Test Bank For College Algebra 8Th Edition by Ziegler, Byleen Barnett

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Test Bank For College Algebra 8Th Edition by Ziegler, Byleen Barnett

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WITH ANSWERS
College Algebra 8Th Edition by Ziegler, Byleen Barnett  Test Bank 

 

Chapter 2

 

  1. Give a description of the indicated subset of the plane in terms of quadrants.

{(x, y) | x < 0, y > 0}

  1. A) Quadrant I    B)  Quadrant II    C)  Quadrant III    D)  Quadrant IV

Ans:  B     Section:  2.1

 

  1. Plot the points in a rectangular coordinate system.

(5, 2), (4, 1), (3, 4), (2, 4)

Ans:

Section:  2.1

 

Use the following to answer questions 3-7:

 

 

 

  1. Find the coordinates of points A, B, C, and D.

Ans:  A = (1, 5), B = (5, 0), C = (4, 3), D = (2, 1)

Section:  2.1

 

  1. Reflect A, B, C, and D through the y-axis and give the coordinates of the reflected points, A , B , C , and D .

Ans:  A = (1, 5), B = (5, 0), C = (4, 3), and D = (2, 1)

Section:  2.1

 

  1. Reflect A, B, C, and D through the x-axis and give the coordinates of the reflected points, A , B , C , and D .

Ans:  A = (1, 5), B = (5, 0), C = (4, 3), and D = (2, 1)

Section:  2.1

 

  1. Reflect A, B, C, and D through the origin and give the coordinates of the reflected points, A , B , C , and D .

Ans:  A = (1, 5), B = (5, 0), C = (4, 3), and D = (2, 1)

Section:  2.1

 

  1. Reflect A, B, C, and D through the x axis and then through the y-axis and give the coordinates of the reflected points, A , B , C , and D .

Ans:  A = (1, 5), B = (5, 0), C = (4, 3), and D = (2, 1)

Section:  2.1

 

Use the following to answer questions 8-12:

 

 

 

  1. Find the coordinates of points A, B, C, and D.
  2. A) A = (0, 1), B = (6, 3), C = (1, 3), D = (5, 2)
  3. B) A = (1, 0), B = (3, 6), C = (3, 1), D = (2, 5)
  4. C) A = (0, 1), B = (6, 3), C = (1, 3), D = (5, 2)
  5. D) A = (1, 0), B = (3, 6), C = (3, 1), D = (2, 5)

Ans:  C     Section:  2.1

 

  1. Reflect A, B, C, and D through the y-axis and give the coordinates of the reflected points, A , B , C , and D .
  2. A) A = (1, 0), B = (3, 6), C = (3, 1), D = (2, 5)
  3. B) A = (0, 1), B = (6, 3), C = (1, 3), D = (5, 2)
  4. C) A = (0, 1), B = (6, 3), C = (1, 3), D = (5, 2)
  5. D) A = (1, 0), B = (3, 6), C = (3, 1), D = (2, 5)

Ans:  B     Section:  2.1

 

  1. Reflect A, B, C, and D through the x-axis and give the coordinates of the reflected points, A , B , C , and D .
  2. A) A = (0, 1), B = (6, 3), C = (1, 3), D = (5, 2)
  3. B) A = (0, 1), B = (6, 3), C = (1, 3), D = (5, 2)
  4. C) A = (1, 0), B = (3, 6), C = (3, 1), D = (2, 5)
  5. D) A = (1, 0), B = (3, 6), C = (3, 1), D = (2, 5)

Ans:  A     Section:  2.1

 

  1. Reflect A, B, C, and D through the origin and give the coordinates of the reflected points, A , B , C , and D .
  2. A) A = (1, 0), B = (3, 6), C = (3, 1), D = (2, 5)
  3. B) A = (0, 1), B = (6, 3), C = (1, 3), D = (5, 2)
  4. C) A = (1, 0), B = (3, 6), C = (3, 1), D = (2, 5)
  5. D) A = (0, 1), B = (6, 3), C = (1, 3), D = (5, 2)

Ans:  D     Section:  2.1

 

  1. Reflect A, B, C, and D through the x-axis and then through the y-axis and give the coordinates of the reflected points, A , B , C , and D .
  2. A) A = (1, 0), B = (3, 6), C = (3, 1), D = (2, 5)
  3. B) A = (0, 1), B = (6, 3), C = (1, 3), D = (5, 2)
  4. C) A = (0, 1), B = (6, 3), C = (1, 3), D = (5, 2)
  5. D) A = (1, 0), B = (3, 6), C = (3, 1), D = (2, 5)

Ans:  C     Section:  2.1

 

Use the following to answer questions 13-14:

 

            y = x 3

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.
  2. A) Symmetric with respect to the x-axis
  3. B) Symmetric with respect to the y-axis
  4. C) Symmetric with respect to the origin
  5. D) No symmetry with respect to x-axis, y-axis, or origin

Ans:  D     Section:  2.1

 

  1. Sketch the graph of the equation.
  2. A)                           C)
  3. B)                           D)

Ans:  A     Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.  State your results and sketch the graph of the equation.

y = 3x

Ans:  Symmetric with respect to the origin.

 

Section:  2.1

 

Use the following to answer questions 16-21:

 

Use the graph to estimate to the nearest integer the missing coordinate of the point.  (Be sure you find all possible answers.)

 

 

  1. (3, ?)

Ans:  2

Section:  2.1

 

  1. (3, ?)
  2. A) 2    B)  2    C)  4    D)  1, 4

Ans:  C     Section:  2.1

 

  1. (0, ?)

Ans:  1

Section:  2.1

 

  1. (?, 2)
  2. A) 1    B)  4    C)  4, 1    D)  4, 1, 6

Ans:  D     Section:  2.1

 

  1. (?, 4)

Ans:  6

Section:  2.1

 

  1. (?, 0)

Ans:  5, 1, 5

Section:  2.1

 

  1. A portion of a graph is shown.  Extend the graph to one that exhibits y-axis symmetry.

 

Ans:

Section:  2.1

 

  1. A portion of a graph is shown.  Extend the graph to one that exhibits origin symmetry.

 

Ans:

Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.

x2 + 6xy + y2 = 1

  1. A) Symmetric with respect to the x-axis
  2. B) Symmetric with respect to the y-axis
  3. C) Symmetric with respect to the origin
  4. D) Symmetric with respect to the x-axis, the y-axis, and the origin

Ans:  C     Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.

x2y + 4y2 = 1

  1. A) Symmetric with respect to the x-axis
  2. B) Symmetric with respect to the y-axis
  3. C) Symmetric with respect to the origin
  4. D) Not symmetric with respect to the x-axis, the y-axis, or the origin

Ans:  B     Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.

x2 3xy2 = 2

Ans:  Symmetric with respect to the x-axis

Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.

x2 + xy2 + 2y = 1

  1. A) Symmetric with respect to the x-axis
  2. B) Symmetric with respect to the y-axis
  3. C) Symmetric with respect to the origin
  4. D) Not symmetric with respect to the x-axis, the y-axis, or the origin

Ans:  D     Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.

x2 + y2 + x2y2 = 4

  1. A) Symmetric with respect to the x-axis
  2. B) Symmetric with respect to the y-axis
  3. C) Symmetric with respect to the origin
  4. D) Symmetric with respect to the x-axis, the y-axis, and the origin

Ans:  D     Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.  Sketch the graph of the equation.

y2 = x + 3

Ans:  Symmetric with respect to the x-axis

 

Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.  Sketch the graph of the equation.

y + 1 = x2

Ans:  Symmetric with respect to the y-axis

 

Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.  Sketch the graph of the equation.

 

  1. A) Symmetric with respect to the x-axis

 

  1. B) Symmetric with respect to the y-axis

 

  1. C) Symmetric with respect to the x-axis, y-axis, and origin

 

  1. D) Symmetric with respect to the x-axis, y-axis, and origin

 

Ans:  D     Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.  Sketch the graph of the equation.

 

  1. A) Symmetric with respect to the origin.

 

  1. B) Symmetric with respect to the origin.

 

  1. C) Symmetric with respect to the origin.

 

  1. D) Symmetric with respect to the origin.

 

Ans:  A     Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.  Sketch the graph of the equation.

 

  1. A) Symmetric with respect to the y-axis.

 

  1. B) Symmetric with respect to the x-axis.

 

  1. C) Symmetric with respect to the y-axis.

 

  1. D) Symmetric with respect to the x-axis.

 

Ans:  B     Section:  2.1

 

  1. Solve for y, producing two equations, and then graph both of these equations in the same viewing window.

 

Ans:

 

 

Section:  2.1

 

  1. Solve for y, producing two equations, and then graph both of these equations in the same viewing window.

 

  1. A)

 

  1. B)

 

  1. C)

 

  1. D)

 

Ans:  A     Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.  Sketch the graph of the equation.

 

  1. A) Symmetric with respect to the origin.

 

  1. B) Symmetric with respect to the origin.

 

  1. C) Symmetric with respect to the x-axis.

 

  1. D) Symmetric with respect to the y-axis.

 

Ans:  A     Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.  Sketch the graph of the equation.

y2 = | x | + 2

Ans:  Symmetric with respect to the x-axis, the y-axis, and the origin

 

Section:  2.1

 

  1. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.  Sketch the graph of the equation.

 

Ans:  Symmetric with respect to the x-axis, the y-axis, and the origin.

 

Section:  2.1

 

  1. Find the distance between  (5, 8) and (4, 4).

Ans:  15

Section:  2.2

 

  1. Find the midpoint of the line segment with endpoints (4, 3) and (10, 9).

Ans:  (7, 6)

Section:  2.2

 

  1. Find the distance between (3, 2) and (1, 4).
  2. A) 27    B)      C)      D)

Ans:  C     Section:  2.2

 

  1. Find the midpoint of the line segment with endpoints (0, 3) and (10, 9).
  2. A) (10, 12)    B)  (10, 6)    C)  (5, 6)    D)  (5, 3)

Ans:  C     Section:  2.2

 

  1. Write the equation of a circle with center (0, 0) and radius 8.

Ans:  x2 + y2 = 64

Section:  2.2

 

  1. Write the equation of a circle with center (0, 0) and radius 4.

Ans:  x2 + y2 = 16

Section:  2.2

 

  1. Write the equation of a circle with center (0, 2) and radius .
  2. A) x2 + (y 2)2 =                                  C)      x2 + (y + 2)2 =
  3. B) x2 + (y 2)2 = 6                                     D)      x2 + (y + 2)2 = 6

Ans:  B     Section:  2.2

 

  1. Write the equation of a circle with center (2, 4) and radius .
  2. A) (x 2)2 + (y 4)2 =                          C)      (x 2)2 + (y 4)2 = 2
  3. B) (x + 2)2 + (y + 4)2 =                         D)      (x + 2)2 + (y + 4)2 = 2

Ans:  C     Section:  2.2

 

  1. Write an equation for the given set of points.  Graph your equation.

The set of all points that are two units from (3, 1)

Ans:  (x + 3)2 + (y 1)2 = 4

 

Section:  2.2

 

  1. The midpoint of the line segment with endpoints (0, 1) and (b1, b2) is (2, 1).  Find b1 and b2.

Ans:  (b1, b2) = (4, 3)

Section:  2.2

 

  1. Find x such that (x, 5) is 10 units from (2, 11)

Ans:  10, 6

Section:  2.2

 

  1. Write the equation of the circle.

 

Ans:  x2 + y2 = 9

Section:  2.2

 

  1. Write the equation of the circle.

 

  1. A) (x + 3)2 + (y 2)2 = 2                             C)      (x + 3)2 + (y 2)2 = 4
  2. B) (x 3)2 + (y + 2)2 = 2                             D)      (x 3)2 + (y + 2)2 = 4

Ans:  C     Section:  2.2

 

  1. Write the equation of the circle.

 

  1. A) x2 + y2 = 6    B)  x2 + y2 = 36    C)  6x2 + 6y2 = 1    D)  y2 = 6x2

Ans:  B     Section:  2.2

 

  1. Write the equation of the circle.

 

Ans:  (x 3)2 + y2 = 16

Section:  2.2

 

  1. M is the midpoint of A and B.  Find the indicated point.  Verify that .

 

  1. A) (9, 24)    B)  (6, 3)    C)  (6, 3)    D)  (11, 12)

Ans:  D     Section:  2.2

 

  1. M is the midpoint of A and B.  Find the indicated point.  Verify that .

 

  1. A) (0.9, 4.7)    B)  (6.1, 5.7)    C)  (6.1, 5.7)    D)  (27.1, 8.7)

Ans:  A     Section:  2.2

 

  1. Find the center and radius of the circle.

x2 + (y 5)2 = 49.

Ans:  Center (0, 5), radius 7

Section:  2.2

 

  1. Graph the circle by finding the center and radius.

(x 2)2 + (y 1)2 = 9

Ans:  Center (2, 1), radius 3

 

Section:  2.2

 

  1. Find the center and radius of the circle.

(x 8)2 + (y 5)2 = 36.

