$35.00

- A parabola has its vertex at the origin, and the equation of its directrix is . Find the coordinates of the focus.
- A) B) C) D)

Ans: C Section: 6.1

- A parabola has its vertex at the origin, and the coordinates of its focus are . Find the equation of the directrix.
- A) B) C) D)

Ans: D Section: 6.1

Use the following to answer questions 3-5:

*y*^{2} = 28*x*

- Find the vertex.
- A) (0, 0) B) (0, –6) C) (0, –24) D) (–24, 0)

Ans: A Section: 6.1

- Find the focus.
- A) (0, –1) B) (0, –4) C) (–1, 0) D) (–4, 0)

Ans: C Section: 6.1

- Find the directrix.
- A)
*y*= –3 B)*y*= 3 C)*x =*–3 D)*x =*3

Ans: C Section: 6.1

Use the following to answer questions 6-8:

*y*^{2} = 12*x*

- Find the focus.

Ans: (3, 0)

Section: 6.1

- Find the directrix.

Ans: *x* = –3

Section: 6.1

- Sketch the graph.

Ans:

Section: 6.1

Use the following to answer questions 9-11:

*x*^{2} = 16*y*

- Find the vertex.

Ans: (0, 0)

Section: 6.1

- Find the focus.

Ans: (0, 6)

Section: 6.1

- Find the directrix.

Ans: *y *= 5

Section: 6.1

Use the following to answer questions 12-14:

*y*^{2} = –8*x*

- Find the focus.
- A) (–2, 0) B) (2, 0) C) (0, –2) D) (0, 2)

Ans: A Section: 6.1

- Find the directrix.
- A)
*x*= –2 B)*y = –*2 C)*x*= 2 D)*y =*2

Ans: C Section: 6.1

- Sketch the graph.
- A) C)
- B) D)

Ans: B Section: 6.1

Use the following to answer questions 15-17:

*x*^{2} = –16*y*

- Locate the focus.

Ans: (0, –4)

Section: 6.1

- Locate the directrix.

Ans: *y* = 4

Section: 6.1

- Sketch the graph.

Ans:

Section: 6.1

Use the following to answer questions 18-20:

*x*^{2} = 14*y*

- Locate the focus.
- A) (7/2, 0) B) (–7/2, 0) C) (0, 7/2) D) (0, –7/2)

Ans: C Section: 6.1

- Locate the directrix.
- A)
*x*= –7/2 B)*y = –*7/2 C)*x*= 7/2 D)*y =*7/2

Ans: B Section: 6.1

- Sketch the graph.
- A) C)
- B) D)

Ans: D Section: 6.1

- Find the coordinates of the focus to two decimal places.

*y*^{2} = 34*x*

Ans: (8.50, 0)

Section: 6.1

- Find the coordinates of the focus to two decimal places.

*x*^{2} = –79*y*

- A) (–19.75, 0) B) (0, –19.75) C) (0, 19.75) D) (–79, 0)

Ans: B Section: 6.1

- Find the equation of the parabola with vertex at the origin, axis of symmetry the
*x*– or*y*-axis, and directrix*y*= 10. - A)
*y*^{2}= –40*x*B)*y*^{2}= 40*x*C)*x*^{2}= –40*y*D)*x*^{2}= 40*y*

Ans: C Section: 6.1

- Find the equation of the parabola with vertex at the origin, axis of symmetry the
*x*– or*y*-axis, and focus (0, –1).

Ans: *x*^{2} = –4*y*

Section: 6.1

- Find the equation of the parabola with vertex at the origin, axis of symmetry the
*x*– or*y*-axis, and directrix*x*= –10.

Ans: *y*^{2} = 40*x*

Section: 6.1

- Find the equation of the parabola with vertex at the origin, axis of symmetry the
*x*– or*y*-axis, and focus (–16, 0). - A)
*y*^{2}= –64*x*B)*y*^{2}= –4*x*C)*x*^{2}= –64*y*D)*x*^{2}= –4*y*

Ans: A Section: 6.1

- Find the equation of the parabola with vertex at the origin, axis of symmetry the
*y*-axis, and passing through (4, 2). - A)
*y*^{2}= 8*x*B)*y*^{2}= 2*x*C)*x*^{2}= 8*y*D)*x*^{2}= 2*y*

Ans: C Section: 6.1

- Find the equation of the parabola with vertex at the origin, axis of symmetry the
*y*-axis, and passing through (–2, 4).

