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Thanks Phill 

Notice  the first few  terms in the expansion of  both terms (where C1, C2, C3....   are  the terms on  the 51st row of Pascal's triangle)

(x +a)^51  =  C1 x^51  + C2x^50 a  + C3x^49a^2 + C4x^48 a^3 + C5x^47a^4  + C6 x^46a^5 +.......+.x^0*a^51

-(x - a)^51 = -C1x^51 + C2x^50a  -  C3x^49a^2   + C4x^48a^3  - C5x^47a^4  +  C6x^46a^5 +  ....+ x^0 * a^51

Adding  these  we  get

2C2x^50a  +  2C4x^48a^3  + C6x^46a^5 +  ....+ 2x^0a^51

The  number of  terms  is   [ 51 + 1]  / 2  =   26

5x = 4x + 11

x = 11

Correct  !!!

calvin coolidge, I believe.

1/ ( x + 2)

The degree of the polynomial in the  numerator  is less than  the  degree of the polynomial in the denominator....thus...we will have a horizontal asymptote  at  y = 0 .....the behavior at  both ends  will  approach  this asymptote y  = 0

See the graph here :  https://www.desmos.com/calculator/s6j0qch9li

21/18 = JM/24

JM = 28

(98.6 - 32)  /  1.8  =   37° C

37 degrees celsius

This is a quadriateral inscribed in a circle......the  opposite  angles sum to 180°

Therefore....

x + 77  + x + 103 =  180

2x  + 180   = 180

2x   =180  - 180

2x   = 0

x   = 0

So  RST =  77°

I've got it!!!

3x + 5 = 2x + 3y

x = 3y - 5

Thank you very much

B. Infinitely many

How did you find that    x = 3y-5   ?

Nvm, I solved it. 

We're going to complete the square. :))

 h(t) = -15t^2 + 45t + 10

h(t) = -15(t-1.5)^2+ 43.75

A square minumn is 0, and we want the (t-1.5)^2 to be as small  as possible, so it's 0. 

h(t) = -15*0+ 43.75

h(t) = 43.75

Our maximum height is 43.75

=^._.^=

Have fun. :))

They are incredibly frustrating, just remember to use google. 

Google is your best friend. 

=^._.^=

Thanks, I've been bored out of my mind lately. I'll be sure to try the puzzles! 

Using the pythogorean theorem, a^2 + b^2 = c^2. I can substitute the values into it, 24^2+7^2=c^2. I simplify the equation and get c^2=625, which is c=25. I'm only learning trig this year, so I don't think I'm qualified to help you after this. But, here's a nice website, I found for sin,cos,tan,cot,etc. That I think can help u. If I'm missing something please tell me. Please keep in mind this answer might be wrong and this is only my second time answering. 
 

Thanks :)

https://www.omnicalculator.com/math/trigonometry

XY = sqrt(40² - 32²) = 24

sinZ = 24 / 40 = 3/5

Angle x = 106 degrees

It is actually 11

5x - 54 + 8x = 180

13x = 234

x = 18

∠STU = 8 * 18 = 144º

∠S = 180 - 2(∠SRT) = 108º

I'm going assume X=A and M=S. This means that x+80=4x+8. 

      x+80=4x+8

       80-8=4x-x

        72=3x

         24=x

This shows x is 24. That also means a is 24. A parallelogram has 360 degrees in total. I have to do 360-24-24/ 2 to find the answer for M.

      360-24-24/2 = 312/2=156=M

This shows that M is 156.  Please note that this answer might be wrong and that this my first time answering a question on this forum. If you have any comments, questions, or concerns please let me know.

Thanks :)

cos (theta - pi) = -3/5 and cos (theta - pi/2) = -4/5.