Question

The variable z varies jointly with x and y. Also, z = -75 when x = 3 and y = -5. What equation describes this variation? What is the constant of variation (k)? When x = 1 and y = -2, what is z?

A. z = -5x - 25y, k = 5. z = 20
B. z = -5x + 25y, k = -5. z = -20
C. z = 5x - 25y, k = -5. z = -20
D. z = 5x + 25y, k = 5. z = 20

Answer 1

The correct answer should be an equation of the form z = 5xy, with k = 5 and z = -10 for x = 1, y = -2, but this does not match the provided options, indicating a possible error.

Step-by-step explanation:

The correct answer is option A. To determine the equation that describes the variation, we must first find the constant of variation, k, using the given values: z = -75 when x = 3 and y = -5.

We know that z varies jointly with x and y, which means z = kxy. Substituting the given values, we get -75 = k(3)(-5). Solving for k, we find k = -75 / (-15) = 5. Therefore, the equation describing the variation is z = 5xy.

Then we proceed to find z when x = 1 and y = -2, resulting in z = (5)(1)(-2) = -10. However, none of the options match exactly, so it seems like there may be a typo in the question or in the options provided.

Based on the process used, we would expect option A to be the correct structure with k = 5, but the calculation for z should be -10, not 20. This suggests an error somewhere in the given choices or the interpretation of the question.