Ans: *y*^{2} = –8*x*

Section: 6.1

- Find the first-quadrant points of intersection for the pair of parabolas to three decimal places.

*x*^{2} = 5*y*

*y*^{2} = 7*x*

Ans: (0, 0) and (5.593, 6.257)

Section: 6.1

- Use the definition of a parabola and the distance formula to find the equation of a parabola with directrix
*y*= –3 and focus (–4, 1). - A)
*y*^{2}+ 8*y*– 8*x*+ 24 = 0 C)*x*^{2}+ 8*x*– 8*y*+ 24 = 0 - B)
*y*^{2}– 8*y*– 8*x*+ 8 = 0 D)*x*^{2}– 8*x*– 8*y*+ 8 = 0

Ans: C Section: 6.1

- Find the distance between the foci of an ellipse that has a major axis of length 10 and a minor axis of length 8.
- A) 3 B) 6 C) 12 D) 9

Ans: B Section: 6.2

- Find the length of the major axis of an ellipse that has the distance between the foci equal to 10 and the length of the minor axis equal to 24.
- A) 13 B) 18 C) 52 D) 26

Ans: D Section: 6.2

- Sketch the graph. Find the coordinates of the foci and the lengths of the major and minor axes.

Ans: Foci at (–3, 0) and (3, 0)

Major axis length = 10, minor axis length = 8

Section: 6.2

- Sketch the graph. Find the coordinates of the foci and the lengths of the major and minor axes.

Ans: Foci at

Major axis length = 8, minor axis length = 6

Section: 6.2

Use the following to answer questions 35-37:

9*x*^{2} + *y*^{2} = 36

- Sketch the graph.
- A) C)
- B) D)

Ans: B Section: 6.2

- Find the coordinates of the foci
- A) C)
- B) D)

Ans: A Section: 6.2

- Find the lengths of the major and minor axes.
- A) Major axis length = 6, minor axis length = 3
- B) Major axis length = 12, minor axis length = 6
- C) Major axis length = 12, minor axis length = 4
- D) Major axis length = 9, minor axis length = 4

Ans: C Section: 6.2

Use the following to answer questions 38-40:

*x*^{2} + 4*y*^{2} = 36

- Sketch the graph.

Ans:

Section: 6.2

- Find the coordinates of the foci.

Ans:

Section: 6.2

- Find the lengths of the major and minor axes.

Ans: Major axis = 12, Minor axis length = 6

Section: 6.2

- Sketch the graph. Find the coordinates of the foci and the lengths of the major and minor axes.

25*x*^{2} + 16*y*^{2} = 400

Ans: Foci at (0, –3) and (0, 3)

Major axis length = 10, Minor axis length = 8

Section: 6.2

Use the following to answer questions 42-44:

25*x*^{2} + *y*^{2} = 100

- Sketch the graph.
- A) C)
- B) D)

Ans: B Section: 6.2

- Find the coordinates of the foci.
- A) C)
- B) D)

Ans: C Section: 6.2

- Find the lengths of the major and minor axes.
- A) Major axis length = 10, minor axis length = 2
- B) Major axis length = 20, minor axis length = 2
- C) Major axis length = 10, minor axis length = 4
- D) Major axis length = 20, minor axis length = 4

Ans: D Section: 6.2

- Sketch the graph. Find the coordinates of the foci and the lengths of the major and minor axes.

5*x*^{2} + 2*y*^{2} = 10

Ans: Foci at

Major axis length = , minor axis length =

Section: 6.2

- Write the equation of the ellipse in the form whose graph is shown.

Ans:

Section: 6.2

- Write the equation of the ellipse in the form whose graph is shown.

- A) B) C) D)

Ans: A Section: 6.2

- Find the equation of an ellipse in the form with major axis along the
*x*-axis, major axis length 14 and minor axis length 6. - A) B) C) D)

Ans: C Section: 6.2

- Write the equation of an ellipse in the form with major axis along the
*x-*axis, major axis length 16, and distance of foci from center = 4.

Ans:

Section: 6.2

- Write the equation of an ellipse in the form with major axis along the
*y-*axis, major axis length 16, and distance of foci from center = 7. - A) B) C) D)

Ans: B Section: 6.2

- Find the equation of an ellipse in the form with major axis along the
*y*-axis, minor axis length 8, and distance of foci from center = 3. - A) B) C) D)

Ans: B Section: 6.2

Use the following to answer questions 52-53:

A landscaper wishes to create an elliptical garden 20 m long and 12 m across with decorative fountains located at the foci.

- How far from the center of the ellipse should the fountains be located? (Round to the nearest 100th of a meter.)
- A) 18 m B) 2.30 m C) 3.32 m D) 4.66 m

Ans: C Section: 6.2

- How far apart are the fountains?
- A) 94 m B) 6.90 m C) 11.62 m D) 12.10 m

Ans: A Section: 6.2

- Find the distance between the foci of a hyperbola that has a transverse axis of length 6 and a conjugate axis of length 8.
- A) 5 B) 20 C) 10 D) 7

Ans: C Section: 6.3

- Match each equation with its graph.
- , B.
- , D.

III.

Ans: A matches II, B matches IV, C matches III, D matches I

Section: 6.3

Use the following to answer questions 56-58:

- Sketch the graph.
- A) C)
- B) D)

Ans: A Section: 6.3

- Find the coordinates of the foci.
- A) C)
- B) D)

Ans: C Section: 6.3

- Find the lengths of the transverse and conjugate axes.
- A) Transverse axis length = 8, conjugate axis length = 4
- B) Transverse axis length = 16, conjugate axis length = 4
- C) Transverse axis length = 4, conjugate axis length = 2
- D) Transverse axis length = 8, conjugate axis length = 2

Ans: A Section: 6.3

Use the following to answer questions 59-61:

- Sketch the graph.

Ans:

Section: 6.3

- Find the coordinates of the foci.

Ans:

Section: 6.3

- Find the lengths of the transverse and conjugate axes.

Ans: Transverse axis length = 4, conjugate axis length = 8

Section: 6.3

- Find the coordinates of the foci.

Ans:

Section: 6.3

Use the following to answer questions 63-65:

- Sketch the graph.

Ans:

Section: 6.3

- Find the coordinates of the foci.

Ans:

Section: 6.3

- Find the lengths of the transverse and conjugate axes.

Ans: Transverse axis length = 4, conjugate axis length = 8

Section: 6.3

- Sketch the graph of the equation. Find the coordinates of the foci, and find the lengths of the transverse and conjugate axes.

4*x*^{2} – 9*y*^{2} = 36

Ans: Foci at

Transverse axis length = 6, conjugate axis length = 4

Section: 6.3

Use the following to answer questions 67-69:

*y*^{2} – 4*x*^{2} = 16

- Sketch the graph.
- A) C)
- B) D)

Ans: C Section: 6.3

- Find the coordinates of the foci.
- A) C)
- B) D)

Ans: D Section: 6.3

- Find the lengths of the transverse and conjugate axes.
- A) Transverse axis length = 8, conjugate axis length = 4
- B) Transverse axis length = 4, conjugate axis length = 8
- C) Transverse axis length = 2, conjugate axis length = 4
- D) Transverse axis length = 4, conjugate axis length = 2

Ans: A Section: 6.3

- Sketch the graph of the equation. Find the coordinates of the foci, and find the lengths of the transverse and conjugate axes.

25*y*^{2} – 4*x*^{2} = 100

Ans: Foci at

Transverse axis length = 4, conjugate axis length = 10

Section: 6.3

- Sketch the graph of the equation. Find the coordinates of the foci, and find the lengths of the transverse and conjugate axes.

9*y*^{2} – 4*x*^{2} = 36

Ans: Foci at

Transverse axis length = 4, conjugate axis length = 6

Section: 6.3

- Find an equation of a hyperbola in the form

whose center is at the origin and whose graph is shown below.

- A) B) C) D)

Ans: D Section: 6.3

- Find an equation of a hyperbola in the form

whose center is at the origin and whose graph is shown below.

Ans:

Section: 6.3

- Find an equation of a hyperbola in the form

whose center is at the origin, whose transverse axis is on the *x*-axis and has length 14, and whose conjugate axis has length 10.

- A) B) C) D)

Ans: D Section: 6.3

- Find an equation of a hyperbola in the form

whose center is at the origin, whose transverse axis is on the *x*-axis and has length 8, and whose foci are a distance of 6 units from the center.

Ans:

Section: 6.3

- Find an equation of a hyperbola in the form

whose center is at the origin, whose transverse axis is on the *y-*axis and has length 6, and whose foci are a distance of 4 units from the center.

- A) B) C) D)

Ans: C Section: 6.3

- Find an equation of a hyperbola in the form

whose center is at the origin, whose conjugate axis is on the *x*-axis and has length 12, and whose foci are a distance of from the center.

Ans:

Section: 6.3

- Find the equations of the asymptotes.

Ans:

Section: 6.3

- Find the equations of the asymptotes.

- A) B) C) D)

Ans: B Section: 6.3

- Find the equations of the asymptotes.

Ans:

Section: 6.3

- Find the equations of the asymptotes.

16*x*^{2} – 25*y*^{2} = 400

- A) B) C) D)

Ans: A Section: 6.3

- A ship is traveling on a course parallel to and 70 miles from a straight shoreline. Two transmitting stations,
*S*_{1}and*S*_{2}, are located 300 miles apart on the shoreline. By timing radio signals from the stations, this ship’s navigator determines that the ship is between the two stations and 40 miles closer to*S*_{2}than to*S*_{1}. Find the distance from the ship to each station. Round answers to one decimal place.

Ans: 185.8 mi from *S*_{1} and 145.8 mi from *S*_{2}

Section: 6.3

- A ship is traveling on a course parallel to and 90 miles from a straight shoreline. Two transmitting stations,
*S*_{1}and*S*_{2}, are located 400 miles apart on the shoreline. By timing radio signals from the stations, this ship’s navigator determines that the ship is between the two stations and 30 miles closer to*S*_{2}than to*S*_{1}. Find the distance from the ship to station*S*_{2}. Round to one decimal place. - A) 2 mi B) 202.6 mi C) 204.4 mi D) 206.8 mi

Ans: C Section: 6.3

**Chapter 7**

- Solve the system by graphing.

*x* + *y* = 4

–*x* +* y* = 2

Ans: (1, 3)

Section: 7.1

- Solve the system by graphing.

*x* – 2*y* = 8

*x* + *y* = –1

Ans: (2, –3)

Section: 7.1

- Solve the system by graphing.

2*x* + *y* = 4

*x* + *y* = 3

Ans: (1, 2)

Section: 7.1

- Solve the system by graphing.

3*x* + *y* = 6

3*x* – *y* = 0

Ans: (1, 3)

Section: 7.1

- Solve the system by graphing.

*x* – *y* = 2

3*x* – 3*y = *6

Ans: Infinitely many solutions (dependent system)

Section: 7.1

- Solve the system of equations.

*x* + *y = *4

*x* – *y* = 2

- A) (1, 3) B) (–1, 5) C) (3, 1) D) (5, –1)

Ans: C Section: 7.1

- Solve the system of equations.

*x* + *y* = 9

*x* – *y* = 9

Ans: (9, 0)

Section: 7.1

- Solve the system of equations.

2*x* + 5*y* = –12

7*x* – 5*y* = 3

- A) (–1, –3) B) (–1, –2) C) (0, –2) D) (0, –3)

Ans: B Section: 7.1

- Solve the system of equations.

*x* – 2*y* = –3

5*x* – 10*y* = –10

Ans: No solution (parallel lines)

Section: 7.1

- Solve the system of equations.

*x* – *y* = 4

*x* + 2*y* = –14

- A) (–2, –6) B) (–3, –6) C) (–2, –5) D) (–3, –5)

Ans: A Section: 7.1

- Solve the system of equations.

*y* = *x* + 3

*y* = 5*x* – 5

Ans: (2, 5)

Section: 7.1

- Solve the system of equations.

7*x *– 2*y* = 5

6*x* + 5*y* = 11

Ans: (1, 1)

Section: 7.1

- Solve the system of equations.

3*x* – 4*y* = 8

6*x + *3*y* = 5

Ans:

Section: 7.1

- Solve the system of equations.

Ans: (–20, 12)

Section: 7.1

- Solve the system of equations.

Ans: (–1, –3, 3)

Section: 7.1

- Solve the system using elimination by addition.

*x* – *y* – *z* = 2

2*x* + *y* – *z* = –3

3*x* + *y* – *z* = –2

Ans: (1, –3, 2)

Section: 7.1

- Solve the system of equations.

*x* – *y* – *z* = 5

–*x* – *y* + 3*z* = –7

2*x* + *y* – *z* = 1

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

Ans: C Section: 7.1

- Solve the system of equations.

