CPhill

We need to have   

2x + 5  =   -8

2x =  -8 - 5

2x =  -13

x = -13/2

So

g(-8)  =   4(-13/2)^2  -3(-13/2)  + 2   =  169 + 39 + 2    =  210

Rearrange as

x^2  - 4x + y^2 - 16 y  =   -c     complete the square on x , y

(x^2  - 4x + 4)  + ( y^2  - 16y  + 64 )  =  -c + 4  + 64

We want    

-c + 4 + 64  =   r^2

-c + 68  =  4^2

-c =  16 -  68

c =  68   -  16

c =  52

(6x + 12) (x  -18)  =   

6x^2 - 96x -  216

The  x coordinate of the  vertex =  (96) /(2 * 6)  =  96 /12  = 8

k is the  y coordinate of the  vertex and   =     (6 (8) + 12) (8  -18)  = 60 (-10)  =   -600

We have   26 ways of choosing the beginning letter   and  by default the last letter is the same

And the middle two letters can be  any one of the 25 remaining letters....so

26 * 25 * 25   =    16,250 possible "words "

At  x = 0   the function   = 1

As x moves toward infinity the function approaches  0

So...the range is  (0 , 1 ]   on the given interval

Choose any 4 of the 9 to be on the first row and arrange them in 4! = 24 ways

The other 5 are assigned to the second row automatically and  can  be arranged in 5!  =120 ways

So....the number of possible displays   =  C(9,4) * 4! * 5!   = 362880  

Triangles   ABC and   EDC  are similar

So

AC  = 9/17   of   AE

CE =  8/17  of   AE

Therefore     

CD =  (8/17)  (20) =   160/17

Simplify as

x^2  +  30x  +  _____

Take 1/2 of 30   =15

Square  it  = 225  is the constant we  need

(x +15)^2  = x^2 +  30x  + 225

23.52  ( 1 + 1.1)  =   $49.39   =   price

And

49.39  ( 1 +  .1475)  ≈  $56.68  =  what he paid

-x^2  + 6x + 20  =  b + x^2 - 4x  + 8      rearrange as

2x^2  -  10x   +  (b - 12 )  = 0

It will have no real roots  when  the discriminant   is <  0

So

10^2   -  4(2) (b - 12)  < 0

100  - 8b  + 96  <   0

196  <  8b

8b > 196

b >   196/ 8

b >  49 /  2

It will have no real roots  when    b >  49  / 2