Answer:
a line with a gradient of
![\frac{ - x}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%20-%20x%7D%7B3%7D%20)
Step-by-step explanation:
parallel lines have equal gradients, i.e the value of m, has to be the same.
therefore:
![x + 3y = - 21 \\ 3y = - x - 21 \\ y = \frac{ - x}{3} - 7](https://tex.z-dn.net/?f=x%20%2B%203y%20%3D%20%20-%2021%20%20%5C%5C%203y%20%20%3D%20%20-%20x%20-%2021%20%5C%5C%20y%20%3D%20%20%5Cfrac%7B%20-%20x%7D%7B3%7D%20%20-%20%207)
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)
Answer:
The result is X-4
and the rest is 4
Step-by-step explanation:
You need to divide step by step
first the quadratic term
![x^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D)
-
-2X------>(X-2)·x---- x is the result
-----------------------------------
2X-6X
-4X
Now divide the linear term
-4X+8---------------------->(X-2)·(-4)--- -4 is the result
---------------------------------------
-8+12
4
You cant continue so the rest is 4
Coeficient= X-4