
According to given figure, The Triangle BDC is a right angled Triangle (Angle D = 90°)
So, we can apply Pythagoras theorem to find the Side a (Hypotenuse)
Now, let's solve ~
Therefore, Length of side a is 5 units ~
There is a really easy way to do this problem and that is to use a graphing website
after punching in the functions:
A. depending of whether it is -5/(2x) or (-5/2)x: intersecting but not perpendicular or parallel
B. These two lines are perpendicular
C. Parallel lines
D. intersecting but not perpendicular
Can you rotate the picture or take another one? This one is really hard to read
Answer:- a.The given expression is equivalent to 
Given expression:- ![[\frac{(3xy^{-5})^3}{(x^{-2}y^2)^{-4}}]^{-2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%283xy%5E%7B-5%7D%29%5E3%7D%7B%28x%5E%7B-2%7Dy%5E2%29%5E%7B-4%7D%7D%5D%5E%7B-2%7D)
![=[\frac{(3)^3x^3y^{-5\times3}}{x^{-2\times-4}y^{2\times-4}}]^{-2}.........(a^m)^n=a^{mn}](https://tex.z-dn.net/?f=%3D%5B%5Cfrac%7B%283%29%5E3x%5E3y%5E%7B-5%5Ctimes3%7D%7D%7Bx%5E%7B-2%5Ctimes-4%7Dy%5E%7B2%5Ctimes-4%7D%7D%5D%5E%7B-2%7D.........%28a%5Em%29%5En%3Da%5E%7Bmn%7D)
![=[\frac{27x^3y^{-15}}{x^8y^{-8}}]^{-2}](https://tex.z-dn.net/?f=%3D%5B%5Cfrac%7B27x%5E3y%5E%7B-15%7D%7D%7Bx%5E8y%5E%7B-8%7D%7D%5D%5E%7B-2%7D)
![=[27x^{3-8}y^{-15-(-8)}]^{-2}............\frac{a^m}{a^n}=a^{m-n}](https://tex.z-dn.net/?f=%3D%5B27x%5E%7B3-8%7Dy%5E%7B-15-%28-8%29%7D%5D%5E%7B-2%7D............%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bm-n%7D)
![=[27x^{-5}y^{-7}]^{-2}=(27)^{-2}(x^{-5})^{-2}(y^{-7})^{-2}.........(a^m)^n=a^{mn}](https://tex.z-dn.net/?f=%3D%5B27x%5E%7B-5%7Dy%5E%7B-7%7D%5D%5E%7B-2%7D%3D%2827%29%5E%7B-2%7D%28x%5E%7B-5%7D%29%5E%7B-2%7D%28y%5E%7B-7%7D%29%5E%7B-2%7D.........%28a%5Em%29%5En%3Da%5E%7Bmn%7D)

Thus a. is the right answer.