Asquare is inscribed in an equilateral triangle that is inscribed in a circle. which represents the area of the shaded region? area of the circle – area of the square – area of the triangle area of the triangle – area of the square + area of the circle area of the triangle + area of the square + area of the circle area of the circle – area of the triangle + area of the square

"area of the circle – area of the triangle + area of the square"

Step-by-step explanation:

The figure is shown in the attached pic.

The red region is what we are looking for.

First of all, the area of square is the area of square.

Now we need to find the 3 sort of semicircles around. That can be found if we subtract the area of the triangle from the area of the circle.

Now, we have:

Area of Circle - Area of Triangle + Area of Square

That is Option D, last option.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .