First of all, we can observe that
![x^2-6x+9 = (x-3)^2](https://tex.z-dn.net/?f=x%5E2-6x%2B9%20%3D%20%28x-3%29%5E2)
So the expression becomes
![\dfrac{x^2-4}{\sqrt{(x-3)^2}} = \dfrac{x^2-4}{|x-3|}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2-4%7D%7B%5Csqrt%7B%28x-3%29%5E2%7D%7D%20%3D%20%5Cdfrac%7Bx%5E2-4%7D%7B%7Cx-3%7C%7D)
This means that the expression is defined for every ![x\neq 3](https://tex.z-dn.net/?f=x%5Cneq%203)
Now, since the denominator is always positive (when it exists), the fraction can only be positive if the denominator is also positive: we must ask
![x^2-4 \geq 0 \iff x\leq -2 \lor x\geq 2](https://tex.z-dn.net/?f=x%5E2-4%20%5Cgeq%200%20%5Ciff%20x%5Cleq%20-2%20%5Clor%20x%5Cgeq%202)
Since we can't accept 3 as an answer, the actual solution set is
![(-\infty,-2] \cup [2,3) \cup (3,\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C-2%5D%20%5Ccup%20%5B2%2C3%29%20%5Ccup%20%283%2C%5Cinfty%29)
400, if you can buy 4 tickets for $6 you can buy 400 for $600
Answer:
x = 30m
Step-by-step explanation:
<u>GIVEN :-</u>
There are 2 right-angled triangles.
In the triangle on the right side ,
- Hypotenuse = 26m
- Base = 10m
In the triangle on the left side ,
<u>TO FIND :-</u>
- Length of the common perpendicular to both triangles.
- Length of the hypotenuse of the triangle on the left side.
<u>FACTS TO KNOW BEFORE SOLVING :-</u>
.![Perpendicular = \sqrt{Hypotenuse^2 - Base^2}](https://tex.z-dn.net/?f=Perpendicular%20%3D%20%5Csqrt%7BHypotenuse%5E2%20-%20Base%5E2%7D)
<u>SOLUTION :-</u>
In the triangle on the right side ,
![Perpendicular = \sqrt{26^2 - 10^2} = \sqrt{676 - 100} = \sqrt{576} = 24m](https://tex.z-dn.net/?f=Perpendicular%20%3D%20%5Csqrt%7B26%5E2%20-%2010%5E2%7D%20%3D%20%5Csqrt%7B676%20-%20100%7D%20%3D%20%5Csqrt%7B576%7D%20%3D%2024m)
⇒ Perpendicular of the triangle on right side = Perpendicular of the triangle on left side.
In the triangle on the left side ,
![Hypotenuse = \sqrt{24^2 + 18^2} = \sqrt{576 + 324} = \sqrt{900} = 30m](https://tex.z-dn.net/?f=Hypotenuse%20%3D%20%5Csqrt%7B24%5E2%20%2B%2018%5E2%7D%20%3D%20%5Csqrt%7B576%20%2B%20324%7D%20%3D%20%5Csqrt%7B900%7D%20%3D%2030m)
∴ x = 30m
Price increase is $ 22-20 =$2 so the percent increase is 2/20 x 100= 10%