Question

The number of mosquitoes in Anchorage,

Alaska (in millions of mosquitoes) as a function
of rainfall (in centimeters) is modeled by:
M(x)=-x^2+12x
After how many inches of rainfall will there not
be any mosquitoes?

Answer 1

After 12 inches of rainfall there not be any mosquitoes

Explanation:

The correct question is

The number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes) as a function of rainfall (in inches) is modeled by:

M(x)=-x^2+12x

After how many inches of rainfall will there not be any mosquitoes?

we have

`M(x)=-x^2+12x`

where

M(x) is number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes)

x is the rainfall in inches

Remember that the x-intercepts are the values of x when the value of the function M(x) is equal to zero

That means ---> The x-intercepts are the values of the rainfall when the number of mosquitoes is equal to zero

Find the x-intercepts

For M(x)=0

`-x^2+12x=0`

Factor -x

`-x(x-12)=0`

The solutions are

x=0 in and x=12 in

therefore

After 12 inches of rainfall there not be any mosquitoes