Given:
The figure of a pentagon.
To find:
The value of the x.
Solution:
We know that, the sum of all interior angles of a pentagon is 540 degrees. So,



Subtract both sides by 12.


Divide both sides by 33.


Therefore, the value of the x is 16.
Years and years a long time ahead
A. Blue: y = -3x + 8
Black: y = 3x + 2
B. You find the ordered pair (x, y) that is a solution for both functions ( find the point where the two lines cross)
C. There’s two ways you can solve algebraically (using the equations); substitution and elimination. I don’t know which you need to use to answer but feel free to use my notes on how to do substitution for help. I don’t really have any on elimination ( it’s so easy you don’t even really need notes) or I would use them to explain.
We first have to find the first derivative before we can find the second. First derivative with respect to x is

so

and

. That's the first derivative. Now for the second it's probably easiest to use the quotient rule, even though it's usually long and drawn out. That looks like this:
![\frac{dy}{dx}= \frac{4y^2(-6x)-[-3x^2(8y \frac{dy}{dx})] }{(4y^2)^2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B4y%5E2%28-6x%29-%5B-3x%5E2%288y%20%5Cfrac%7Bdy%7D%7Bdx%7D%29%5D%20%7D%7B%284y%5E2%29%5E2%7D%20%20)
which simplifies a bit to

. We will multiply both sides by that denominator to get rid of it which leaves us with

. Get both dy/dx terms on the same side, and then factor it out.

. Divide to isolate the dy/dx:

. There's no simplifying you could do after that that would make any significant difference.