Please help me with these it’s geometry I’m not very good at this and I so appreciate the help

Problem 8

The triangles are congruent, which means their corresponding pieces must also be congruent.

Focus on the second equation above. We can further say

angle B = angle E

E = B

12x+30 = 50

12x = 50-30

12x = 20

x = 20/12

x = 10/6

Now move to the equation involving C and F to get

F = C

(y/2) - 10 = 40

y/2 = 40+10

y/2 = 50

y = 2*50

y = 100

And finally,

D = A

sqrt(z) = 90

z = 90^2

z = 8100

Problem 11

The radius of the circle is r = 5.

The area of the circle is A = pi*r^2 = pi*5^2 = 25pi

The diameter of the circle is 2*r = 2*5 = 10, which is the side length of the square because the circle is fit perfectly inside the square.

Since the square side length is 10, the area is 10^2 = 100

Subtract the two areas: large-small = square - circle = 100 - 25pi

We subtract the areas because we're basically kicking out the circle area when we don't shade it. Think of it like sawing out that portion of a wooden block perhaps.

Problem 19

Part (a)

The point P is directly below the center and it is on the circle.

The location of point P is (18,0) because the x coordinates of both points are the same (so that P is directly below the center) and P resides on the x axis. All points on the x axis have y coordinate 0.

Part (b)

The radius of the circle is r = 10 which is the distance from the center to point P.

The area of the circle is therefore A = pi*r^2 = pi*10^2 = 100pi

100pi