3*x* + 2*y* + 3*z* = 6

4*x* + 3*y* + 2*z* = 5

6*x* + 4*y* + 5*z* = 11

Ans: (3, –3, 1)

Section: 7.1

- Solve the system of equations.

2*x* – 3*y* + 4*z* = –19

5*x* – 2*y* + *z* = –19

–7*x* + 5*y* – 5*z* = 39

- A) (–4, –3, –5) B) (–4, –4, –4) C) (–4, –2, –6) D) No solution

Ans: D Section: 7.1

- Solve the system of equations.

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

Ans: C Section: 7.1

- Solve using elimination by addition.

Ans:

Section: 7.1

- Solve the system of equations.

2*x* + 3*y* – 4*z* = –9

–6*x* – *y* + *z* = –18

4*x* – 2*y* + 3*z* = 28

Ans: No solution

Section: 7.1

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

Ans: Boat: 14 mi/h; current: 2 mi/h

Section: 7.1

- 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

- 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

- 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

- 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%?
- A) $4,000 B) $7,000 C) $6,000 D) $5,000

Ans: C Section: 7.1

- 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

- Is the matrix in reduced form?

- A) Yes B) No

Ans: A Section: 7.2

- Is the matrix in reduced form?

- A) Yes B) No

Ans: B Section: 7.2

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

Ans: *x*_{1} = 1, *x*_{2} = –1, *x*_{3} = –4

Section: 7.2

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

- A)
*x*_{1}= –7*t*+ 4,*x*_{2}= –*t*+ 5,*x*_{3}=*t*,*t*any real number - B)
*x*_{1}= 7*t*+ 4,*x*_{2}= –*t*+ 5,*x*_{3}=*t*,*t*any real number - C)
*x*_{1}= –7*t*+ 4,*x*_{2}= –*t*– 5,*x*_{3}=*t*,*t*any real number - D)
*x*_{1}= 7*t*– 4,*x*_{2}= –*t*+ 5,*x*_{3}=*t*,*t*any real number

Ans: A Section: 7.2

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

–2R1 + R2 → R2

Ans:

Section: 7.2

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

R1 + R2 → R2; –2R1 + R3 → R3

- A) C)
- B) D)

Ans: B Section: 7.2

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

Ans:

Section: 7.2

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

- A) C)
- B) D)

Ans: D Section: 7.2

- Solve the system using Gauss-Jordan elimination.

*x*_{1} – 4*x*_{2} = –17

4*x*_{1} + *x*_{2} = –17

- A)
*x*_{1}= –5,*x*_{2}= 2 B)*x*_{1}= –4,*x*_{2}= 3 C)*x*_{1}= –5,*x*_{2}= 3 D) No solution

Ans: C Section: 7.2

- Solve the system using Gauss-Jordan elimination.

–10*x*_{1} – 5*x*_{2} = 35

2*x*_{1} + *x*_{2} = 7

- A)
*x*_{1}= 5,*x*_{2}= –4 B)*x*_{1}= 6,*x*_{2}= –3 C)*x*_{1}= 5,*x*_{2}= –3 D) No solution

Ans: D Section: 7.2

- Solve the system using Gauss-Jordan elimination.

–3*x*_{1} + 3*x*_{2} = 9

2*x*_{1} – 2*x*_{2} = –6

Ans: *x*_{1} = *s *– 3, *x*_{2} = *s*, *s* any real number

Section: 7.2

- Solve the system using Gauss-Jordan elimination.

–*x*_{1} – *x*_{2} + *x*_{3} = –4

*x*_{1} + *x*_{2} – 3*x*_{3} = 2

5*x*_{1} – *x*_{2} + *x*_{3} = 14

- A)
*x*_{1}= 3,*x*_{2}= 2,*x*_{3}= 1 C)*x*_{1}= 4,*x*_{2}= 1,*x*_{3}= 2 - B)
*x*_{1}= 3,*x*_{2}= 2,*x*_{3}= 2 D) No solution

Ans: A Section: 7.2

- Solve the system using Gauss-Jordan elimination.

–*x*_{1} – *x*_{2} – *x*_{3} = 0

*x*_{1} + *x*_{2} + 5*x*_{3} = –4

–2*x*_{1} – *x*_{2} + *x*_{3} = –5

Ans: *x*_{1} = 3, *x*_{2} = –2, *x*_{3} = –1

Section: 7.2

- Solve the system using Gauss-Jordan elimination.

3*x*_{1} – 9*x*_{2} + 2*x*_{3} = –7

–6*x*_{1} + 18*x*_{2} + *x*_{3} = –11

9*x*_{1} – 27*x*_{2} + 5*x*_{3} = –16

- A)
*x*_{1}= 4,*x*_{2}= 1,*x*_{3}= –5 - B)
*x*_{1}= 3*s*+ 1,*x*_{2}=*s*+ 2,*x*_{3}=*s*,*s*any real number - C)
*x*_{1}= 3*s*+ 1,*x*_{2}=*s*,*x*_{3}= –5,*s*any real number - D) No solution

Ans: C Section: 7.2

- Solve the system using Gauss-Jordan elimination.

–*x*_{1} + *x*_{2} + 5*x*_{3} = 7

–5*x*_{1} + *x*_{2} – *x*_{3} = –17

–20*x*_{1} + 4*x*_{2} – 4*x*_{3} = –69

- A)
*x*_{1}= 3,*x*_{2}= 0,*x*_{3}= 2 C)*x*_{1}= 3,*x*_{2}= 1,*x*_{3}= 1 - B)
*x*_{1}= 3,*x*_{2}= 0,*x*_{3}= 1 D) No solution

Ans: D Section: 7.2

- Solve the system using Gauss-Jordan elimination.

3*x*_{1} + 6*x*_{2} + 10*x*_{3} + 6*x*_{4} = 30

*x*_{1} + 2*x*_{2} + 3*x*_{3} + *x*_{4} = 9

Ans: *x*_{1} = –2*s + *8*t*, *x*_{2} = *s*, *x*_{3} = –3*t* + 3, *x*_{4} = *t*, *s* and *t *any real numbers

Section: 7.2

- Find
*a*,*b*, and*c*so that the graph of the parabola with equation*y*=*ax*^{2}+*bx*+*c*passes through the points (1, 6), (–2, 21), and (3, 16).

Ans: *a = *2, *b* = –3, *c* = 7

Section: 7.2

- Find
*a*,*b*, and*c*so that the graph of the circle with equation*x*^{2}+*y*^{2}+*ax*+*by*+*c*= 0 passes through the points (0, 7), (–6, –1), and (1, 0).

Ans: *a = *6, *b* = –6, *c* = –7

Section: 7.2

- Add, if possible.

Ans:

Section: 7.3

- Add, if possible.

Ans:

Section: 7.3

- Add, if possible.

- A) B) C) D) Not defined

Ans: D Section: 7.3

- Subtract, if possible.

Ans:

Section: 7.3

- Multiply.

Ans:

Section: 7.3

- Multiply, if possible.

- A) B) C) D) Not defined

Ans: C Section: 7.3

- Find
*AB*, if possible.

Ans:

Section: 7.3

- Find
*A*^{2}, if possible.

- A) B) C) D) Not defined

Ans: D Section: 7.3

- Find
*A*^{2}, if possible.

Ans:

Section: 7.3

- Find the value of
*a*,*b*,*c*, and*d*if

+ = .

Ans: *a* = –3, *b* = –2, *c* = 9, *d* = –5

Section: 7.3

- Find the value of
*a*,*b*,*c*, and*d*if

.

- A) C)
- B) D)

Ans: D Section: 7.3

- A company with two different plants makes shoes and hiking boots. The production costs for each item are given in the following matrices.

Find the matrix and explain what information it provides.

Ans:

This is the average cost of materials and labor for each product at the two plants.

Section: 7.3

- A car dealer sells two models of a car. Current dealer invoice price (cost) and the retail price for the basic models and the indicated options are given in the following two matrices.

The markup matrix is defined to be Economic conditions have resulted in an across-the-board increase of 15% in costs to the dealer for next year’s models. To stay competitive, the dealer will only increase the retail price by 10%. Calculate the markup matrix for next year’s models and the indicated options. (Compute results to the nearest dollar.)

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

Ans: B Section: 7.3

- A company with manufacturing plants located in different parts of the country has labor-hour and wage requirements for the manufacturing of two types of inflatable boats as given in the following matrices.

Find the labor costs for a one-person boat manufactured at plant I.

- A) $17.50 B) $18.60 C) $23.70 D) $13.80

Ans: D Section: 7.3

- Multiply.

Ans:

Section: 7.4

- Multiply.

- A) B) C) D)

Ans: D Section: 7.4

- Use matrix products to determine if the matrices are inverses of each other.

and

- A) Yes B) No

Ans: A Section: 7.4

- Write the matrix equation as a system of linear equations.

Ans:

Section: 7.4

- Write the system in the form of a matrix equation.

Ans:

Section: 7.4

- Write the system in the form of a matrix equation.

- A) C)
- B) D)

Ans: A Section: 7.4

- Find
*x*_{1}and*x*_{2}.

Ans: *x*_{1} = 2, *x*_{2} = 5

Section: 7.4

- Find
*x*_{1}and*x*_{2}.

- A)
*x*_{1}= 12,*x*_{2}= 8 B)*x*_{1}= 8,*x*_{2}= 12 C)*x*_{1}= 10,*x*_{2}= 6 D)*x*_{1}= 6,*x*_{2}= 10

Ans: C Section: 7.4

- Find the inverse of the matrix, if it exists.

Ans:

Section: 7.4

- Find the inverse of the matrix, if it exists.

- A) B) C) D) The inverse does not exist.

Ans: D Section: 7.4

- Find
*A*^{–1}, if it exists.

Ans:

Section: 7.4

- Write the system as a matrix equation and solve using inverses.

*x*_{1} + 2*x*_{2} = 18

4*x*_{1} + *x*_{2} = 16

Ans: *x*_{1} = 2, *x*_{2} = 8

Section: 7.4

- Write the system as a matrix equation and solve using inverses.

*x*_{1} – 2*x*_{2} + *x*_{3} = –4

–2*x*_{1} + *x*_{2} + 5*x*_{3} = –1

2*x*_{1} + *x*_{2} – *x*_{3} = 7

- A)
*x*_{1}= 3,*x*_{2}= 2,*x*_{3}= 1 C)*x*_{1}= 2,*x*_{2}= 3,*x*_{3}= 0 - B)
*x*_{1}= 2,*x*_{2}= 3,*x*_{3}= 1 D)*x*_{1}= 2,*x*_{2}= 2,*x*_{3}= 1

Ans: C Section: 7.4

- Write the system as a matrix equation and solve using inverses.

*x*_{1} – *x*_{2} – *x*_{3} = 0

–2*x*_{1} + *x*_{2} – 5*x*_{3} = 5

5*x*_{1} – 5*x*_{2} + *x*_{3} = –6

Ans: *x*_{1} = 1, *x*_{2} = 2, *x*_{3} = –1

Section: 7.4

- Adult tickets for a play cost $8 and child tickets cost $6. If there were 20 people at a performance and the theatre collected $152 from ticket sales, how many adults and how many children attended the play?

Ans: 16 adults and 4 children

Section: 7.4

- Evaluate the second-order determinant.

- A) –10 B) 30 C) 10 D) 8

Ans: B Section: 7.5

- Solve the system using Cramer’s rule.

- A) B) C) D)

Ans: A Section: 7.5

- Solve the system using Cramer’s rule.

- A) , C) ,
- B) , D) ,

Ans: D Section: 7.5

- Consider the following determinant.

Write the minor of the element . Leave the answer in determinant form.

- A) B) C) D)

Ans: C Section: 7.5

- Consider the following determinant.

Evaluate the cofactor of the element .

- A) 52 B) –52 C) 28 D) –28

Ans: A Section: 7.5

- Evaluate the following determinant using cofactors.

- A) 20 B) –20 C) 70 D) –70

Ans: A Section: 7.5

- Solve the system using Cramer’s rule.

- A) , C) ,
- B) , D) ,

Ans: D Section: 7.5

- Solve the system using Cramer’s rule.

- A) C)
- B) D)

Ans: C Section: 7.5

- Solve the system using Cramer’s rule.

- A) , , C) , ,
- B) , , D) , ,

Ans: D Section: 7.5

- Discuss the number of solutions for the system below where
*a*and*b*are real numbers. Use Cramer’s rule where appropriate and Gauss-Jordan elimination otherwise.

Ans: If and there are an infinite number of solutions. If and there are no solutions. If there is one solution.

Section: 7.5

- Use Cramer’s rule to solve for
*x*only.

- A) B) C) D)

Ans: C Section: 7.5

- Use Cramer’s rule to solve for
*y*only.

- A) B) C) D)

Ans: B Section: 7.5

- Use Cramer’s rule to solve for
*z*only.

- A) B) C) D)

Ans: A Section: 7.5

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