The variable z is directly proportional to x, and inversely proportional to y. When x is 4 and y is 10, z has the value 0.8. What is the value of z when x= 13, and y= 18

Answer:13/9Step-by-step explanation:Directly proportional means it will be multiply to our constant k.Inversely proportional means it will divide our k.So we are given z is directly proportional to x and inversely proportional to y.This means:[tex]z=k \cdot \frac{x}{y}[/tex].We are given (x=4,y=10,z=0.8).  We can use this to find k.  The k we will find using the point will work for any point (x,y,z) since k is a constant.  A constant means it is to remain the same no matter what.[tex]0.8=k \cdot \frac{4}{10}[/tex][tex]0.8=k(.4)[/tex]Divide both sides by .4:[tex]\frac{0.8}{0.4}=k[/tex][tex]k=2[/tex]The equation for any point (x,y,z) is therefore:[tex]z=2 \cdot \frac{x}{y}[/tex].We want to find z given x=13 and y=18.[tex]z=2 \cdot \frac{13}{18}[/tex][tex]z=\frac{2 \cdot 13}{18}[/tex][tex]z=\frac{13}{9}[/tex]