Part 1 of 2 - Lesson 6 Questions 15.0/ 50.0 Points

Online Exam 7_06

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Part 1 of 2 - Lesson 6 Questions 15.0/ 50.0 Points

Question 1 of 40

0.0/ 2.5 Points

Use Cramer’s Rule to solve the following system.

2x = 3y + 2

5x = 51 - 4y

A. {(8, 2)}

B. {(3, -4)}

C. {(2, 5)}

D. {(7, 4)}

Question 2 of 40

0.0/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + 3y = 0

x + y + z = 1

3x - y - z = 11

A. {(3, -1, -1)}

B. {(2, -3, -1)}

C. {(2, -2, -4)}

D. {(2, 0, -1)}

Question 3 of 40

2.5/ 2.5 Points

If AB = -BA, then A and B are said to be anticommutative.

Are A = 0

1 -1

0 and B = 1

0 0

-1 anticommutative?

A. AB = -AB so they are not anticommutative.

B. AB = BA so they are anticommutative.

C. BA = -BA so they are not anticommutative.

D. AB = -BA so they are anticommutative.

Question 4 of 40

0.0/ 2.5 Points

Solve the system using the inverse that is given for the coefficient matrix.

2x + 6y + 6z = 8

2x + 7y + 6z =10

2x + 7y + 7z = 9

The inverse of:

2

2

2 6

7

7 6 6 7

is

7/2

-1

0 0

1

-1 -3 0 1

A. {(1, 2, -1)}

B. {(2, 1, -1)}

C. {(1, 2, 0)}

D. {(1, 3, -1)}

Question 5 of 40

0.0/ 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

5x + 8y - 6z = 14

3x + 4y - 2z = 8

x + 2y - 2z = 3

A. {(-4t + 2, 2t + 1/2, t)}

B. {(-3t + 1, 5t + 1/3, t)}

C. {(2t + -2, t + 1/2, t)}

D. {(-2t + 2, 2t + 1/2, t)}

Question 6 of 40

0.0/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

3x1 + 5x2 - 8x3 + 5x4 = -8

x1 + 2x2 - 3x3 + x4 = -7

2x1 + 3x2 - 7x3 + 3x4 = -11

4x1 + 8x2 - 10x3+ 7x4 = -10

A. {(1, -5, 3, 4)}

B. {(2, -1, 3, 5)}

C. {(1, 2, 3, 3)}

D. {(2, -2, 3, 4)}

Question 7 of 40

0.0/ 2.5 Points

Use Cramer’s Rule to solve the following system.

4x - 5y - 6z = -1

x - 2y - 5z = -12

2x - y = 7

A. {(2, -3, 4)}

B. {(5, -7, 4)}

C. {(3, -3, 3)}

D. {(1, -3, 5)}

Question 8 of 40

2.5/ 2.5 Points

Find the products AB and BA to determine whether B is the multiplicative inverse of A.

A = 0

0

1 1

0

0 0

1

0

B = 0

1

0 0

0

1 1

00

A. AB = I; BA = I3; B = A

B. AB = I3; BA = I3; B = A-1

C. AB = I; AB = I3; B = A-1

D. AB = I3; BA = I3; A = B-1

Question 9 of 40

2.5/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y + z = 4

x - y - z = 0

x - y + z = 2

A. {(3, 1, 0)}

B. {(2, 1, 1)}

C. {(4, 2, 1)}

D. {(2, 1, 0)}

Question 10 of 40

0.0/ 2.5 Points

Use Cramer’s Rule to solve the following system.

4x - 5y = 17

2x + 3y = 3

A. {(3, -1)}

B. {(2, -1)}

C. {(3, -7)}

D. {(2, 0)}

Question 11 of 40

0.0/ 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

2w + x - y = 3

w - 3x + 2y = -4

3w + x - 3y + z = 1

w + 2x - 4y - z = -2

A. {(1, 3, 2, 1)}

B. {(1, 4, 3, -1)}

C. {(1, 5, 1, 1)}

D. {(-1, 2, -2, 1)}

Question 12 of 40

0.0/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + 2y = z - 1

x = 4 + y - z

x + y - 3z = -2

A. {(3, -1, 0)}

B. {(2, -1, 0)}

C. {(3, -2, 1)}

D. {(2, -1, 1)}

Question 13 of 40

2.5/ 2.5 Points

Use Cramer’s Rule to solve the following system.

12x + 3y = 15

2x - 3y = 13

A. {(2, -3)}

B. {(1, 3)}

C. {(3, -5)}

D. {(1, -7)}

Question 14 of 40

2.5/ 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

3x + 4y + 2z = 3

4x - 2y - 8z = -4

x + y - z = 3

A. {(-2, 1, 2)}

B. {(-3, 4, -2)}

C. {(5, -4, -2)}

D. {(-2, 0, -1)}

Question 15 of 40

2.5/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

2x - y - z = 4

x + y - 5z = -4

x - 2y = 4

A. {(2, -1, 1)}

B. {(-2, -3, 0)}

C. {(3, -1, 2)}

D. {(3, -1, 0)}

Question 16 of 40

0.0/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y - z = -2

2x - y + z = 5

-x + 2y + 2z = 1

A. {(0, -1, -2)}

B. {(2, 0, 2)}

C. {(1, -1, 2)}

D. {(4, -1, 3)}

Question 17 of 40

0.0/ 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

8x + 5y + 11z = 30

-x - 4y + 2z = 3

2x - y + 5z = 12

A. {(3 - 3t, 2 + t, t)}

B. {(6 - 3t, 2 + t, t)}

C. {(5 - 2t, -2 + t, t)}

D. {(2 - 1t, -4 + t, t)}

Question 18 of 40

0.0/ 2.5 Points

Find values for x, y, and z so that the following matrices are equal.

2x

z y + 7

4 = -10

6 13

4

A. x = -7; y = 6; z = 2

B. x = 5; y = -6; z = 2

C. x = -3; y = 4; z = 6

D. x = -5; y = 6; z = 6

Question 19 of 40

0.0/ 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

w - 2x - y - 3z = -9

w + x - y = 0

3w + 4x + z = 6

2x - 2y + z = 3

A. {(-1, 2, 1, 1)}

B. {(-2, 2, 0, 1)}

C. {(0, 1, 1, 3)}

D. {(-1, 2, 1, 1)}

Question 20 of 40

0.0/ 2.5 Points

Use Gauss-Jordan elimination to solve the system.

-x - y - z = 1

4x + 5y = 0

y - 3z = 0

A. {(14, -10, -3)}

B. {(10, -2, -6)}

C. {(15, -12, -4)}

D. {(11, -13, -4)}

Part 2 of 2 - Lesson 7 Questions 17.5/ 50.0 Points

Question 21 of 40

0.0/ 2.5 Points

Locate the foci of the ellipse of the following equation.

25x2 + 4y2 = 100

A. Foci at (1, -√11) and (1, √11)

B. Foci at (0, -√25) and (0, √25)

C. Foci at (0, -√22) and (0, √22)

D. Foci at (0, -√21) and (0, √21)

Question 22 of 40

0.0/ 2.5 Points

Locate the foci and find the equations of the asymptotes.

x2/100 - y2/64 = 1

A. Foci: ({= ±2√21, 0); asymptotes: y = ±2/5x

B. Foci: ({= ±2√31, 0); asymptotes: y = ±4/7x

C. Foci: ({= ±2√41, 0); asymptotes: y = ±4/7x

D. Foci: ({= ±2√41, 0); asymptotes: y = ±4/5x

Question 23 of 40

0.0/ 2.5 Points

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Foci: (0, -3), (0, 3)

Vertices: (0, -1), (0, 1)

A. y2 - x2/4 = 0

B. y2 - x2/8 = 1

C. y2 - x2/3 = 1

D. y2 - x2/2 = 0

Question 24 of 40

0.0/ 2.5 Points

Find the vertex, focus, and directrix of each parabola with the given equation.

(x + 1)2 = -8(y + 1)

A. Vertex: (-1, -2); focus: (-1, -2); directrix: y = 1

B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1

C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1

D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1

Question 25 of 40

0.0/ 2.5 Points

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Foci: (-4, 0), (4, 0)

Vertices: (-3, 0), (3, 0)

A. x2/4 - y2/6 = 1

B. x2/6 - y2/7 = 1

C. x2/6 - y2/7 = 1

D. x2/9 - y2/7 = 1

Question 26 of 40

0.0/ 2.5 Points

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (0, -4), (0, 4)

Vertices: (0, -7), (0, 7)

A. x2/43 + y2/28 = 1

B. x2/33 + y2/49 = 1

C. x2/53 + y2/21 = 1

D. x2/13 + y2/39 = 1

Question 27 of 40

2.5/ 2.5 Points

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (-5, 0), (5, 0)

Vertices: (-8, 0), (8, 0)

A. x2/49 + y2/ 25 = 1

B. x2/64 + y2/39 = 1

C. x2/56 + y2/29 = 1

D. x2/36 + y2/27 = 1

Question 28 of 40

0.0/ 2.5 Points

Find the standard form of the equation of the ellipse satisfying the given conditions.

Endpoints of major axis: (7, 9) and (7, 3)

Endpoints of minor axis: (5, 6) and (9, 6)

A. (x - 7)2/6 + (y - 6)2/7 = 1

B. (x - 7)2/5 + (y - 6)2/6 = 1

C. (x - 7)2/4 + (y - 6)2/9 = 1

D. (x - 5)2/4 + (y - 4)2/9 = 1

Question 29 of 40

0.0/ 2.5 Points

Locate the foci of the ellipse of the following equation.

x2/16 + y2/4 = 1

A. Foci at (-2√3, 0) and (2√3, 0)

B. Foci at (5√3, 0) and (2√3, 0)

C. Foci at (-2√3, 0) and (5√3, 0)

D. Foci at (-7√2, 0) and (5√2, 0)

Question 30 of 40

0.0/ 2.5 Points

Locate the foci and find the equations of the asymptotes.

4y2 – x2 = 1

A. (0, ±√4/2); asymptotes: y = ±1/3x

B. (0, ±√5/2); asymptotes: y = ±1/2x

C. (0, ±√5/4); asymptotes: y = ±1/3x

D. (0, ±√5/3); asymptotes: y = ±1/2x

Question 31 of 40

0.0/ 2.5 Points

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Center: (4, -2)

Focus: (7, -2)

Vertex: (6, -2)

A. (x - 4)2/4 - (y + 2)2/5 = 1

B. (x - 4)2/7 - (y + 2)2/6 = 1

C. (x - 4)2/2 - (y + 2)2/6 = 1

D. (x - 4)2/3 - (y + 2)2/4 = 1

Question 32 of 40

0.0/ 2.5 Points

Find the vertex, focus, and directrix of each parabola with the given equation.

(x - 2)2 = 8(y - 1)

A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1

B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1

C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1

D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1

Question 33 of 40

2.5/ 2.5 Points

Find the vertex, focus, and directrix of each parabola with the given equation.

(y + 1)2 = -8x

A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2

B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3

C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1

D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5

Question 34 of 40

2.5/ 2.5 Points

Convert each equation to standard form by completing the square on x and y.

9x2 + 16y2 - 18x + 64y - 71 = 0

A. (x - 1)2/9 + (y + 2)2/18 = 1

B. (x - 1)2/18 + (y + 2)2/71 = 1

C. (x - 1)2/16 + (y + 2)2/9 = 1

D. (x - 1)2/64 + (y + 2)2/9 = 1

Question 35 of 40

2.5/ 2.5 Points

Find the focus and directrix of each parabola with the given equation.

y2 = 4x

A. Focus: (2, 0); directrix: x = -1

B. Focus: (3, 0); directrix: x = -1

C. Focus: (5, 0); directrix: x = -1

D. Focus: (1, 0); directrix: x = -1

Question 36 of 40

0.0/ 2.5 Points

Locate the foci of the ellipse of the following equation.

7x2 = 35 - 5y2

A. Foci at (0, -√2) and (0, √2)

B. Foci at (0, -√1) and (0, √1)

C. Foci at (0, -√7) and (0, √7)

D. Foci at (0, -√5) and (0, √5)

Question 37 of 40

2.5/ 2.5 Points

Convert each equation to standard form by completing the square on x and y.

9x2 + 25y2 - 36x + 50y - 164 = 0

A. (x - 2)2/25 + (y + 1)2/9 = 1

B. (x - 2)2/24 + (y + 1)2/36 = 1

C. (x - 2)2/35 + (y + 1)2/25 = 1

D. (x - 2)2/22 + (y + 1)2/50 = 1

Question 38 of 40

0.0/ 2.5 Points

Convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola.

y2 - 2y + 12x - 35 = 0

A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9

B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6

C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6

D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8

Question 39 of 40

2.5/ 2.5 Points

Convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola.

x2 - 2x - 4y + 9 = 0

A. (x - 4)2 = 4(y - 2); vertex: (1, 4); focus: (1, 3) ;directrix: y = 1

B. (x - 2)2 = 4(y - 3); vertex: (1, 2); focus: (1, 3) ;directrix: y = 3

C. (x - 1)2 = 4(y - 2); vertex: (1, 2); focus: (1, 3) ;directrix: y = 1

D. (x - 1)2 = 2(y - 2); vertex: (1, 3); focus: (1, 2) ;directrix: y = 5

Question 40 of 40

2.5/ 2.5 Points

Convert each equation to standard form by completing the square on x and y.

4x2 + y2 + 16x - 6y - 39 = 0

A. (x + 2)2/4 + (y - 3)2/39 = 1

B. (x + 2)2/39 + (y - 4)2/64 = 1

C. (x + 2)2/16 + (y - 3)2/64 = 1

D. (x + 2)2/6 + (y - 3)2/4 = 1