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I don't get it.

See here :  https://web2.0calc.com/questions/help-please_46127

For any  regular  polygon, themeasure of an interior angle is

(n - 2) (180)

_________      where n is the number of sides

       n

So

(5 - 2) (180)              3 * 180            

_________   =         ______   =    3 * 36   =    108°

       5                          5

Take  (1/2) of 144   =   72

Square 72  =  5184  =   c

x(3x - 4)  ≤ 20

3x^2  - 4x  - 20  ≤   0

(3x   - 10)  ( x + 2) ≤   0       (1)

Set  factors to 0   and solve  for  x to  find the  critical points

x = 10/ 3      x  =  -2

We have  three intervals  that we can test

(-inf, -2 ]   ,  [ -2, 10/3 ]     and [ 10/3, inf ) 

  Picking an x  in each interval  to test in (1)  shows that the  solution      =  [ -2, 10/3  ]   

xy  =  6  - 2x   - 3y

yz  =  6  - 4y   - 2z

xz =  156  - 4x   - 3z

xy + 3y  =  6 - 2x                     xz + 3z  = 156  - 4x

y ( x + 3)  = 5 -2x                    z( x + 3)  =  156 - 4x

y =      (6-2x) / ( x + 3)             z   =  (156 - 4x)  / ( x + 3)

(6-2x)(156 - 4x)  / (x + 3)^2   =  6  - 4 ( 6-2x)/(x + 3)  -2 (156 - 4x)/(x + 3)    simplify

(6 -2x) (156 - 4x)  =  6( x + 3)^2  - 4(6 - 2x)(x + 3)  - 2(156- 4x)(x + 3)

8x^2 -336x +936  =  6x^2 + 36x + 54  + 8x^2   -72 + 8x^2 -288x -936

14x^2  +  84x   -1890  =  0 

7x^2  + 42x   -  945  =   0

x^2  +  6x  - 135  =   0   

(x -9) ( x + 15)   =  0

x  = 9   is the positive  solution   for x

that's incorrect... sorry

Maxmimal value of ax^2 + bx + c is when x = -b/a

t^2 - 9t - 36 = 0

max t = 9/1 = 9

quadratic is maximized when t = 9

Coordinate      y = 4 + (50 - 4²) / 2

The probability is 43/64, so the answer is 43 + 64 = 107.

Case 1: All green

3/5 * 3/5 * 3/5 = 27 / 125

Case 2: All red

2/5 * 2/5 * 2/5 = 8 / 125

8+ 27 = 35

7/25

radius of cylinder = 2

height = 4

16 pi

6/2 = 3

3^2 = 9

add 9 to both sides:

14 + 9 = 23

The sum of the interior angles of any polygon with n sides is (n – 2) • 180^o  

So, a hexagon is 4 • 180^o  =  720^o  

_.

9 - 9 - 8 - 1/8 = -8 - 1/8 = -65/8

It should just use substitution to get x=9

4,2

4^2 = 16

2^4 = 16

Using synthetic division

6  [  6     0         -29         12  ]

            36        216     1122

     _________________________

       6    36        187    1134      

R = 1134

In the diagram below, we have AB = 24, angle ADB = 90, and angles A and C are acute. If sin A = 1/2 and sin C = 1/4, then what is BC?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

BC = [24*sin(A)] / sin(C)  ==> BC = (24 * 1/2) / 1/4 = 48

Very difficult  (if not impossible)  to detect any  patterns for this, phmqt   !!!!

We  have  this cumbersome system

a  + b + c  + d  +  e + f  =  2

32a  + 16b + 8c + 4d + 2e + f  = 3

243a + 81b + 27c + 9d +3e + f   = 4

1024a  + 256b + 64c + 16d + 4e + f  =5

3125 a  + 625b + 125c + 25d + 5e + f  = 6

7776a  + 1296b + 216c + 36d  + 6e + f  =  -113

This is very time-consuming to  solve  (but it's do-able)...so...I will use  some tecnology to  find  f  (what we are really looking for )

The polynomial   is

  a           b            c            d           e          f

-1x^5  + 15x^4   - 85x^3 +225x^2 -273x + 121

g(0)  = f   =  121 

Verified with Desmos, here : https://www.desmos.com/calculator/4dm3cbtuxo 

(6-2)(180)/ 6  =  (3/4) 180 =  135  = BAD           Agreed; it's BAD!

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Angle BAC = 120 - 108 = 12º 

(10 nCr 3) * (1/6)^3 * (5/6)^7 =0.155

i was curiouse how you simplified 2^2x+1 to 2(2/3)^x

The  base  will   have  the dimensions   ( 12 - 2* .5x)  and  ( 16  - 2 *.5x)

And the  height will be   .5x

Where  x is the  multiple we are looking for

V =  (12 - 2 *.5x)   (16 - 2*.5x)  (.5x) 

V = (12 - x) ( 16 - x) (.5x)

V =  ( 192 - 28x  + x^2) ( 1/2)x

V  =  ( 1/2)x^3  - 14x^2 + 96 x)

Take the derivative and set to   0

V'=  (3/2)x^2  -  28x  +  96  = 0

3x^2  -  56x  +  192  = 0 

This gives  us some messy roots

Look  at the graph here :   https://www.desmos.com/calculator/imswwfyroh

The box has  a  max  volume of  ≈  194.1 in^3   when  x ≈  4.5

Thank you!!