The variable z is directly proportional to x, and inversely proportional to y. when x is 8 and y is 18, z has the value 1.3333333333333. what is the value of z when x= 13, and y= 22

The variable z is directly proportional to x, and inversely proportional to y.

and

So,

where, k is the constant of proportionality.

When, x=8 and y=18, z is 1.33.

So, plugging x,y and z in z=k\frac{x}{y} to get the value of k we get,

To isolate, k let us multiply by 18 on both sides

1.33*18=k

23.99=k

So, 23.99=8k

To solve for k, let us divide by 8 on both sides

2.99=

k=3

Let us plug k=3, x=13 and y=22 to solve for z

z=

z=1.77

z=1.77

7.25

step-by-step explanation:

we know that 7 equals to 7.0. we also know that 1/4=0.25. so we can add the two together and we get 7.25