Suppose y varies jointly as x and z. Find y when x = - 13 and z = 7, if y = 205 when x = - 5 and z = - 8. Round your answer to the nearest hundredth, if necessary.

Answer: y = - 466.375

Step-by-step explanation:

y varies jointly as x and z.

This means that y varies directly as x and also varies directly as z.

In order to remove the proportionality symbol, we will introduce a constant of proportionality, k. Therefore,

y = kxz

The next step is to determine the value of k

if y = 205 when x = - 5 and z = - 8.

we will substitute these values into the equation to determine k.

205 = k * - 5 * - 8

205 = 40k

k = 205/40 = 5.125

Therefore, the equation becomes

y = 5.125xz

We want to determine y when x = - 13 and z = 7

y = 5.125 * - 13 * 7

y = 5.125 * - 91

y = - 466.375