Question

A farmer has a rectangular plot of land. The length of the plot is (12x + 5) feet and the width of the plot is (7x − 6) feet. A fenced-off vegetable patch on the farm has a length of (5x − 4) feet and a width of 3x feet, as shown.

Select the function that represents the area, in square feet, of the shaded region.

A. A(x) = 15x2 − 12x

B. A(x) = 69x2 − 25x − 30

C. A(x) = 84x2 − 37x − 30

D. A(x) = 99x2 − 49x − 30

Answer 1

Step-by-step explanation: the answer is d

Answer 2

Option B. A(x) = 69x² - 25x - 30

Explanation:

The given rectangular plot of land has the dimensions as

Length = (12x + 5) feet

Width = (7x -6) feet

Now area of the plot = Length × width = (12x + 5)×(7x - 6) = 12x(7x - 6) + 5(7x - 6) = 84x² - 72x + 35x - 30 = (84x² - 37x -30) feet²

Dimensions of vegetable patch are

Length = (5x - 4) feet

width = 3x feet

Area of vegetable patch = (5x - 4)(3x) = (15x² - 12x) feet²

Now area of the shaded part = Area of rectangular plot - Area of vegetable patch = (84x² - 37x - 30)-(15x² - 12x) = 84x² - 37x - 30 - 15x² + 12x = (69x²-25x -30) square feet

Now function that represents the area of shaded region will be

A(x) = 69x² - 25x - 30

Option B. is the answer.