ANSWER
x = 1.2226
EXPLANATION
To solve this equation we have to apply the property of the logarithm of the base,
![\log _bb=1](https://tex.z-dn.net/?f=%5Clog%20_bb%3D1)
Thus, we can apply the natural logarithm - whose base is e, to both sides of the equation,
![\ln e^{4x}=\ln 133](https://tex.z-dn.net/?f=%5Cln%20e%5E%7B4x%7D%3D%5Cln%20133)
Now we apply the property of the logarithm of a power,
![\log a^b=b\log a](https://tex.z-dn.net/?f=%5Clog%20a%5Eb%3Db%5Clog%20a)
In our equation,
![\begin{gathered} 4x\ln e^{}=\ln 133 \\ 4x^{}=\ln 133 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%204x%5Cln%20e%5E%7B%7D%3D%5Cln%20133%20%5C%5C%204x%5E%7B%7D%3D%5Cln%20133%20%5Cend%7Bgathered%7D)
Then divide both sides by 4 and solve,
![\begin{gathered} \frac{4x^{}}{4}=\frac{\ln 133}{4} \\ x\approx1.2226 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B4x%5E%7B%7D%7D%7B4%7D%3D%5Cfrac%7B%5Cln%20133%7D%7B4%7D%20%5C%5C%20x%5Capprox1.2226%20%5Cend%7Bgathered%7D)
The solution to this equation is x = 1.2226, rounded to four decimal places.
Answer:
![(\frac{-9}{2},\frac{11}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B-9%7D%7B2%7D%2C%5Cfrac%7B11%7D%7B2%7D%29)
Step-by-step explanation:
you have to use the midpoint formula which is
![(\frac{x1+x2}{2},\frac{y1+y2}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx1%2Bx2%7D%7B2%7D%2C%5Cfrac%7By1%2By2%7D%7B2%7D%29)
so you plug your numbers in
![(\frac{-12+3}{2},\frac{-3+-8}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B-12%2B3%7D%7B2%7D%2C%5Cfrac%7B-3%2B-8%7D%7B2%7D%29)
Add the tops
![(\frac{-9}{2} ,\frac{-11}{2} )](https://tex.z-dn.net/?f=%28%5Cfrac%7B-9%7D%7B2%7D%20%2C%5Cfrac%7B-11%7D%7B2%7D%20%29)
if possible simplify
and that is your answer
Vertical angles i believe is the right answer to this problem
Just multiply 4*12 and add 6.
answer =54