  1. A) Center (8, 5) and radius 6                 C)      Center (8, 5) and radius 36
  2. B) Center (8, 5) and radius 6                     D)      Center (8, 5) and radius 36

Ans:  B     Section:  2.2

 

  1. Graph the circle by finding the center and radius.

(x 2)2 + (y + 3)2 = 16

Ans:  Center (2, 3), radius 4

 

Section:  2.2

 

  1. Graph the circle by finding the center and radius.

x2 + 6x + y2 = 7

Ans:  (x + 3)2 + y2 = 16

Center (3, 0), radius 4

 

Section:  2.2

 

  1. Find the center and radius of the circle.

x2 + y2 + 16y = 36

Ans:  Center (0, 8), radius 10

Section:  2.2

 

  1. Find the center and radius of the circle.

x2 + y2 6x 4y = 13

Ans:  Center (3, 2), radius

Section:  2.2

 

  1. Graph the circle by finding the center and radius.

x2 + y2 4x + 6y = 3

Ans:  (x 2)2 + (y + 3)2 = 16

Center (2, 3), radius 4

 

Section:  2.2

 

  1. Find the center and radius of the circle.

3x2 + 3y2 + 36x + 18y 57 = 0

  1. A) Center (6, 3) and radius 8                 C)      Center (6, 3) and radius 64
  2. B) Center (6, 3) and radius 8                     D)      Center (6, 3) and radius 64

Ans:  A     Section:  2.2

 

  1. Write the equation of a circle whose diameter has endpoints (2, 7) and (2, 1).

Ans:  (x 2)2 + (y + 3)2 = 16

Section:  2.2

 

  1. Find the standard form of the equation of the circle with center (5, 0) that passes through the point (1, 2).
  2. A)                                  C)
  3. B)                                  D)

Ans:  B     Section:  2.2

 

  1. Find the equation of a circle with center (2, 3) and the graph of which contains the point (3, 4).
  2. A) (x 2)2 + (y + 3)2 = 50                           C)      (x 2)2 + (y + 3)2 =
  3. B) (x + 2)2 + (y 3)2 = 50                           D)      (x + 2)2 + (y 3)2 =

Ans:  A     Section:  2.2

 

  1. An arched doorway is formed by placing a circular arc on top of a rectangle (see the figure).  If the doorway is w = 10 feet wide and the height of the arc above its ends is 1 foot, what is the radius of the circle containing the arc?  [Hint: Note that (5, r 1) must satisfy .]

 

 

Ans:  13 feet

Section:  2.2

 

  1. Town B is located 18 miles east and 24 miles north of town A (see the figure).  A local telephone company wants to position a relay tower so that the distance from the tower to town B is twice the distance from the tower to town A.

(A) Show that the tower must lie on a circle, and find the center and radius of this circle.

(B) If the company decides to position the tower on this circle at a point directly east of town A, how far from town A should they place the tower?  Compute the answer to one decimal place.

 

Ans:  (A) Center = (6, 8); radius = 20

(B) x = 12.3 mi

Section:  2.2

 

Use the following to answer questions 70-73:

 

 

 

  1. Find the x-intercept of the line.

Ans:  2

Section:  2.3

 

  1. Find the y-intercept of the line.

Ans:  4

Section:  2.3

 

  1. Find the slope of the line.

Ans:  2

Section:  2.3

 

  1. Write the equation of the line in slope-intercept form.

Ans:  y = 2x + 4

Section:  2.3

 

Use the following to answer questions 74-77:

 

 

 

  1. Find the x-intercept of the line.
  2. A) 3    B)  0    C)  3    D)  No x-intercept

Ans:  C     Section:  2.3

 

  1. Find the y-intercept of the line.
  2. A) 3    B)  0    C)  3    D)  No y-intercept

Ans:  D     Section:  2.3

 

  1. Find the slope of the line.
  2. A) 3    B)  0    C)  3    D)  Undefined

Ans:  D     Section:  2.3

 

  1. Write the equation of the line.
  2. A) y = 3x    B)  y = 3x    C)  x = 3    D)  y = 3

Ans:  C     Section:  2.3

 

  1. Graph y = .  Indicate the slope, if it exists.

Ans:  Slope =

 

Section:  2.3

 

  1. Graph .  Indicate the slope, if it exists.

Ans:  Slope =

 

Section:  2.3

 

  1. Graph .  Indicate the slope, if it exists.

Ans:  Slope =

 

Section:  2.3

 

  1. Graph 6x + 2y = 0.  Indicate the slope, if it exists.

Ans:  Slope = 3

 

Section:  2.3

 

  1. Graph 2x 5y = 10.  Indicate the slope, if it exists.

Ans:  Slope =

 

Section:  2.3

 

  1. Graph 4x 3y = 6.  Indicate the slope, if it exists.

Ans:  Slope =

 

Section:  2.3

 

Use the following to answer questions 84-85:

 

3x + 4y = 12

 

  1. Graph the line.
  2. A)                           C)
  3. B)                           D)

Ans:  B     Section:  2.3

 

  1. Indicate the slope.
  2. A)     B)      C)      D)

Ans:  C     Section:  2.3

 

Use the following to answer questions 86-87:

 

3x + 2y = 6

 

  1. Graph the line.
  2. A)                          C)
  3. B)                          D)

Ans:  C     Section:  2.3

 

  1. Indicate the slope.
  2. A)     B)      C)      D)

Ans:  B     Section:  2.3

 

  1. Graph .  Indicate the slope, if it exists.

Ans:  Slope =

 

Section:  2.3

 

  1. Graph .  Indicate the slope, if it exists.

Ans:  Slope =

 

Section:  2.3

 

Use the following to answer questions 90-91:

 

            x = 3

 

  1. Graph the line.
  2. A)                              C)
  3. B)                              D)

Ans:  B     Section:  2.3

 

  1. Indicate the slope, if it exists.
  2. A) 3    B)  0    C)  3    D)  Undefined

Ans:  D     Section:  2.3

 

Use the following to answer questions 92-93:

 

y = 3

 

  1. Graph the line.
  2. A)                           C)
  3. B)                           D)

Ans:  B     Section:  2.3

 

  1. Indicate the slope, if it exists.
  2. A) 3    B)  0    C)  3    D)  Undefined

Ans:  B     Section:  2.3

 

  1. Find the equation of the line with slope 6 and y-intercept 4.  Write the equation in standard form

Ax + By = C, A 0.

  1. A) 6x y = 4    B)  6x y = 4    C)  6x + y = 4    D)  6x + y = 4

Ans:  C     Section:  2.3

 

  1. Write the equation of the line with slope  and y-intercept 5.  Write the equation in standard form Ax + By = C, A 0.

Ans:  2x 3y = 15

Section:  2.3

 

  1. Write the equation of the line with slope  and y-intercept 3.  Write the equation in standard form Ax + By = C, A 0.

Ans:  x + 2y = 6

Section:  2.3

 

  1. Write the equation of the line with slope 0 and y-intercept 3.  Write the equation in standard form Ax + By = C, A 0.
  2. A) 3x y = 0    B)  3x + y = 0    C)  y = 3    D)  x = 3

Ans:  C     Section:  2.3

 

  1. Write the equation of the line that passes through point (0, 3) with slope .  Give your answer in the slope-intercept form y = mx + b.

Ans:  y = x + 3

Section:  2.3

 

  1. Sketch a graph of the line that contains the point (0, 3) and has slope 3.  Then write the equation of the line in the slope intercept form y = mx + b.

Ans:  y = 3x + 3.

 

Section:  2.3

 

  1. Write the equation of the line that passes through point (3, 15) with a slope of 3.  Give your answer in the slope-intercept form y = mx + b.

Ans:  y = 3x + 6

Section:  2.3

 

  1. Write the equation of the line passing through (4, 13) and (3, 1).  Write your answer in the slope-intercept form y = mx + b.

Ans:  y = 2x 5

Section:  2.3

 

  1. Write the equation of the line passing through (3, 5) and (3, 0).  Write your answer in the slope-intercept form y = mx + b.
  2. A)     B)      C)      D)

Ans:  B     Section:  2.3

 

  1. Write the equation of the line passing through (3, 9) and (6, 9).  Write your answer in the slope-intercept form y = mx + b.

Ans:  y = 9

Section:  2.3

 

  1. Write the equation of the line passing through (2, 8) and (2, 6).
  2. A) x = 2    B)  y = 2    C)  y = x 2    D)  y = 2x

Ans:  A     Section:  2.3

 

  1. Write the equation of the line with x-intercept (12, 0) and y-intercept (0, 3).  Write your answer in the slope-intercept form y = mx + b.

Ans:

Section:  2.3

 

  1. Write an equation of the line passing through (3, 13) and parallel to y = 7x + 8.  Write your answer in standard form Ax + By = C, A 0.

Ans:  7x y = 8

Section:  2.3

 

  1. Write an equation of the line passing through (8, 3) and perpendicular to y = .  Write your answer in standard form Ax + By = C, A 0.
  2. A) 4x + y = 35    B)  4x y = 35    C)  x + 4y = 20    D)  x 4y = 20

Ans:  A     Section:  2.3

 

  1. Write the equation of the line passing through (0, 5) and perpendicular to x 5y = 20.  Write your answer in standard form Ax + By = C, A 0.

Ans:  5x + y = 5

Section:  2.3

 

  1. Write the equation of the line which passes through (2, 1) and is perpendicular to the line with equation 3y x = 1.
  2. A) 3x + y = 5    B)  3x y = 7    C)  x + 3y = 1    D)  x 3y = 5

Ans:  A     Section:  2.3

 

  1. Refer to the quadrilateral with vertices P = (5, 3), Q = (17, 33), R = (27, 29), and S = (15, 1).  Show that PQ || SR.
  2. A)                                       C)
  3. B)                                    D)

Ans:  A     Section:  2.3

 

  1. Refer to the quadrilateral with vertices P = (6, 5), Q = (2, 1), R = (10, 7), and S = (6, 13).  Show that PQ ^ QR.
  2. A)                                       C)
  3. B)                                    D)

Ans:  C     Section:  2.3

 

  1. Refer to the quadrilateral with vertices P = (10, 3), Q = (2, 9), R = (4, 5), and S = (4, 7).  Find an equation of the perpendicular bisector of PQ.  The perpendicular bisector of a line segment is a line perpendicular to the segment and passing through its midpoint. Write your answer in standard form Ax + By = C, A 0.
  2. A)     B)      C)      D)

Ans:  B     Section:  2.3

 

  1. Recall that a line tangent to a circle at a point is perpendicular to the radius drawn to that point (see the figure).  Find the equation of the line tangent to the circle at the indicated point.  Write the answer in the standard form Ax + By = C, A 0.  Graph the circle and the tangent line on the same coordinate system.

 

 

Ans:  4x + 3y = 50

 

Section:  2.3

 

Use the following to answer questions 114-115:

 

The Number Two Plumbing Co. charges $35 per hour plus a fixed service call charge of $65.

 

  1. Write an equation that will allow you to compute the total bill for any number of hours, x, that it takes to complete a job.
  2. A) C = 30x + 45    B)  C = 45x + 30    C)  45x + 30C = 0    D)  30x + 45C = 0

Ans:  A     Section:  2.3

 

  1. If the bill comes to $120.25, how many hours did the job take?
  2. A) 85 hours    B)  2.05 hours    C)  2.15 hours    D)  2.35 hours

Ans:  C     Section:  2.3

 

Use the following to answer questions 116-119:

 

A driver going down a straight highway is traveling at 70 ft/sec on cruise control when he begins accelerating at a rate of 4.2 ft/sec2.  The velocity of the car in ft/sec is given by the function V = 4.2t + 70, where t is in seconds.

 

  1. Interpret the meaning of the slope of this model.

Ans:  Every second the velocity is increasing by 4.2 ft/sec.

Section:  2.4

 

  1. What is the effect of a 1 second increase in time traveled?

Ans:  The velocity increases by 4.2 ft/sec.

Section:  2.4

 

  1. Determine the velocity of the car after 10.4 seconds.
  2. A) 40 ft/sec    B)  112.32 ft/sec    C)  113.68 ft/sec    D)  114.54 ft/sec

Ans:  C     Section:  2.4

 

  1. If the car is traveling at 100 ft/sec, for how long did it accelerate?  (Round to the nearest tenth of a second.)
  2. A) 9 seconds    B)  7.1 seconds    C)  7.3 seconds    D)  7.5 seconds

Ans:  B     Section:  2.4

 

  1. The speed of sound through the air near sea level is linearly related to the temperature of the air.  If sound travels at 1122 ft/sec when the air temperature is 64F and at 1144 ft/sec when the air temperature is 84F:

(a)  Construct a linear model relating the speed of sound s to the air temperature t.

(b)  Interpret the slope of this model.

Ans:  (a)  s = 1.1t + 1051.6

(b)  The speed of sound increases 1.1 ft/sec for each 1F increase in temperature.

Section:  2.4

 

Use the following to answer questions 121-124:

 

A business purchases a copier for $7,500 and anticipates it will be worth $4,500 after 5 years.

 

  1. Use straight-line depreciation to find a linear model for the depreciated value V of the copy machine after t years of use.
  2. A) V = 7,500 + 300 t                                C)      V = 300 + 7,500 t
  3. B) V = 300 7,500 t                                   D)      V = 7,500 300t

Ans:  D     Section:  2.4

 

  1. Interpret the slope of the linear model for the depreciated value of the copy machine.
  2. A) The copiers value is decreasing by $400 per year.
  3. B) The copiers value is decreasing by $7,500 per year.
  4. C) The copiers original value was $400.
  5. D) The copiers original value was $7,500.

