Find the area of this shaded region.

9.13

Step-by-step explanation:There are three lines from the center to the sides. So they are all the same. you can see that the radius is 8 from one of the sides. You can find the area of the big triangle by knowing that 2 of the sides are 8 and 360-270=90 and that is a right triangle so we can use the pythagorean theorem to find the hypotenuse. 8^2+8^2=√128. And we can find the area by doing (8^2+8^2)/2=32 so each triangle is 16 units^2. To find out the lengths of the left triangle we have (.5*√128)^2=√32. So 8^2-32=x² x=√32. if the radius is 8 and the one side of the radius is √32 it would be 8-√32. and the other line touching the shaded area it √128 so we can say that the area of the non-little circle is the area of the whole circle-the almost circle. The area of the whole circle it 8^2*pi≈201.06. The area of the almost circle is 201.06*.75=150.79 because 270/360=.75 plus the area of the triangle (32) so the area is 182.79. So the area of the little thing is 201.06-182.79=18.27 divided by 2 =9.13

8/9n - 1 1/3

BTW * MEANS TIMES

Step-by-step explanation:

Given that:   4/9(2n - 3) [1]

The distributive property says that:

a * (b + c) = a * b + a* c

Apply the distributive property in equation [1] we get;

4/9 *  2n + 4/9 * (-3)

Simplify:

8/9n - 4/3

We can write 4/3  in mixed fraction as:

4/3 = 1 1/3

then;

8/9n - 1 1/3

Therefore, the expression which is equivalent to 4/9(2n - 3)  is, 8/9n - 1 1/3