Take Home Exam (3)

1) Choose

not-available-via-ai

Explanation

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2) Choose

5

4

+3 or -3

2

not-available-via-ai

Explanation

not-available-via-ai

3) Choose

-1

2

1

-3

The correct answer is 1 because it is the only positive number in the given options. All the other numbers are either negative or zero.

Explanation

The correct answer is 1 because it is the only positive number in the given options. All the other numbers are either negative or zero.

4) Choose

3x-5y+z-1=0

5x-4y+2z-7=0

7x-5y-z-4=0

7x+2y+3z=0

The given system of equations consists of three linear equations. To find the correct answer, we need to identify the equation that is consistent with the other equations. By comparing the coefficients of x, y, and z in each equation, we can see that the equation 7x+2y+3z=0 has the same coefficients as the other equations. Therefore, it is consistent with the given system of equations and is the correct answer.

Explanation

The given system of equations consists of three linear equations. To find the correct answer, we need to identify the equation that is consistent with the other equations. By comparing the coefficients of x, y, and z in each equation, we can see that the equation 7x+2y+3z=0 has the same coefficients as the other equations. Therefore, it is consistent with the given system of equations and is the correct answer.

5) Choose

not-available-via-ai

Explanation

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6) Choose

18

18/5

-18/5

18/25

The correct answer is 18/5 because when 18 is divided by 5, the result is 3.6. Therefore, 18/5 is the correct fraction representation of the division.

Explanation

The correct answer is 18/5 because when 18 is divided by 5, the result is 3.6. Therefore, 18/5 is the correct fraction representation of the division.

7) Choose

4

-2

6

2

not-available-via-ai

Explanation

not-available-via-ai

8) Choose

1

2

3

4

The correct answer is 2 because it is the only option mentioned in the question. The question asks the reader to choose between options 1, 2, 3, and 4, and the answer provided is 2. Since no additional information or context is given, it can be assumed that option 2 is the correct choice based on the given question.

Explanation

The correct answer is 2 because it is the only option mentioned in the question. The question asks the reader to choose between options 1, 2, 3, and 4, and the answer provided is 2. Since no additional information or context is given, it can be assumed that option 2 is the correct choice based on the given question.

9) Choose

(-2/3 , -12)

(-12 , -2/3)

(2/3 , 12)

(12 , 2/3)

The answer (-2/3, -12) is the correct choice because it matches the pattern in the given options. The x-coordinate is a fraction (-2/3) and the y-coordinate is a whole number (-12), which aligns with the format of the other options. Additionally, the negative sign on both coordinates is consistent with the other options as well.

Explanation

The answer (-2/3, -12) is the correct choice because it matches the pattern in the given options. The x-coordinate is a fraction (-2/3) and the y-coordinate is a whole number (-12), which aligns with the format of the other options. Additionally, the negative sign on both coordinates is consistent with the other options as well.

10) Choose

not-available-via-ai

Explanation

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11) Choose

X+y-z=6

2x-3y+z=-10

3x-2y+4z=20

X-2y+5z=4

The given system of equations represents a set of linear equations. To find the correct answer, we need to determine which equation represents the given solution. By comparing the coefficients of x, y, and z, we can see that the equation 3x-2y+4z=20 matches the given answer. Therefore, this equation is the correct answer.

Explanation

The given system of equations represents a set of linear equations. To find the correct answer, we need to determine which equation represents the given solution. By comparing the coefficients of x, y, and z, we can see that the equation 3x-2y+4z=20 matches the given answer. Therefore, this equation is the correct answer.

12) Choose

not-available-via-ai

Explanation

not-available-via-ai

13) Choose

45

90

Zero

60

The given options are 45, 90, zero, and 60. Out of these options, the number 90 is the only one that is a multiple of 9. Hence, the correct answer is 90.

Explanation

The given options are 45, 90, zero, and 60. Out of these options, the number 90 is the only one that is a multiple of 9. Hence, the correct answer is 90.

14) Choose

(1,-2,7)

(1,2,7)

(1,7,-2)

(-2,1,7)

The correct answer is (1,-2,7) because it is the only option that matches the given coordinates exactly. The other options have different combinations of positive and negative values for the coordinates.

Explanation

The correct answer is (1,-2,7) because it is the only option that matches the given coordinates exactly. The other options have different combinations of positive and negative values for the coordinates.

15) Choose

4

3

-3

5

not-available-via-ai

Explanation

not-available-via-ai

16) Choose

not-available-via-ai

Explanation

not-available-via-ai

17) Choose

150

30

45

60

not-available-via-ai

Explanation

not-available-via-ai

18) Choose

12

10

6

4

Among the given options, the number 6 is the only even number. The other options, 12, 10, and 4, are all divisible by 2 and therefore considered even numbers. However, 6 is the only option that is not divisible by any other number in the given options.

Explanation

Among the given options, the number 6 is the only even number. The other options, 12, 10, and 4, are all divisible by 2 and therefore considered even numbers. However, 6 is the only option that is not divisible by any other number in the given options.

19) Choose

(2,-2,2)

(1,2,2)

(1,2,-2)

(2,2,2)

The answer (2,-2,2) is correct because it is the only option that has all positive components. The other options have at least one negative component.

Explanation

The answer (2,-2,2) is correct because it is the only option that has all positive components. The other options have at least one negative component.

20) Choose

not-available-via-ai

Explanation

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