Question 1

Find the center and radius of the circle with the given equation.
-$$x ^ { 2 } + y ^ { 2 } + 14 x + 10 y = - 25$$

Accepted Answer

A)  Center $( - 7 , - 5 ) , r = 7$ 
B)  Center $( 5,7 ) , r = 49$ 
C)  Center $( - 5 , - 7 ) , r = 7$ 
D)  Center $( 7,5 ) , r = 49$ 
A)  Center $( - 7 , - 5 ) , r = 7$ 
B)  Center $( 5,7 ) , r = 49$ 
C)  Center $( - 5 , - 7 ) , r = 7$ 
D)  Center $( 7,5 ) , r = 49$

Question 2

Find the slope of the line.
-

Accepted Answer

A) 1 
B) -1 
C) -6 
D) 6 
A) 1 
B) -1 
C) -6 
D) 6

Question 3

Find the equation of the line described, and express your answer in the specified form.
-Parallel to the line 5x - 6y = -3; passes through the point (3, 0); standard form

Accepted Answer

A) 5x - 6y = 15 
B) -6x - 5y = -18 
C) 5x - 6y = -18 
D) -6x - 5y = -15 
A) 5x - 6y = 15 
B) -6x - 5y = -18 
C) 5x - 6y = -18 
D) -6x - 5y = -15

Question 4

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
-(6, 0)

Accepted Answer

A)  Quadrant II
  
B)  $y$-axis
  
C)  $x$-axis
  
D)  $x$-axis
  
A)  Quadrant II
  
B)  $y$-axis
  
C)  $x$-axis
  
D)  $x$-axis

Question 5

Find the equation of the line passing through the indicated two points. Write the equation in point-slope form.
-(-2, 15)and (4, -9)

Accepted Answer

A) y + 15 = -4(x + 2)or y + 9 = -4(x + 4) 
B) y - 15 = -4(x + 2)or y + 9 = -4(x - 4) 
C) y + 15 = -4(x - 2)or y - 9 = -4(x + 4) 
D) y - 15 = -4(x - 2)or y - 9 = -4(x - 4) 
A) y + 15 = -4(x + 2)or y + 9 = -4(x + 4) 
B) y - 15 = -4(x + 2)or y + 9 = -4(x - 4) 
C) y + 15 = -4(x - 2)or y - 9 = -4(x + 4) 
D) y - 15 = -4(x - 2)or y - 9 = -4(x - 4)

Question 6

Find the slope of the line.
-

Accepted Answer

A)  6 
B)  $\frac { 1 } { 6 }$ 
C)  $- 6$ 
D)  $- \frac { 1 } { 6 }$ 
A)  6 
B)  $\frac { 1 } { 6 }$ 
C)  $- 6$ 
D)  $- \frac { 1 } { 6 }$

Question 7

Find the equation of the given line.
-

Accepted Answer

A) y = -4 
B) x = 4 
C) x = -4 
D) y = 4 
A) y = -4 
B) x = 4 
C) x = -4 
D) y = 4

Question 8

Sketch the line with the given slope that passes through the indicated point.
-$\text { Slope }=-\frac{3}{4} ; \text { line passes through the point }(4,0)$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Find the midpoint of the line segment joining the points A and B.
-A = (y, 2); B = (0, 8)

Accepted Answer

A)  $\left( \frac { y } { 2 } , 5 \right)$ 
B)  $( y , 5 )$ 
C)  $( \mathrm { y } , 10 )$ 
D)  $\left( - \frac { y } { 2 } , 6 \right)$ 
A)  $\left( \frac { y } { 2 } , 5 \right)$ 
B)  $( y , 5 )$ 
C)  $( \mathrm { y } , 10 )$ 
D)  $\left( - \frac { y } { 2 } , 6 \right)$

Question 10

Sketch the line with the given slope that passes through the indicated point.
-Slope $ =\frac{2}{5} ; $ line passes through the point $ (-2,0) $

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 11

Find the equation of the line described, and express your answer in the specified form.
-Perpendicular to the line -4x + 3y = 5; passes through the point (0, -1); standard form

