Genie has 100 feet of fence with which to make a rectangular cage for her rabbit. If she uses the wall of her house as one side, the area of the cage in square feet is given by the polynomial -2w^2 + 100w, where w is the width of the cage in feet. What is the area of the cage if the width is 15 feet?

My answer: 1,050 ft.?

To find the area of the cage when the width is 15 feet, you need to substitute the value of w = 15 into the polynomial -2w^2 + 100w.

Area = -2w^2 + 100w

Substituting w = 15:
Area = -2(15)^2 + 100(15)
Area = -2(225) + 1500
Area = -450 + 1500
Area = 1050 square feet

So, the correct answer is 1050 square feet, not 1,050 ft.

To find the area of the cage when the width is 15 feet, you can substitute the value of w = 15 into the polynomial -2w^2 + 100w.

Substituting w = 15 into the polynomial, we have:
Area = -2(15)^2 + 100(15)

First, calculate the value of 15^2:
Area = -2(225) + 100(15)

Now, multiply -2 by 225, then 100 by 15:
Area = -450 + 1500

Finally, add the values together:
Area = 1050 ft^2

So, the area of the cage when the width is 15 feet is 1050 square feet. Therefore, your answer of 1,050 ft^2 is correct.

You're boring with your questions.