To graph it, just graph
![y=-3^{-x}-6](https://tex.z-dn.net/?f=y%3D-3%5E%7B-x%7D-6)
and
![y=-3^x+10](https://tex.z-dn.net/?f=y%3D-3%5Ex%2B10)
and see where they intersect
I would like to solve it by using math and not graphing
if you don't want to see the math, just don't scroll down
the graphical meathod is above, first line, just read it
hmm
multiply both sides by -1
![3^{-x}+6=3^x-10](https://tex.z-dn.net/?f=3%5E%7B-x%7D%2B6%3D3%5Ex-10)
multiply both sides by
![3^x](https://tex.z-dn.net/?f=3%5Ex)
![3^0+6(3^x)=3^{2x}-10(3^x)](https://tex.z-dn.net/?f=3%5E0%2B6%283%5Ex%29%3D3%5E%7B2x%7D-10%283%5Ex%29)
![1+6(3^x)=3^{2x}-10(3^x)](https://tex.z-dn.net/?f=1%2B6%283%5Ex%29%3D3%5E%7B2x%7D-10%283%5Ex%29)
minus 1 from both sides and minus 6(3^x) from both sides
![0=3^{2x}-16(3^x)-1](https://tex.z-dn.net/?f=0%3D3%5E%7B2x%7D-16%283%5Ex%29-1)
use u subsitution
![u=3^x](https://tex.z-dn.net/?f=u%3D3%5Ex)
we can rewrite it as
![0=u^2-16u-1](https://tex.z-dn.net/?f=0%3Du%5E2-16u-1)
now factor
I mean use quadratic formula
for
![x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%2B%2F-%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
so for 0=u^2-16u-1, a=1, b=-16, c=-1
![u=\frac{-(-16)+/-\sqrt{(-16)^2-4(1)(-1)}{2(1)}](https://tex.z-dn.net/?f=u%3D%5Cfrac%7B-%28-16%29%2B%2F-%5Csqrt%7B%28-16%29%5E2-4%281%29%28-1%29%7D%7B2%281%29%7D)
![u=8+/-\sqrt{65}](https://tex.z-dn.net/?f=u%3D8%2B%2F-%5Csqrt%7B65%7D)
remember that u=3^x so u>0
if we have u=8+√65, it's fine, but u=8-√65 is negative and not allowed
so therfor
![u=8+\sqrt{65}=3^x](https://tex.z-dn.net/?f=u%3D8%2B%5Csqrt%7B65%7D%3D3%5Ex)
![8+\sqrt{65}=3^x](https://tex.z-dn.net/?f=8%2B%5Csqrt%7B65%7D%3D3%5Ex)
if you take the log base 3 of both sides you get
![log_3(8+\sqrt{65})=x](https://tex.z-dn.net/?f=log_3%288%2B%5Csqrt%7B65%7D%29%3Dx)
if you use ln then
![ln(8+\sqrt{65})=xln(3)](https://tex.z-dn.net/?f=ln%288%2B%5Csqrt%7B65%7D%29%3Dxln%283%29)
then
let's recall that on the IV Quadrant the x/cosine is positive and the y/sine is negative, and of course the hypotenuse is just a radius unit and therefore never negative.
![\bf sin(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{hypotenuse}{15}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20sin%28%5Ctheta%20%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B-7%7D%7D%7B%5Cstackrel%7Bhypotenuse%7D%7B15%7D%7D%5Cimpliedby%20%5Ctextit%7Blet%27s%20find%20the%20%5Cunderline%7Badjacent%20side%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Ctextit%7Busing%20the%20pythagorean%20theorem%7D%20%5C%5C%5C%5C%20c%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20%5Csqrt%7Bc%5E2-b%5E2%7D%3Da%20%5Cqquad%20%5Cbegin%7Bcases%7D%20c%3Dhypotenuse%5C%5C%20a%3Dadjacent%5C%5C%20b%3Dopposite%5C%5C%20%5Cend%7Bcases%7D)
![\bf \pm\sqrt{15^2-(-7)^2}=a\implies \pm\sqrt{176}=a\implies \stackrel{\textit{IV Quadrant}}{+\sqrt{176}=a} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{\sqrt{176}}}{\stackrel{hypotenuse}{15}}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cpm%5Csqrt%7B15%5E2-%28-7%29%5E2%7D%3Da%5Cimplies%20%5Cpm%5Csqrt%7B176%7D%3Da%5Cimplies%20%5Cstackrel%7B%5Ctextit%7BIV%20Quadrant%7D%7D%7B%2B%5Csqrt%7B176%7D%3Da%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20cos%28%5Ctheta%20%29%3D%5Ccfrac%7B%5Cstackrel%7Badjacent%7D%7B%5Csqrt%7B176%7D%7D%7D%7B%5Cstackrel%7Bhypotenuse%7D%7B15%7D%7D~%5Chfill)
Number 1.
2x to the second power minus 2x minus 4
Number 2.
2a to the second power minus 3b minus a plus b to the second power.
Hope it helped :)
Answer:
2A/h = b
Step-by-step explanation:
The formula for area of a triangle is
A = 1/2 bh
Multiply each side by 2
2A = 2*1/2 bh
2A = bh
Divide each side by h
2A/h = bh/h
2A/h = b
First, isolate y on one side to find some information about the graph.
3x+4y=-10
4y=-10-3x
y=(-10-3x)/4
Now find out the x and y intercepts of this equation;
(0)=(-10-3x)/4
4x0=-10-3x
0=-10-3x
3x=-10
x=-10/3 or -3.3333 (x-intercept)
y=(-10-3(0))/4
4y=-10
y=-10/4 or -5/2 = -2.5 (y-intercept)
Plot these points onto your graph and connect the lines.
I have attached a graph below, I'm sorry I couldn't do it on paper.
Hope I helped :)