Okay so, we switch out f(x) with y - I’m sure you know this and we get y=2+3x/x-2.
Now just interchange x and y -> x=2+3y/y-2, now multiply both sides with (y-2), we get (y-2)x=2+3y.
Multiply x with the brackets, getting xy-2x=2+3y. Move 3y to the left changing it’s sign, also for -2x to the right: xy-3y=2+2x.
Factor out y from (xy-3y) and get (3-x)y=2+2x - now divide both sides by (3-x) resulting in y=2+2x/3-x .
Opposite sides of a rectangle have the same length
if short side is 150 the opposite side is also 150. total sum = 300 leaving 660 for the 2 longer sides
divide 660 by 2
therefor the longer sides are each 330
Answer:
the answer is : 93.6 millimeters
Answer:
and ![\frac{-2-7\sqrt{2} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-2-7%5Csqrt%7B2%7D%20%7D%7B2%7D)
Step-by-step explanation:
<em>hey there,</em>
<em />
< The way you solve right angle triangle problems are using the Pythagorean theorem. (I hope you have already learned it but if you haven't feel free to ask me.)
Pythagorean theorem states: ![a^2 + b^2 = c^2](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%3D%20c%5E2)
The two sides of the triangle that touch the right angle are (x+5) and (x-3).
Those two values count as "a" and "b". "c" would be 9.
Let's put them into the equation now.
![(x+5)^2 + (x-3)^2 = 9^2](https://tex.z-dn.net/?f=%28x%2B5%29%5E2%20%2B%20%28x-3%29%5E2%20%3D%209%5E2)
Simplify:
![(x^2 + 10x + 25) + (x^2-6x+9) = 81](https://tex.z-dn.net/?f=%28x%5E2%20%2B%2010x%20%2B%2025%29%20%2B%20%28x%5E2-6x%2B9%29%20%3D%2081)
![2x^2 + 4x + 34 = 81](https://tex.z-dn.net/?f=2x%5E2%20%2B%204x%20%2B%2034%20%3D%2081)
![2(x^2+2x+17) = 81\\x^2+2x+17 = \frac{81}{2}](https://tex.z-dn.net/?f=2%28x%5E2%2B2x%2B17%29%20%3D%2081%5C%5Cx%5E2%2B2x%2B17%20%3D%20%5Cfrac%7B81%7D%7B2%7D)
![x^2 +2x+ (17-\frac{81}{2})=0\\ x^2+2x+(\frac{-47}{2}) = 0\\](https://tex.z-dn.net/?f=x%5E2%20%2B2x%2B%20%2817-%5Cfrac%7B81%7D%7B2%7D%29%3D0%5C%5C%20x%5E2%2B2x%2B%28%5Cfrac%7B-47%7D%7B2%7D%29%20%3D%200%5C%5C)
From there, you can solve to x (it might be a little tricky, so sorry if you don't understand these steps).
![2x^2 + 4x - 47 = 0\\\frac{-b ±(\sqrt{b^2-4ac})}{2a}](https://tex.z-dn.net/?f=2x%5E2%20%2B%204x%20-%2047%20%3D%200%5C%5C%5Cfrac%7B-b%20%C2%B1%28%5Csqrt%7Bb%5E2-4ac%7D%29%7D%7B2a%7D)
final answer:
and
>
<u>Hope this helped. sorry for the bad explanation but feel free to ask anything else.</u>