The slope-intercept equation is y=mx+b.
The slope formula is ![\frac{y_{2}-y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D-y_%7B1%7D%20%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%20%7D)
Our three points are (5,5), (-5,-7) and (0,-1)
Using our slope formula our slope becomes ![\frac{-7-5}{-5-5} =\frac{12}{10} =\frac{6}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B-7-5%7D%7B-5-5%7D%20%3D%5Cfrac%7B12%7D%7B10%7D%20%3D%5Cfrac%7B6%7D%7B5%7D)
Then, if we use one of our points (pick whichever you want, although (0,1) is the easiest) to solve the equation. So,
. When we solve for x and y, we get -1=0+b, or b=-1.
When we plug that back into the equation, we get
.
Answer:
5/18
Step-by-step explanation:
note: 5/9 is the same as 10/18 (we get this by multiplying both numerator and denominator by 2)
hence
5/9-5/18
= 10/18 - 5/18
= (10-5) / 18
= 5/18
<em>Note: Your equation seems a little unclear. But, I am assuming that your equation is:</em>
![e^x\:+\:e^{-1}=\:2](https://tex.z-dn.net/?f=e%5Ex%5C%3A%2B%5C%3Ae%5E%7B-1%7D%3D%5C%3A2)
<em>Because my solution would still clear your concept about this topic, no matter what the question is.</em>
Answer:
Please check the explanation.
Step-by-step explanation:
Given the equation
![e^x\:+\:e^{-1}=\:2](https://tex.z-dn.net/?f=e%5Ex%5C%3A%2B%5C%3Ae%5E%7B-1%7D%3D%5C%3A2)
subtract
from both sides
![e^x+e^{-1}-e^{-1}=2-e^{-1}](https://tex.z-dn.net/?f=e%5Ex%2Be%5E%7B-1%7D-e%5E%7B-1%7D%3D2-e%5E%7B-1%7D)
![e^x=2-\frac{1}{e}](https://tex.z-dn.net/?f=e%5Ex%3D2-%5Cfrac%7B1%7D%7Be%7D)
![\ln \left(e^x\right)\:=\ln \:\left(2-\frac{1}{e}\right)](https://tex.z-dn.net/?f=%5Cln%20%5Cleft%28e%5Ex%5Cright%29%5C%3A%3D%5Cln%20%5C%3A%5Cleft%282-%5Cfrac%7B1%7D%7Be%7D%5Cright%29)
![\:x\cdot ln\left(e\right)=\ln \:\:\left(2-\frac{1}{e}\right)](https://tex.z-dn.net/?f=%5C%3Ax%5Ccdot%20ln%5Cleft%28e%5Cright%29%3D%5Cln%20%5C%3A%5C%3A%5Cleft%282-%5Cfrac%7B1%7D%7Be%7D%5Cright%29)
∵ ![\:\:\ln \left(e\right)=1](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5Cln%20%5Cleft%28e%5Cright%29%3D1)
![x=0.5](https://tex.z-dn.net/?f=x%3D0.5)
Answer:
7th term = -2187
Step-by-step explanation:
The formula for nth term of a geometric sequence is given by:
![a_n=a*r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da%2Ar%5E%7Bn-1%7D)
Where
- a is the first term,
- r is the common ratio,
- n is the nth term (term number)
Since the question gives us the formula and wants to know 7th term, we just plug in 7 into n:
![a_n=(-3)*(3)^{n-1}\\a_n=(-3)*(3)^{7-1}\\a_n=(-3)*(3)^6\\a_n=-2187](https://tex.z-dn.net/?f=a_n%3D%28-3%29%2A%283%29%5E%7Bn-1%7D%5C%5Ca_n%3D%28-3%29%2A%283%29%5E%7B7-1%7D%5C%5Ca_n%3D%28-3%29%2A%283%29%5E6%5C%5Ca_n%3D-2187)