Answer:
z = [tex]\frac{20}{9}[/tex]
Step-by-step explanation:
Given that z varies directly with x and inversely with y then the equation relating them is
z = [tex]\frac{kx}{y}[/tex] ← k is the constant of variation
To find k use the condition when x = 6 and y = 2, z = 15, thus
15 = [tex]\frac{6k}{2}[/tex] ( multiply both sides by 2 )
30 = 6k ( divide both sides by 6 )
5 = k
z = [tex]\frac{6x}{y}[/tex] ← equation of variation
When x = 4 and y = 9, then
z = [tex]\frac{5(4)}{9}[/tex] = [tex]\frac{20}{9}[/tex]
