Answer:
Option 3
Step-by-step explanation:
When it says 12 less, that means -12.
Hope I helped. :)
You need to find the change in x and y
change in x = 12
change in y = 16
to find the distance you use a^2+ b^2 = c^2
or in this case x^2 + y^2 = d^2
144+256 = 400
![\sqrt{400}](https://tex.z-dn.net/?f=%20%5Csqrt%7B400%7D%20)
=20
so distance equals 20
I hope this helps!
The answer to your question is 11 world championships
The simplification of 3log(x + 4) – 2log(x – 7) + 5log(x - 2) - log(x^2) is ![\log \left(\frac{(x+4)^{3} \times(x-2)^{5}}{(x-7)^{2} \times x^{2}}\right)](https://tex.z-dn.net/?f=%5Clog%20%5Cleft%28%5Cfrac%7B%28x%2B4%29%5E%7B3%7D%20%5Ctimes%28x-2%29%5E%7B5%7D%7D%7B%28x-7%29%5E%7B2%7D%20%5Ctimes%20x%5E%7B2%7D%7D%5Cright%29)
<u>Solution:</u>
Given, expression is ![3 \log (x+4)-2 \log (x-7)+5 \log (x-2)-\log \left(x^{2}\right)](https://tex.z-dn.net/?f=3%20%5Clog%20%28x%2B4%29-2%20%5Clog%20%28x-7%29%2B5%20%5Clog%20%28x-2%29-%5Clog%20%5Cleft%28x%5E%7B2%7D%5Cright%29)
We have to write in as single logarithm by simplifying it.
Now, take the given expression.
![\rightarrow 3 \log (x+4)-2 \log (x-7)+5 \log (x-2)-\log \left(x^{2}\right)](https://tex.z-dn.net/?f=%5Crightarrow%203%20%5Clog%20%28x%2B4%29-2%20%5Clog%20%28x-7%29%2B5%20%5Clog%20%28x-2%29-%5Clog%20%5Cleft%28x%5E%7B2%7D%5Cright%29)
Rearranging the terms we get,
![\left.\rightarrow 3 \log (x+4)+5 \log (x-2)-2 \log (x-7)+\log \left(x^{2}\right)\right)](https://tex.z-dn.net/?f=%5Cleft.%5Crightarrow%203%20%5Clog%20%28x%2B4%29%2B5%20%5Clog%20%28x-2%29-2%20%5Clog%20%28x-7%29%2B%5Clog%20%5Cleft%28x%5E%7B2%7D%5Cright%29%5Cright%29)
![\text { since a } \times \log b=\log \left(b^{a}\right)](https://tex.z-dn.net/?f=%5Ctext%20%7B%20since%20a%20%7D%20%5Ctimes%20%5Clog%20b%3D%5Clog%20%5Cleft%28b%5E%7Ba%7D%5Cright%29)
![\rightarrow \log (x+4)^{3}+\log (x-2)^{5}-\left(\log (x-7)^{2}+\log \left(x^{2}\right)\right)](https://tex.z-dn.net/?f=%5Crightarrow%20%5Clog%20%28x%2B4%29%5E%7B3%7D%2B%5Clog%20%28x-2%29%5E%7B5%7D-%5Cleft%28%5Clog%20%28x-7%29%5E%7B2%7D%2B%5Clog%20%5Cleft%28x%5E%7B2%7D%5Cright%29%5Cright%29)
![\text { We know that } \log a \times \log b=\log a b](https://tex.z-dn.net/?f=%5Ctext%20%7B%20We%20know%20that%20%7D%20%5Clog%20a%20%5Ctimes%20%5Clog%20b%3D%5Clog%20a%20b)
![\rightarrow \log \left((x+4)^{3} \times(x-2)^{5}\right)-\left(\log \left((x-7)^{2} \times\left(x^{2}\right)\right)\right.](https://tex.z-dn.net/?f=%5Crightarrow%20%5Clog%20%5Cleft%28%28x%2B4%29%5E%7B3%7D%20%5Ctimes%28x-2%29%5E%7B5%7D%5Cright%29-%5Cleft%28%5Clog%20%5Cleft%28%28x-7%29%5E%7B2%7D%20%5Ctimes%5Cleft%28x%5E%7B2%7D%5Cright%29%5Cright%29%5Cright.)
![\text { We know that } \log a-\log b=\log \frac{a}{b}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20We%20know%20that%20%7D%20%5Clog%20a-%5Clog%20b%3D%5Clog%20%5Cfrac%7Ba%7D%7Bb%7D)
![\rightarrow \log \left(\frac{(x+4)^{3} \times(x-2)^{5}}{(x-7)^{2} \times x^{2}}\right)](https://tex.z-dn.net/?f=%5Crightarrow%20%5Clog%20%5Cleft%28%5Cfrac%7B%28x%2B4%29%5E%7B3%7D%20%5Ctimes%28x-2%29%5E%7B5%7D%7D%7B%28x-7%29%5E%7B2%7D%20%5Ctimes%20x%5E%7B2%7D%7D%5Cright%29)
Hence, the simplified form ![\rightarrow \log \left(\frac{(x+4)^{3} \times(x-2)^{5}}{(x-7)^{2} \times x^{2}}\right)](https://tex.z-dn.net/?f=%5Crightarrow%20%5Clog%20%5Cleft%28%5Cfrac%7B%28x%2B4%29%5E%7B3%7D%20%5Ctimes%28x-2%29%5E%7B5%7D%7D%7B%28x-7%29%5E%7B2%7D%20%5Ctimes%20x%5E%7B2%7D%7D%5Cright%29)
Answer:
A. AAS
Step-by-step explanation:
In both triangles, the line mn and jh are congruent, the angles k and g are congruent, and h and m are congruent.