Q:

The current area of the city park is represented by the expression 11x2 + 4x + 6. The city will expand the park this summer by a factor of 5x − 3. If one-fourth of the new park is to be wooded, which expression represents the new area of the park that is not wooded?

Accepted Solution

A:
we have that
the current area of the city park is represented by--------> [11x² + 4x + 6]

the new area of the city park is represented by----- >[11x² + 4x + 6]*[5x-3]
 [11x² + 4x + 6]*[5x-3]-------> [55x³+20x²+30x-33x²-12x-18]
 [55x³+20x²+30x-33x²-12x-18]=[55x³-13x²+30x+18x-18]

the new area of the city park is represented by---->[55x³-13x²+30x+18x-18]

we know that
if (1/4) of the new park is to be wooded
then 
(3/4) of the new park  is not wooded

therefore
the area of the new park that 
is not wooded is represented by--> (3/4)*[55x³-13x²+30x+18x-18]
 [41.25x³-9.75x²+22.5x+13.5]


the answer is  [41.25x³-9.75x²+22.5x+13.5]