Afarmer 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.

option B

Step-by-step explanation:

i attach the full question in the image below.

The area of the rectangle is defined as

Area = width*length

width_plot = (7x -6) ft

length_plot = (12x + 5) ft

Area_plot =  (7x -6)* (12x + 5) ft^2

Area_plot =  [ (7x)* (12x + 5) +(-6)*(12x + 5) ]    ft^2

Area_plot =  [ 84x^2 + 35x  - 72x - 30 ]    ft^2

Area_plot =  [ 84x^2 - 37x - 30 ]    ft^2

The area of the fenced off vegetable patch is

Area_patch =  (5x -4)* (3x) ft^2

Area_patch =  (15x^2  -12x)   ft^2

The area of the shaded region is equal to

A_shaded = Area_plot  - Area_patch

= [ 84x^2 - 37x - 30 ]    ft^2   -  (15x^2  -12x)   ft^2

= [69 x^2   -25x  - 30]   ft^2

Answer is option B

step-by-step :

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step-by-step explanation: