Logarhythm

(9 x 6) + (6 x 31) + (12 x 13)

= 54 + 186 + 156

= 396 ft²

let n = nickels, and d = dimes

n + d = 44

5n + 10d = 295

5n + 10d = 295

5n + 5d = 220

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          5d = 75

            d = 15

n + d = 44

n + (15) = 44

n = 29 

He has 29 nickels. 

Interior angles add up to 180 degrees.

This means: 
 

(11x - 28) + (7x - 8) = 180

18x - 36 = 180

18x = 216

x = 12

Distance Formula = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Im going to label the points for ease:

A(-6, 0) , B(2, 8) , C(6, 5) , D(-2, -3)

Now using the distance formula, we can find the dimensions of this rectangle. 

AB = \(\sqrt{128} = 8\sqrt{2} ≈ 11.31\)

BC = \(\sqrt{25} = 5\)

CD = \(\sqrt{128} = 8\sqrt{2} ≈ 11.31\)

DA = \(\sqrt{25} = 5\)

(of course, since it's a rectangle, you could just find the dimensions of two of the sides)

This means the area of the rectangle is = \(8\sqrt{2} \cdot 5 = 40\sqrt{2} ​​≈ 56.57 \)

And the perimeter is = \(2(8\sqrt{2} + 5) = 16\sqrt{2} + 10 ≈ 32.63 \)

s + 17 = 2s

17 = s

b + 28 = 2b

28 = b

7z = z + 54

6z = 54

z = 9

c = \(\sqrt{3^2 + 4^2} = 5\)

This means b = \(\sqrt{(a + 3)^2 - c^2}\)

but b also equals = \(\sqrt{a^2 + 4^2}\)

We can put these two into an equation:

\(\sqrt{(a + 3)^2 - c^2} = \sqrt{a^2 + 4^2}\)

\(a^2 + 6a + 9 - c^2 = a^2 + 16\)

\(6a - c^2 = 7\)

and since c = 5, 

\(6a - 25 = 7\)

\(6a = 32\)

\(a = 5\frac{1}{3}\)

First, we know that each square in the window has an area of 100 inch². This means the dimensions are 10 x 10. 

To find the area of the window, I'm going to split up the square part and the semicircle. 

This means the area of the square part is (10 x 4) x (10 x 4) = 40 x 40 = 1600 inch². This is because this area is 4 squares by 4 squares. 

Now, the area of the semicircle is \(\frac{1}{2} (10 \cdot 2)^2 π = 200π ≈ 628\)

This means the area of the window is 2228 inch²

The shade is 4 inches beyond, and so the dimensions of the 4 by 4 square would be (40 + 4 + 4) by (40 + 4 + 4). 

This means the area is 48 x 48 = 2304 

Then the semicircle's radius would be (20 + 4). Which means the area is \(\frac{1}{2} (20 + 4)^2π = 288π ≈ 904\)

This means the area of the shade is 3208 inch²