CPhill

(x - 1/3)  ( x - 4) ( x - 3)  =

(x - 1/3)  ( x^2 - 7x + 12)  =   { distribute the terms in the first set of parentheses over the terms in the second }

x (x^2 - 7x + 12)   -  (1/3)   (  x^2 - 7x + 12)  =

x^3  - 7x^2  + 12x    - (1/3)x^2  + (7/3) x  - 4         combine like terms

x^3  +  ( -7 - 1/3)x^2 +  (12 + 7/3)x  - 4

x^3  +  (  -21/3 - 1/3)x^2  +  (36/3 + 7/3)x  - 4  

x^3  +  ( -22/3)x^2  +  ( 43/3)x   - 4

x^3  - (22/3)x^2  + (43/3)x  - 4

Check my math, Manuel....I did this one rather hurriedly.....LOL!!!

First one :

A + 121  = 180    subtract 121 from both sides

A   = 180  - 121  =  59°

Second one :

(4x + 5)  + (x + 15)  = 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°

Third one : 

(6x + 19) + x  = 180

7x + 19  = 180       subtract 19 from both sides

7x  =  161         divide both sides by 

x  = 23

B  = 6*23 + 19   = 157°

Last  one  :

B + D  = 180....so....

3x  + (x + 20)  = 180

4x + 20  = 180       subtract 20 from both sides

4x   =  160           divide both sides by 4

x  = 40

So      A +  C   = 180    ......so....

(2 * 40  +  38 )  + C    = 180

118  + C  = 180           subtract  118 from  both sides

C  = 62°

HAHAHA!!!!.....excellent, Donut  !!!!

Here's a pic :

We don't need as much work as the guest has laid out.....

First find angle ACB  = 180 - BAC  - CBA  = 180  - 180  - 46 - 71 =  63°

EHDC forms a quadrilateral whose interior angles sum to 360°

So   angle EHD  = 360 -  90 - 90 - 63  = 117°

And AHB  is a vertical angle to EHD =  117°

This is easy, Manuel

If   a,b  are integer zeroes....we just need to expand this ( x -a)  ( x - b)

So....since  7, -4 are zeroes....we have

(x  - 7 )  (  x  -   -4)   =

( x - 7 )  ( x + 4)   =

x^2 - 7x + 4x  - 28  =

x^2 - 3x  - 28

Pretty easy, huh  ??

Area of a sector   =   pi * radius^2  *  (central angle measure of the sector / 360) ....so we have..

72 pi  = pi (r^2)  (180/ 360)  divide out pi

72  = (1/2) r^2       multiply both sides by 2

144  = r^2       take the positive root

12 in  =   r

Thanks, adore....and good luck to you  !!!!

The number of boxes on the top row  is

23   - 3 (6-1)   =  8 in the first row

To find the total sum  we have

[ Number in  first row + Number in last row ]  * rows / 2  =

[ 23 + 8 ] * 6 / 2  =       31 * 3   =  93 boxes in the entire display

Sum  =  50  ( 1 - 2^8 )  / ( 1 - 2)  =  12750 visitors in the first 8 weeks

First one :

DHG is an inscribed angle...it measures 1/2 of minor arc DG....so arc DG  =  2 * 55  = 110° 

Second one :

arc BAC  = 360 - 290  = 70°

Third one :  The inscribed angle is !/2 the intercepted arc ....so...

(3x  -1.5)  = (1/2) (3x + 9)   multiply both sides by 2

2(3x  - 1.5)  =  3x + 9    simplify

6x - 3  = 3x + 9       add 3 to both sides....subtract 3x from both sides

3x  =  12   divide both sides by 3

x = 4

So  arc AC  =  3(4) + 9   =   21° 

Fourth one : 

A little tricky.....the angle that has both sides terminating at the diameter ends   = 90°

Three angles of a triangle sum to 180°

So  

68 + 90 + x  = 180

158 +  x   = 180     subtract  158 from  bth sides

x  = 22°

Hope that helps  !!