Hi everyone, so I was doing some math homework and I got stuck. Please help me with these two questions (numbers 7 and 8). Thank you! I'll also try my hardest to help you in return!

7). x = 6,

8). x = 2

Step-by-step explanation:

7). Area of a circle = πr²

   Here 'r' = radius of the circle

Area of the shaded region of the circle = Area of the large circle - Area of the small circle

                                                                 = π(x)² -

                                                                 =

                                                                 =

                                                                 = in²

If area of the shaded region is (8πx - 21π) in²

3x² = 32x - 84

3x²- 32x + 84 = 0

3x² - 14x - 18x + 84 = 0

x(3x - 14) - 6(3x - 14) = 0

(x - 6)(3x - 14) = 0

x = 6,

8). Area of the shaded region = Area of the largest circle - Area of the smaller semicircle - Area of the smallest semicircle

Area of the largest circle = π(2x + 2x)²

                                         = 16πx²

Area of the smaller semicircle =

                                                  = 4.5(πx²)

Area of the smallest semicircle =

                                                    = 2πx²

Now area of he shaded region = 16πx² - [4.5(πx²) + 2πx²]

                                                    = 16πx² - 6.5πx²

                                                    = 9.5πx² mm²

If the area of the shaded region = 12πx + 14π

12πx + 14π = 9.5πx²

12x + 14 = 9.5x²

9.5x² - 12x - 14 = 0

19x² - 24x - 28 = 0

19x² - 38x + 14x - 28 = 0

19x(x - 2) + 14(x - 2) = 0

(19x + 14)(x - 2) = 0

x =

But the radius o a circle can't be negative.

Therefore, x = 2 will be the answer.

step-by-step explanation:

answers available in this download

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a. she will receive a refund of $278.

step-by-step explanation: