Question

A rancher has a roll of fencing to enclose a rectangular area. The table shows how the area that the rancher can enclose with the fencing depends on the width of the rectangle.

Width (w)ft Area (A) ft2
10 900
20 1,600
30 2,100

Which quadratic equation gives the area A of the rectangle in square feet given its width in w feet?

A. A(w)= -w to the power of 2+200w
B. A(w)= -w to the power of 2+100w
C. A(w)= w to the power of 2+40w
D. A(w)= w to the power of 2+90w

Answer 1

10, 900
and then the second one
B

Answer 2

Checking for each option

Option A:
`A(w) = -w^2+200w`

Substitute w = 10 and check if we'd get 900 as the answer

`A(10) = -(10)^2+200(10) = -100+2000 = 1900`

Option B:
`A(w) = -w^2+100w`
Substitute w = 10 and check if we'd get 900 as the answer

`A(10)=-(10)^2+100(10)=-100+1000=900`

Option C:
`A(w)=w^2+40w`
Substitute w = 10 and check if we'd get 900 as the answer

`A(10) = 10^2+40(10)=100+400=500`

Option D:
`A(w) = w^2+90w`
Substitue w = 10 and check if we'd get 900 as the answer

`A(10)=10^2+90(10) = 100+900=1000`

Answer: Option B