CPhill

A: Construct the angle bisector of angle R.

BTW.....here's this step-by-step....pretty easy, actually  !!!

https://www.mathsisfun.com/geometry/construct-triangleinscribe.html

5.  If the directrix  is  above the vertex, as in this case,  this parabola turns downward

So.....p  = the distance from the directrix to the vertex  = 5

So....we have the form

-4py  = x^2

-4(5)y = x^2

-20y  = x^2      divide both sides by -20

y  = (-1/20)x^2

6)  First.. in the form  x  = ay^2  ...the vertex is at the origin

x = (1/24)y^2    multiply both sides by 24

24x = y^2

We have the form

4px  = y^2         so   4p  = 24  ⇒   p  = 6

This parabola opens to the right  so  the focus  is   (0 + p, 0)  = (0 + 6 , 0 )  = (6, 0)

The directrix   is    x =  0 - p   ⇒  x  = 0 - 6  ⇒  x  = -6

C  will be supplemental to A

So

A + C  =  180

89 + C  =  180      subtract 89 from both sides

C  = 91°

This is known as a cyclic quadrilateral......the opposite angles are suppllementary

So

x^2 + 78  + 10x + 46  = 180

x^2 + 10x + 124  =  180       subtract 180 from both sides

x^2 + 10x - 56  =  0  factor

(x - 4) ( x + 14)  = 0

Setting each factor to 0  and solving for x  produces

x = 4       and   x  =  -14

Reject the second since it produces negative angles

So  C  =   10(4)  + 46   =  86°

Your transformation rule is correct  !!!!!

The scale factor .....( since the radius is a linear measure)  from Circle 1  to Circle 2  is  just   9 / 15  =

3/5

Very nice, hectictar  !!!

Since the sine and cosine are co-functions, the sum of these two angles will  =  90°

So we have

[x + 34 ]  + [ 2x + 20]   =  90    simplify

3x + 54  = 90     subtract 54 from both sides

3x  = 36      divide both sides by 3

x = 12

https://prnt.sc/itygip

We can use the Law of Sines, here

AC / sin (71.6)  = 13 / sin ( 85.2)

AC  =  13sin (71.6) / sin (85.2)   = 12.378 cm =  12 cm  (rounded)

https://prnt.sc/ityh19

Using the Law of Cosines, we can find the missing side, M

M^2  = 220^2 + 143^2  - 2(220* 143) cos(75.7)

M = √ [ 220^2 + 143^2  - 2(220* 143) cos(75.7)]  ≈ 230.885 = 231  (rounded)

The equation is

( x - h)^2  + (y - k)^2  = r^2

Where  (h, k)  is the center and r is the radius

So  we have

(x - (-7) )^2  +  ( y  -  (-6) ) ^2  =  2^2

(x + 7)^2  + ( y + 6)^2  = 4 

10)   3 left, 4 up

The first equation  can be written as

(x - 0)^2  + (y - 0)^2  =  49     ⇒   center  =  (0, 0)

Moving to the left 3, we add 3 to the x coordinate of the center

Moving up 4, we subtract 4 from the y coordinate of the center 

( x - 0  + 3 )^2   + ( y - 0 - 4)^2  =  49

(x + 3)^2  + (y - 4)^2  = 49