Answer:
The missing value x is, [tex]\frac{15}{2}[/tex] or [tex]7\frac{1}{2}[/tex]
Step-by-step explanation:
The Inverse variation problems can be solved by using the equation, i.e,
[tex]y \propto \frac{1}{x}[/tex].
use constant variation k to write the above equation as:
[tex]y=\frac{k}{x}[/tex] ......[1]
Now, use the given information to calculate the value of k;
we need to find the value of k ; when x=9 and y=5
[tex]5=\frac{k}{9}[/tex] or
[tex]k =9\times 5[/tex]
Simplify:
k =45.
Rewrite the equation [1] by substituting the value of k =45,
⇒ [tex]y = \frac{45}{x}[/tex] ......[2]
Substitute the value y=6 in equation[2] to find x:
[tex]6 =\frac{45}{x}[/tex] or
[tex]x = \frac{45}{6}[/tex] or [tex]x=\frac{15}{2}=7\frac{1}{2}[/tex]
Therefore, the missing value x is, [tex]\frac{15}{2}=7\frac{1}{2}[/tex]
