How do you solve number #4?

b

Step-by-step explanation:

Area of the shaded region =[ (3x-2)(x+3) ] - [ x*6 ]

= 3x*x +3x*3 + (-2)*x  + (-2)*3 - 6x

=3x² + 9x - 2x - 6 - 6x      {bring like term together}

=3x² + 9x - 2x - 6x - 6

= 3x² + x - 6           {9x - 2x - 6x = 9x - 8x = x}

Area = 24 square units

3x² + x - 6 = 24

3x² + x - 6 - 24 = 0

3x² + x - 30 = 0

Product = 3* -30 = -90

Sum = 1

Factors = 10 , (-1)

3x² + x - 30 = 0

3x² - 9x + 10x - 10*3 = 0

3x*(x - 3) +10*(x - 3) = 0

(x-3)(3x +10) = 0

3x + 10 is ignored because measurements will not be in negative values.

x - 3 = 0

x = 3

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).