Life hack: if you own a TI-84 graphing calculator you can just input that into the calculator on the graphing part and then you see which equation’s graph matches the graph you were given in the problem.
Answer:
3x+180=0 x= -60
Step-by-step explanation:
equal everything to 0.
3x+180=0
3x= -180
x= -60
Answer:
10 and 40 I think maybe?
Step-by-step explanation:
I hope this is correct if not I am so so so so so so sorry
Answer:
The first term is 3 and common difference is 8.
And
The formula for sequence is: ![a_n = -5+8n](https://tex.z-dn.net/?f=a_n%20%3D%20-5%2B8n)
Function is: ![f(n) = f(n-1)+8](https://tex.z-dn.net/?f=f%28n%29%20%3D%20f%28n-1%29%2B8)
Step-by-step explanation:
Given that
![a_4 = 27\\a_8 = 59](https://tex.z-dn.net/?f=a_4%20%3D%2027%5C%5Ca_8%20%3D%2059)
The general formula for arithmetic sequence is:
![a_n = a+(n-1)d](https://tex.z-dn.net/?f=a_n%20%3D%20a%2B%28n-1%29d)
Here
a is the first term
n is the term number
and d is the common difference
for 4th term
![a_4 = a+(4-1)d\\27 = a+3d\ \ \ Eqn\ 1](https://tex.z-dn.net/?f=a_4%20%3D%20a%2B%284-1%29d%5C%5C27%20%3D%20a%2B3d%5C%20%5C%20%5C%20Eqn%5C%201)
For 8th term
![59 = a+ (8-1)d\\59= a+7d\ \ \ \ \ Eqn\ 2](https://tex.z-dn.net/?f=59%20%3D%20a%2B%20%288-1%29d%5C%5C59%3D%20a%2B7d%5C%20%5C%20%5C%20%5C%20%5C%20Eqn%5C%202)
subtracting equation 1 from equation 2
![59-27 = a+7d-(a+3d)\\32 = a+7d-a-3d\\32 = 4d\\d =\frac{32}{4}\\d = 8](https://tex.z-dn.net/?f=59-27%20%3D%20a%2B7d-%28a%2B3d%29%5C%5C32%20%3D%20a%2B7d-a-3d%5C%5C32%20%3D%204d%5C%5Cd%20%3D%5Cfrac%7B32%7D%7B4%7D%5C%5Cd%20%3D%208)
Putting d = 8 in equation 1
![a+3d = 27\\a+3(8) = 27\\a+24=27\\a = 27-24\\a = 3](https://tex.z-dn.net/?f=a%2B3d%20%3D%2027%5C%5Ca%2B3%288%29%20%3D%2027%5C%5Ca%2B24%3D27%5C%5Ca%20%3D%2027-24%5C%5Ca%20%3D%203)
Now for the function
![a_n = a+(n-1)d\\a_n = 3+(n-1)(8)\\a_n = 3 + 8n-8\\a_n = -5+8n](https://tex.z-dn.net/?f=a_n%20%3D%20a%2B%28n-1%29d%5C%5Ca_n%20%3D%203%2B%28n-1%29%288%29%5C%5Ca_n%20%3D%203%20%2B%208n-8%5C%5Ca_n%20%3D%20-5%2B8n)
The sequence can also be expressed as a function as:
![f(n) = f(n-1) + 8](https://tex.z-dn.net/?f=f%28n%29%20%3D%20f%28n-1%29%20%2B%208)
Hence,
The first term is 3 and common difference is 8.
And
The formula for sequence is: ![a_n = -5+8n](https://tex.z-dn.net/?f=a_n%20%3D%20-5%2B8n)
Function is: ![f(n) = f(n-1)+8](https://tex.z-dn.net/?f=f%28n%29%20%3D%20f%28n-1%29%2B8)