B is the midpoint of AC. If AB= X +5 and BC = 2X -11, find the measure of AB

Mathematics

2 answers:

Murljashka [212]3 years ago

5 0

First, you know that B is the mid point, meaning AB is equal to BC. Therefore, you can set up the equation: x+5=2x-11. Then, you solve for x. Once you are done solving, you should get 16. Hope this helps!

Dahasolnce [82]3 years ago

3 0

Hi! Actually, the answer is 21. Because x+5 and 2x-11 are equivalent, set them equal to one another in an equation. Solve for x

You can see my steps in the picture i attached for you!!

Then, once you have x, you need to plug it back in to the expression x+5 (AB) to get 21. I hope this helps you!! :))

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$\begin{bmatrix}-8x+y=-32\\ -3x-10=y\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:-8x+y=-32:\quad x=-\frac{-32-y}{8}\\\\\mathrm{Subsititute\:}x=-\frac{-32-y}{8}\\\begin{bmatrix}-3\left(-\frac{-32-y}{8}\right)-10=y\end{bmatrix}\\\\Simplify\\\begin{bmatrix}\frac{3\left(-32-y\right)}{8}-10=y\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:\frac{3\left(-32-y\right)}{8}-10=y:\quad y=-16\\\\\mathrm{For\:}x=-\frac{-32-y}{8}\\\\\mathrm{Subsititute\:}y=-16\\x=-\frac{-32-\left(-16\right)}{8}\\$