Ans:  A     Section:  2.4

 

  1. What is the copiers value after 4 years of use?
  2. A) $8,250    B)  $8,300    C)  $8,350    D)  $8,400

Ans:  B     Section:  2.4

 

  1. How many years will it take for the copiers value to decrease to $1700?
  2. A) 4 years    B)  5 years    C)  6 years    D)  7 years

Ans:  D     Section:  2.4

 

Use the following to answer questions 125-126:

 

The regression model for the data shown in the table is y = 3.0x + 134.6.

 

x y
10 114
8 108
15 77
14 87
20 75
17 94

 

 

  1. Plot the data and the model on the same axes.

Ans:

Section:  2.4

 

  1. Use the model to estimate y when x = 18.5.
  2. A) 7    B)  78.9    C)  79.1    D)  79.3

Ans:  C     Section:  2.4

 

Use the following to answer questions 127-128:

 

The regression model for the data shown in the table is y = 2.3x + 3.9.

 

x y
4 14
1 6
3 9
2 9
5 17
7 20
6 16

 

 

  1. Plot the data and the model on the same axes.

Ans:

Section:  2.4

 

  1. Use the model to estimate y when x = 5.5.

Ans:  16.55

Section:  2.4

Chapter 7

 

  1. Solve the system by graphing.

x + y = 4

x + y = 2

Ans:  (1, 3)

 

Section:  7.1

 

  1. Solve the system by graphing.

x 2y = 8

x + y = 1

Ans:  (2, 3)

 

Section:  7.1

 

  1. Solve the system by graphing.

2x + y = 4

x + y = 3

Ans:  (1, 2)

 

Section:  7.1

 

  1. Solve the system by graphing.

3x + y = 6

3x y = 0

Ans:  (1, 3)

 

Section:  7.1

 

  1. Solve the system by graphing.

x    y = 2

3x 3y = 6

Ans:  Infinitely many solutions (dependent system)

 

Section:  7.1

 

  1. Solve the system of equations.

x + y = 4

x y = 2

  1. A) (1, 3)    B)  (1, 5)    C)  (3, 1)    D)  (5, 1)

Ans:  C     Section:  7.1

 

  1. Solve the system of equations.

x + y = 9

x y = 9

Ans:  (9, 0)

Section:  7.1

 

  1. Solve the system of equations.

2x + 5y = 12

7x 5y = 3

  1. A) (1, 3)    B)  (1, 2)    C)  (0, 2)    D)  (0, 3)

Ans:  B     Section:  7.1

 

  1. Solve the system of equations.

x 2y = 3

5x 10y = 10

Ans:  No solution (parallel lines)

Section:  7.1

 

  1. Solve the system of equations.

x y = 4

x + 2y = 14

  1. A) (2, 6)    B)  (3, 6)    C)  (2, 5)    D)  (3, 5)

Ans:  A     Section:  7.1

 

  1. Solve the system of equations.

y = x + 3

y = 5x 5

Ans:  (2, 5)

Section:  7.1

 

  1. Solve the system of equations.

7x 2y = 5

6x + 5y = 11

Ans:  (1, 1)

Section:  7.1

 

  1. Solve the system of equations.

3x 4y = 8

6x + 3y = 5

Ans:

Section:  7.1

 

  1. Solve the system of equations.

 

Ans:  (20, 12)

Section:  7.1

 

  1. Solve the system of equations.

 

Ans:  (1, 3, 3)

Section:  7.1

 

  1. Solve the system using elimination by addition.

x y z = 2

2x + y z = 3

3x + y z = 2

Ans:  (1, 3, 2)

Section:  7.1

 

  1. Solve the system of equations.

x y z = 5

x y + 3z = 7

2x + y z = 1

  1. A) (1, 3, 2)    B)  (0, 2, 2)    C)  (0, 2, 3)    D)  No solution

Ans:  C     Section:  7.1

 

  1. Solve the system of equations.

3x + 2y + 3z = 6

4x + 3y + 2z = 5

6x + 4y + 5z = 11

Ans:  (3, 3, 1)

Section:  7.1

 

  1. Solve the system of equations.

2x 3y + 4z = 19

5x 2y + z = 19

7x + 5y 5z = 39

  1. A) (4, 3, 5)    B)  (4, 4, 4)    C)  (4, 2, 6)    D)  No solution

Ans:  D     Section:  7.1

 

  1. Solve the system of equations.

 

  1. A) (1, 7, 0)
  2. B) (3, 3, 2)
  3. C) {(2s 3, 5s 7, s) | s is any real number}
  4. D) No solution

Ans:  C     Section:  7.1

 

  1. Solve using elimination by addition.

 

Ans:

Section:  7.1

 

  1. Solve the system of equations.

2x + 3y 4z = 9

6x y + z = 18

4x 2y + 3z = 28

Ans:  No solution

Section:  7.1

 

  1. A boat traveled 48 mi up a river in 4 hours.  Returning downstream, the boat took 3 hours.  What is the boats rate in still water, and what is the rate of the rivers current?

Ans:  Boat: 14 mi/h; current: 2 mi/h

Section:  7.1

 

  1. A chemist wants to combine a 30% alcohol solution with a 50% alcohol solution to form 400 mL of a 35% alcohol solution.  How much of each solution should the chemist use to form the mixture?

Ans:  300 mL of 30% solution and 100 mL of 50% solution

Section:  7.1

 

  1. A coin jar contains nickels, dimes, and quarters.  There are 30 coins in all.  There are 11 more nickels than quarters.  The value of the dimes is $1.70 less than the value of the quarters.  How many coins of each type are in the jar?

Ans:  nickels: 19, dimes: 3, quarters: 8

Section:  7.1

 

  1. Angus invested $12,000, part at 15% and part at 9%.  If the total interest at the end of the year is $1,440, how much did he invest at each rate?

Ans:  $6,000 at 15% and $6,000 at 9%

Section:  7.1

 

  1. Janet invested $10,000, part at 2% and part at 12%.  If the total interest at the end of the year is $600, how much did she invest at 2%?
  2. A) $4,000    B)  $7,000    C)  $6,000    D)  $5,000

Ans:  C     Section:  7.1

 

  1. A company manufactures three products, tables, chairs, and bookcases.  The labor, material and shipping costs for manufacturing one unit of each product are given in the table.  The weekly allocations for labor, materials, and shipping are $62,800, $56,700, and $26,300, respectively.  How many of each type of product should be manufactured each week in order to exactly use the weekly allocations?

_____________________________________________

  Product         Table               Chair               Bookcase  

                          Labor             $40                  $65                  $50

Materials       $85                  $45                  $60

  Shipping        $40                  $20                  $30            

Ans:  120 tables, 700 chairs, and 250 bookcases

Section:  7.1

 

  1. Is the matrix in reduced form?

 

  1. A) Yes    B)  No

Ans:  A     Section:  7.2

 

  1. Is the matrix in reduced form?

 

  1. A) Yes    B)  No

Ans:  B     Section:  7.2

 

  1. Write the linear system corresponding to the reduced augmented matrix and solve.

 

Ans:  x1 = 1, x2 = 1, x3 = 4

Section:  7.2

 

  1. Write the linear system corresponding to the reduced augmented matrix and solve.

 

  1. A) x1 = 7t + 4, x2 = t + 5, x3 = t, t any real number
  2. B) x1 = 7t + 4, x2 = t + 5, x3 = t, t any real number
  3. C) x1 = 7t + 4, x2 = t 5, x3 = t, t any real number
  4. D) x1 = 7t 4, x2 = t + 5, x3 = t, t any real number

Ans:  A     Section:  7.2

 

  1. Perform the indicated row operation, then write the new matrix.

2R1 + R2 R2

Ans:

Section:  7.2

 

  1. Perform the indicated row operations, then write the new matrix.

R1 + R2 R2; 2R1 + R3 R3

  1. A)                                   C)
  2. B)                                   D)

Ans:  B     Section:  7.2

 

  1. Use row operations to change the matrix to reduced form.

 

Ans:

Section:  7.2

 

  1. Use row operations to change the matrix to reduced form.

 

  1. A)                                     C)
  2. B)                                     D)

Ans:  D     Section:  7.2

 

  1. Solve the system using Gauss-Jordan elimination.

x1 4x2 = 17

4x1 + x2 = 17

  1. A) x1 = 5, x2 = 2    B)  x1 = 4, x2 = 3    C)  x1 = 5, x2 = 3    D)  No solution

Ans:  C     Section:  7.2

 

  1. Solve the system using Gauss-Jordan elimination.

10x1 5x2 = 35

2x1 + x2 = 7

  1. A) x1 = 5, x2 = 4    B)  x1 = 6, x2 = 3    C)  x1 = 5, x2 = 3    D)  No solution

Ans:  D     Section:  7.2

 

  1. Solve the system using Gauss-Jordan elimination.

3x1 + 3x2 = 9

2x1 2x2 = 6

Ans:  x1 = s 3, x2 = s, s any real number

Section:  7.2

 

  1. Solve the system using Gauss-Jordan elimination.

x1 x2 + x3 = 4

x1 + x2 3x3 =

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