30 points i really need your pronto!

so for the first one, i need with how to solve the equation. detailed or not

the second one i understand a bit more i think i have to increase the size or radius by 3 move it 8 units to the right and 2 units up. however, i'm not sure if i should increase the radius by 3 or 4.

the third one i'm just plain lost i don't even know where to start.

Part 1) the center is , the radius is

Part 2) see the procedure

Part 3)

Step-by-step explanation:

Part 1) we know that

The equation of a circle in center radius form is equal to

where

(h,k) is the center of the circle

r is the radius

In this problem we have

so

the center is the point

the radius is

Part 2) we know that

The center of circle F' is and the radius is  

The center of circle F is and the radius is  

step 1

Move the center of the circle F' onto the center of the circle F

the transformation has the following rule

8 units right and 2 units up

so

center circle F' is now equal to center circle F  

The circles are now concentric (they have the same center)

step 2

A dilation is needed to increase the size of circle F' to coincide with circle F

scale factor=radius circle F/radius circle F'=4/2=2

radius circle F' will be=2*scale factor=2*2=4 units

radius circle F' is now equal to radius circle F  

A translation, followed by a dilation will map one circle onto the other

Part 3) we know that

The sum of the interior angles in a quadrilateral is equal to 360 degrees

so

substitute the values

solve for x

The measure of angle B is

so