Answer:
![Area = 93.21in^2](https://tex.z-dn.net/?f=Area%20%3D%2093.21in%5E2)
Step-by-step explanation:
Given
vertex angle
base angle
![\theta = 3\alpha](https://tex.z-dn.net/?f=%5Ctheta%20%3D%203%5Calpha)
-- congruent sides
Required
The area of the triangle
First, calculate the angles
----- angles in an isosceles triangle
Substitute ![\theta = 3\alpha](https://tex.z-dn.net/?f=%5Ctheta%20%3D%203%5Calpha)
![3\alpha + \alpha + \alpha = 180^o](https://tex.z-dn.net/?f=3%5Calpha%20%2B%20%5Calpha%20%2B%20%5Calpha%20%3D%20180%5Eo)
![5\alpha = 180^o](https://tex.z-dn.net/?f=5%5Calpha%20%3D%20180%5Eo)
Divide both sides by 5
![\alpha = 36^o](https://tex.z-dn.net/?f=%5Calpha%20%3D%2036%5Eo)
Recall that: ![\theta = 3\alpha](https://tex.z-dn.net/?f=%5Ctheta%20%3D%203%5Calpha)
![\theta = 3 * 36^o](https://tex.z-dn.net/?f=%5Ctheta%20%3D%203%20%2A%2036%5Eo)
![\theta = 108^o](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20108%5Eo)
The area is then calculated as:
![Area = \frac{1}{2}l^2 \sin(\theta)](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7Dl%5E2%20%5Csin%28%5Ctheta%29)
![Area = \frac{1}{2}*14^2 \sin(108^o)](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A14%5E2%20%5Csin%28108%5Eo%29)
![Area = \frac{1}{2}*196 *0.9511](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A196%20%2A0.9511)
![Area = 93.21in^2](https://tex.z-dn.net/?f=Area%20%3D%2093.21in%5E2)
112.363 rounded to the nearest hundredths place would be 112.36 :)
Answer: First answer: hexagon
second answer: triangle
Step-by-step explanation: right on edge 2020
Answer:
![x=32768.000](https://tex.z-dn.net/?f=x%3D32768.000)
Step-by-step explanation:
One is given the following expression:
![log_2(x)+log_4(x)=5](https://tex.z-dn.net/?f=log_2%28x%29%2Blog_4%28x%29%3D5)
Use the logarithm base change rule, which states the following:
![log_b(y)=\frac{log(y)}{log(b)}](https://tex.z-dn.net/?f=log_b%28y%29%3D%5Cfrac%7Blog%28y%29%7D%7Blog%28b%29%7D)
Remember, a logarithm with not base indicated is another way of writing a logarithm to the base of (10). One can apply the base change rule to this situation:
![log_2(x)+log_4(x)=5](https://tex.z-dn.net/?f=log_2%28x%29%2Blog_4%28x%29%3D5)
![\frac{log(x)}{log(2)}+\frac{log(x)}{log(4)}=5](https://tex.z-dn.net/?f=%5Cfrac%7Blog%28x%29%7D%7Blog%282%29%7D%2B%5Cfrac%7Blog%28x%29%7D%7Blog%284%29%7D%3D5)
Factor out (log(x)),
![(log(x))(\frac{1}{log(2)}+\frac{1}{log(4)})=5](https://tex.z-dn.net/?f=%28log%28x%29%29%28%5Cfrac%7B1%7D%7Blog%282%29%7D%2B%5Cfrac%7B1%7D%7Blog%284%29%7D%29%3D5)
Inverse operations:
![log(x)=\frac{5}{\frac{1}{(log(2)+log(4)}}](https://tex.z-dn.net/?f=log%28x%29%3D%5Cfrac%7B5%7D%7B%5Cfrac%7B1%7D%7B%28log%282%29%2Blog%284%29%7D%7D)
Simplify,
![log(x)=5(log(2)+log(4))](https://tex.z-dn.net/?f=log%28x%29%3D5%28log%282%29%2Blog%284%29%29)
![log(x)=4.51545](https://tex.z-dn.net/?f=log%28x%29%3D4.51545)
Now rewrite the logarithm, remember, a logarithm is another way of writing an exponent, in the following format:
![b^x=y\ \ -> log_b(y)=x](https://tex.z-dn.net/?f=b%5Ex%3Dy%5C%20%5C%20-%3E%20log_b%28y%29%3Dx)
![log(x)=4.51545](https://tex.z-dn.net/?f=log%28x%29%3D4.51545)
![10^4^.^5^1^5^4^5=x](https://tex.z-dn.net/?f=10%5E4%5E.%5E5%5E1%5E5%5E4%5E5%3Dx)
![32768.000=x](https://tex.z-dn.net/?f=32768.000%3Dx)