CPhill

Here is the graph :  http://prntscr.com/m7ze53

We want to permute any 3 of 10 numbers....so....

P (10, 3)   =  720  combinations

The base angles of the bottom triangle are equal because they  are opposite equal radii

So....the apex angle of the bottom triangle = 180 - 50 - 50  = 80°

And c   is an inscribed angle intercepting the same arc as this central angle of  80°

So....c has 1/2 the measure of this angle =  40°

Three units to the left

One unit down

The denominator has 3 terms

x + 2 is a factor of the denominator

12 is a term in numerator and denominator

Hard to see...but

26.   Angle 9 = Angle 3  ⇒  corresponding angles

27.  Angle 4 is supplemental to angle 7.....so it equals 60

       Angle 5 =40

       So Angle 2 =  180 - 60 - 40  = 80

       Angle 3 = Angle 5  = 40    alternate interior angles

      So Angle 1  = 180 - Angle 2 - Angle 3

           Angle 1  =  180  - 80 - 40  =  60

28.  Angle 5 supplemental to angle 8  = 180 - 145 =  35

       Angle 3  = Angle 5  = 35      alternate interior angles

       Angle 2  =  180 - Angle 1 - Angle 3

        Angle 2  =  180 - 37 - 35  =  108

29.  Angle 4 = Angle 1  =  57   alternate interior angles

        Angle 3 = 180 - Angle 1 - Angle 2

         Angle 3  = 180 - 57 - 72  =  51

30. Angle 5 supplemental to angle 6 = 180 - 139   = 41

      Angle 4 = 180 - Angle 5 - Angle 2

      Angle 4 =   180 - 41 -68   = 71

      Angle 7 supplemental to Angle 4 = 180 - 71   = 109

[ 11 - 10 ] / 10  x 100%  =

1 /10   x   100%   =

10%

Only 10% longer

OK......

12

3xy  + x  = y - 6      rearrange as

y - 3xy  = x + 6       factor out y

y ( 1 - 3x)  = x + 6   divide both sides by 1 - 3x

y =   [ x + 6 ] / [ 1 - 3x ]

13

y^2 + 6y + 9  = x + 8      factor the left side

(y + 3)^2  =  x + 8          take both roots

y + 3 =  ±√ [ x + 8 ]        subtract 3 from both sides

y = - 3 ±√ [ x + 8 ]

18  looks good

19 

 -(3x - 2)^2  + 3(3x - 2) + 10

- [ 9x^2 - 12x + 4]  + 9x - 6 + 10

-9x^2 + 12x - 4  + 9x - 6 + 10

-9x^2 + 21x - 10 + 10

-9x^2 + 21x

Good job    !!!!!

We have the following form

f(x)  =  Acos (Bx + C) + D

A = the amplitude  =    [ high point - low point ] / 2 =   [ 4.5 - 3.5 ] / 2  =  1/2

The period is pi

So

B =   2pi / period  =  2pi / pi   =  2

C = phase shift   ....there is none

D =  this is the  cosine graph  with an amplitude of 1/2 shifted up 4 units......so  4  

So....the graph is

f(x)  = (1/2) cos (2x) + 4

Thanks to EP for pointing out my error.....!!!