The variable z is directly proportional to x, and inversely proportional to y. when x is 3 and y is 6, z has the value 9.5. what is the value of z when x=8, and y= 12

round to at least thee thousandths place if needed.

Directly proportional to x

z=kx

And inversely proportional to y

z=kx/y  we are given the point (x,y,z) of (3, 6, 9.5) so

9.5=3k/6  now multiply both sides by 6

57=3k  divide both sides by 3

19=k so now that we know the constant of proportionality:

z=19x/y,  and we want to solve for z when x=8 and y=12 so:

z=19(8)/12

z=12 2/3  exact

z≈12.667  (rounded to the nearest thousandth)

Think of it as five or above give it a shove. change the 5 or above to the right to a zero and add one to the number on the left.