answer

The answer of Find the center of a circle if...

Question 34

A map of a hiking area is drawn so that the Visitor Center is at the origin of a rectangular grid. Two hikers are located at positions (-3, 1) and (2, 3) with respect to the Visitor Center where all units are in
Miles. A campground is located exactly halfway between the hikers. What are the coordinates of the
Campground?

Accepted Answer

The answer of A map of a hiking area is...

Question 35

Find the midpoint of the line segment between the two given points. (-0.2, -4.5) and (-3.7, -2.1)&#10;A) (1.75, -1.2)&#10;B) (-2.35, -2.9)&#10;C) (-1.95, -1.2)&#10;D) (-1.95, -3.3)

Accepted Answer

The answer of Find the midpoint of the line segment...

Question 36

Use the equation of the parabola in standard form   to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph&#10;The parabola.

Accepted Answer

The answer of Use the equation of the parabola in...

Question 37

Find the x- and y-intercepts of the ellipse   = 1 and graph the ellipse.

Accepted Answer

The answer of Find the x- and y-intercepts of the...

Question 38

Find the midpoint of the line segment between the two given points. (-4, -6) and (2, -10)&#10;A) (-1, -8)&#10;B) (-8, -1)&#10;C) (-5, -4)&#10;D) (-2, -16)

Accepted Answer

The answer of Find the midpoint of the line segment...

Question 39

Determine the vertex by using the vertex formula.  &#10;A) (-6, 9)&#10;B) (-6, -9)&#10;C) (9, -6)&#10;D) (-9, -6)

Accepted Answer

The answer of Determine the vertex by using the vertex...

Question 40

Identify the center of the ellipse   Then graph the ellipse.

Accepted Answer

The answer of Identify the center of the ellipse ...

Question 41

Give the coordinates of the vertices for the following hyperbola.

Accepted Answer

The answer of Give the coordinates of the vertices for...

Question 42

Sketch the system of equations. Then solve the system by the substitution method.

Accepted Answer

The answer of Sketch the system of equations. Then solve...

Question 43

Graph the hyperbola centered at (h, k) by following these guidelines. First locate the center. Then
draw the reference rectangle relative to the center (h, k). Using the reference rectangle as a guide, sketch
the hyperbola.

Accepted Answer

The answer of Graph the hyperbola centered at (h, k)...

Question 44

Solve the system by the substitution method.

Accepted Answer

The answer of Solve the system by the substitution method....

Question 45

Write the word or phrase that best completes each statement or answers the question.&#10;Determine whether the transverse axis of the hyperbola   is horizontal or vertical.

Accepted Answer

The answer of Write the word or phrase that best...

Question 46

Write the word or phrase that best completes each statement or answers the question.&#10;Solve the system by the substitution method.

Accepted Answer

The answer of Write the word or phrase that best...

Question 47

Determine whether the transverse axis of the hyperbola   is horizontal or vertical.

Accepted Answer

The answer of Determine whether the transverse axis of the...

Question 48

Solve the system of nonlinear equations by the substitution method.

Accepted Answer

The answer of Solve the system of nonlinear equations by...

Question 49

Give the coordinates of the vertices for the following hyperbola.   [The fundamental rectangle and asymptotes are shown in dashed lines.]&#10;A) (6, 5), (6, -1), (-4, -1), and (-4, 5)&#10;B) (1, 2)&#10;C) (5, 1) and (-1, 1)&#10;D) (1, 5) and (1, -1)