CPhill

This is a parabola.....In this form.....when the coefficient in  front of x is negative

y  = -ax^2  + bx  + c.....we have a parabola that opens downward  with the vertex the highest point on the graph

So......we have

y  = (-1)x^2  +  (-2)x  + 8

The  x coordinate of the vertex  is given by   -b/ [ 2a]

So  b = -2     and  a  = -1

So....the x coordinate of the vertex  =    - (-2) / [2 (-1)]  = 2/-2  = -1

Since this is the highest point on the graph of this parabola....the function will increase  on this interval :    (-inf, -1 )

However we must find out where the parabola is positive......we can  find the x intercepts by letting y  =0  and solving for x....so we have

0  = -x^2 -2x + 8        multiply through by  -1

0  =x^2 + 2x  - 8        factor

0 = (x - 2) ( x + 4)

Setting each factor to 0  and solving for x  produces the x intercepts of  x  = 2  and x  = -4

So......the graph will  be positive  and increasing from    -4 < x < -1  

See the graph here to get a feel for this :

https://www.desmos.com/calculator/bkyaq6zmzv

This is known as a cyclic quadrilateral.....the opposite angles sum to 180 degrees

So

J + L  =  180

68 + L  = 180     subtrct 68 from both sides

L  = 180  - 68  =  112°

We  can calculate the  area, A,  as

A  =  pi * radius^2   *  ( angle measure / 360 )

If the diameter is 8 ft.....the radius is 1/2 of this = 4 feet....so we have

A  = pi * (4)^2 ( 45 / 360)

A=  pi * 16  ( 1/8)

A = pi *2

A  ≈   6.28  ft^2

The original ppopulation  is  " a"

If it triples everyday....after the 1st day  it is 3a

After the second day  it is 9a  , etc

 So....we have this

P  =  a(3)^x     so.....k  = 3

Notice that   

When x  = 1,   P  = 3a

When x = 2, P  = 9a  ....etc.... 

This is a cyclic quadrilateral.....the opposite angles are supplementary  (add to 180 degrees)

So

(x + 15)  + ( 4x +  5  ) =   180     simplify

5x  +  20   =  180     subtract 20 from both sides

5x  =  160       divide both sides by 5

x  = 32

So

A  =  4(32) + 5   =   133°

We have this

A =  Beginning Amount  (  1  -  rate of decay)^t

Where  the  beginning amount is   0.65 kilograms

And the rate of decay  = 8%  =  .08.....so we have

A  =  0.65 ( 1  - .08)^t

A  = 0.65 ( .92)^t

So.....the rate of decay  is  8%   ⇒  A

1.  Construct the angle bisector of angle R.

Here's  a procedure describing this  :

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

2. Construct the angle bisector of ∠J.

Here's a procedure for this, too :

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

3.  Inscribed Angle Theorem

     The sum of arcs that make a circle  = 360 degrees 

     Division Property of Equality

     Definition of Supplementary Angles

4.   theta / 360

      theta / [ 2pi ]

Good luck...I had a lousy Geometry teacher in high school, too....most of the Geometry I know  I learned on my own....

Just the opposite of what you might think  for the left/right translation

4 left  and 3 up =

y  =  (x + 4)^2  +  3  ⇒  B

7 right  and 2 up

y  = √[ x - 7]  + 2  ⇒  D

1 yard  =  3ft

So   .....the radius is  1/2 of the diameter  = 3/2 ft

So.....the circumference is

2 * 3.14 * (r)  =

6.28  (3/2)   ft  =      471/50  ft  ≈   (9.42 ft)   as Donut found  !!!

The measure  of an inscribed angle is  1/2  that of its intercepted arc....so....

m angle ABC  = (1/2)arc AC      (first answer )