Accepted Answer

A) -4x + 3y = -3 
B) 3x + 4y = -3 
C) -4x + 3y = 4 
D) 3x + 4y = -4 
A) -4x + 3y = -3 
B) 3x + 4y = -3 
C) -4x + 3y = 4 
D) 3x + 4y = -4

Question 12

Find the slope and y-intercept of the line.
--x + 12y = 48

Accepted Answer

A)  slope $= - 1 ; y$-intercept $= 48$ 
B)  slope $= \frac { 1 } { 12 } ; y$-intercept $= 4$ 
C)  slope $= - \frac { 1 } { 12 } ; y$-intercept $= 4$ 
D)  slope $= 12 ; y$-intercept $= - 48$ 
A)  slope $= - 1 ; y$-intercept $= 48$ 
B)  slope $= \frac { 1 } { 12 } ; y$-intercept $= 4$ 
C)  slope $= - \frac { 1 } { 12 } ; y$-intercept $= 4$ 
D)  slope $= 12 ; y$-intercept $= - 48$

Question 13

Decide whether the pair of lines is parallel, perpendicular, or neither.
-3x - 6y = 8 18x + 9y = 7

Accepted Answer

A) parallel 
B) perpendicular 
C) neither 
A) parallel 
B) perpendicular 
C) neither

Question 14

Find the slope-intercept form of the equation of the line with the given properties.
-Find the equation of the horizontal line passing through the point (-10, -5).

Accepted Answer

A) x = -10 
B) x = -5 
C) y = -5 
D) y = -10 
A) x = -10 
B) x = -5 
C) y = -5 
D) y = -10

Question 15

Find the midpoint of the line segment joining the points A and B.
-A = (9y, 9); B = (10y, 8)

Accepted Answer

A)  $( 19 y , 17 )$ 
B)  $( y , 1 )$ 
C)  $\left( \frac { 19 \mathrm { y } } { 2 } , \frac { 17 } { 2 } \right)$ 
D)  $\left( \frac { 17 y } { 2 } , \frac { 19 } { 2 } \right)$ 
A)  $( 19 y , 17 )$ 
B)  $( y , 1 )$ 
C)  $\left( \frac { 19 \mathrm { y } } { 2 } , \frac { 17 } { 2 } \right)$ 
D)  $\left( \frac { 17 y } { 2 } , \frac { 19 } { 2 } \right)$

Question 16

Find the equation of the given line.
-

Accepted Answer

A) y = 2 
B) x = 2 
C) y = -2 
D) x = -2 
A) y = 2 
B) x = 2 
C) y = -2 
D) x = -2

Question 17

Find the equation of the line passing through the indicated two points. Write the equation in point-slope form.
-$\left( 1 , \frac { 9 } { 14 } \right)$ and $\left( 7 , \frac { 3 } { 2 } \right)$

Accepted Answer

A)  $y = \frac { 9 } { 14 } = 7 ( x - 1 )$ or $y - \frac { 3 } { 2 } = 7 ( x - 7 )$ 
B)  $y + \frac { 9 } { 14 } = 7 ( x + 1 )$ or $y + \frac { 3 } { 2 } = 7 ( x + 7 )$ 
C)  $\mathrm { y } - \frac { 9 } { 14 } = \frac { 1 } { 7 } ( \mathrm { x } - 1 )$ or $\mathrm { y } - \frac { 3 } { 2 } = \frac { 1 } { 7 } ( \mathrm { x } - 7 )$ 
D)  $y + \frac { 9 } { 14 } = \frac { 1 } { 7 } ( x + 1 )$ or $y + \frac { 3 } { 2 } = \frac { 1 } { 7 } ( x + 7 )$ 
A)  $y = \frac { 9 } { 14 } = 7 ( x - 1 )$ or $y - \frac { 3 } { 2 } = 7 ( x - 7 )$ 
B)  $y + \frac { 9 } { 14 } = 7 ( x + 1 )$ or $y + \frac { 3 } { 2 } = 7 ( x + 7 )$ 
C)  $\mathrm { y } - \frac { 9 } { 14 } = \frac { 1 } { 7 } ( \mathrm { x } - 1 )$ or $\mathrm { y } - \frac { 3 } { 2 } = \frac { 1 } { 7 } ( \mathrm { x } - 7 )$ 
D)  $y + \frac { 9 } { 14 } = \frac { 1 } { 7 } ( x + 1 )$ or $y + \frac { 3 } { 2 } = \frac { 1 } { 7 } ( x + 7 )$

Question 18

Find the intercepts of the circle. Round to the nearest hundredth, when necessary.
-$$121 x ^ { 2 } + 121 y ^ { 2 } - 66 x - 132 y - 438 = 0$$

Accepted Answer

A) The x-intercept is x ≈41.7, and the y-intercept is y ≈40.65. 
B) There are no intercepts. 
C) The two x-intercepts are x ≈4.12 and x ≈-3.57, and the two y-intercepts are y ≈4.5 and y ≈-3.41. 
D) The two x-intercepts are x ≈2.19 and x ≈-1.65, and the two y-intercepts are y ≈2.52 and y ≈-1.43. 
A) The x-intercept is x ≈41.7, and the y-intercept is y ≈40.65. 
B) There are no intercepts. 
C) The two x-intercepts are x ≈4.12 and x ≈-3.57, and the two y-intercepts are y ≈4.5 and y ≈-3.41. 
D) The two x-intercepts are x ≈2.19 and x ≈-1.65, and the two y-intercepts are y ≈2.52 and y ≈-1.43.

Question 19

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram,
determine whether it is also a rhombus.
-A(-2, 6), B(1, 7), C(3, -1), D(6, 2)

Accepted Answer

A) Yes, it is a parallelogram but it is not also a rhombus. 
B) Yes, it is a parallelogram and it is also a rhombus. 
C) No, it is not a parallelogram (nor is it a rhombus). 
A) Yes, it is a parallelogram but it is not also a rhombus. 
B) Yes, it is a parallelogram and it is also a rhombus. 
C) No, it is not a parallelogram (nor is it a rhombus).

Question 20

Find the center and radius of the circle with the given equation.
-$$x ^ { 2 } + y ^ { 2 } = 9$$

Accepted Answer

A)  Center $( 3,3 ) , r = 3$ 
B)  Center $( 0,0 ) , r = 3$ 
C)  Center $( 3,3 ) , r = 9$ 
D)  Center $( 0,0 ) , r = 9$ 
A)  Center $( 3,3 ) , r = 3$ 
B)  Center $( 0,0 ) , r = 3$ 
C)  Center $( 3,3 ) , r = 9$ 
D)  Center $( 0,0 ) , r = 9$

Find the center and radius of the circle with the given equation. - $x ^ { 2 } + y ^ { 2 } + 14 x + 10 y = - 25$

Find the slope of the line. -

Find the equation of the line described, and express your answer in the specified form. -Parallel to the line 5x - 6y = -3; passes through the point (3, 0); standard form

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(6, 0)

Find the equation of the line passing through the indicated two points. Write the equation in point-slope form. -(-2, 15)and (4, -9)

Find the slope of the line. -

Find the equation of the given line. -

Find the midpoint of the line segment joining the points A and B. -A = (y, 2); B = (0, 8)

Sketch the line with the given slope that passes through the indicated point. -Slope $=\frac{2}{5} ;$ line passes through the point $(-2,0)$ $Sketch the line with the given slope that passes through the indicated point. -Slope =\frac{2}{5} ; line passes through the point (-2,0)$

Find the equation of the line described, and express your answer in the specified form. -Perpendicular to the line -4x + 3y = 5; passes through the point (0, -1); standard form

Find the slope and y-intercept of the line. --x + 12y = 48

Decide whether the pair of lines is parallel, perpendicular, or neither. -3x - 6y = 8 18x + 9y = 7

Find the slope-intercept form of the equation of the line with the given properties. -Find the equation of the horizontal line passing through the point (-10, -5).

Find the midpoint of the line segment joining the points A and B. -A = (9y, 9); B = (10y, 8)

Find the equation of the given line. -

Find the equation of the line passing through the indicated two points. Write the equation in point-slope form. - $\left( 1 , \frac { 9 } { 14 } \right)$ and $\left( 7 , \frac { 3 } { 2 } \right)$

Find the intercepts of the circle. Round to the nearest hundredth, when necessary. - $121 x ^ { 2 } + 121 y ^ { 2 } - 66 x - 132 y - 438 = 0$

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus. -A(-2, 6), B(1, 7), C(3, -1), D(6, 2)

Find the center and radius of the circle with the given equation. - $x ^ { 2 } + y ^ { 2 } = 9$

Equations, Inequalities, and Applications

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Exam 2: The Rectangular Coordinate System, Lines, and Circles

Find the center and radius of the circle with the given equation. - x2+y2+14x+10y=−25x ^ { 2 } + y ^ { 2 } + 14 x + 10 y = - 25x2+y2+14x+10y=−25

Find the slope of the line. -

Find the equation of the line described, and express your answer in the specified form. -Parallel to the line 5x - 6y = -3; passes through the point (3, 0); standard form

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(6, 0)

Find the equation of the line passing through the indicated two points. Write the equation in point-slope form. -(-2, 15)and (4, -9)

Find the slope of the line. -

Find the equation of the given line. -

Sketch the line with the given slope that passes through the indicated point. - Slope =−34; line passes through the point (4,0)\text { Slope }=-\frac{3}{4} ; \text { line passes through the point }(4,0) Slope =−43​; line passes through the point (4,0)

Find the midpoint of the line segment joining the points A and B. -A = (y, 2); B = (0, 8)

Sketch the line with the given slope that passes through the indicated point. -Slope =25; =\frac{2}{5} ; =52​; line passes through the point (−2,0) (-2,0) (−2,0)

Find the equation of the line described, and express your answer in the specified form. -Perpendicular to the line -4x + 3y = 5; passes through the point (0, -1); standard form

Find the slope and y-intercept of the line. --x + 12y = 48

Decide whether the pair of lines is parallel, perpendicular, or neither. -3x - 6y = 8 18x + 9y = 7

Find the slope-intercept form of the equation of the line with the given properties. -Find the equation of the horizontal line passing through the point (-10, -5).

Find the midpoint of the line segment joining the points A and B. -A = (9y, 9); B = (10y, 8)

Find the equation of the given line. -

Find the equation of the line passing through the indicated two points. Write the equation in point-slope form. - (1,914)\left( 1 , \frac { 9 } { 14 } \right)(1,149​) and (7,32)\left( 7 , \frac { 3 } { 2 } \right)(7,23​)

Find the intercepts of the circle. Round to the nearest hundredth, when necessary. - 121x2+121y2−66x−132y−438=0121 x ^ { 2 } + 121 y ^ { 2 } - 66 x - 132 y - 438 = 0121x2+121y2−66x−132y−438=0

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus. -A(-2, 6), B(1, 7), C(3, -1), D(6, 2)

Find the center and radius of the circle with the given equation. - x2+y2=9x ^ { 2 } + y ^ { 2 } = 9x2+y2=9

Equations, Inequalities, and Applications

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Find the center and radius of the circle with the given equation. - $x ^ { 2 } + y ^ { 2 } + 14 x + 10 y = - 25$

Sketch the line with the given slope that passes through the indicated point. -Slope $=\frac{2}{5} ;$ line passes through the point $(-2,0)$ $Sketch the line with the given slope that passes through the indicated point. -Slope =\frac{2}{5} ; line passes through the point (-2,0)$

Find the equation of the line passing through the indicated two points. Write the equation in point-slope form. - $\left( 1 , \frac { 9 } { 14 } \right)$ and $\left( 7 , \frac { 3 } { 2 } \right)$

Find the intercepts of the circle. Round to the nearest hundredth, when necessary. - $121 x ^ { 2 } + 121 y ^ { 2 } - 66 x - 132 y - 438 = 0$

Find the center and radius of the circle with the given equation. - $x ^ { 2 } + y ^ { 2 } = 9$