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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

2 Answers

5 votes
10, 900
and then the second one
B
User Georgehardcore
by
8.2k points
4 votes
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



User Raja Jawahar
by
8.3k points