Answer:
<h2>
y = 3x - 16</h2>
Step-by-step explanation:
Equation of line with a given slope of a and containing a given point (x₀, y₀):
y - y₀ = a(x - x₀)
a = 3, x₀ = 5, y₀ = -1
So:
y - (-1) = 3(x - 5)
y = 3x - 15 - 1
<u>y = 3x - 16</u>
(9,3) I believe. Because to get from -3 to -9 you multiply by three, as well as 5 to 15. So you simply multiply multiply these coordinates by three.
ANSWER
![a_ {10} = \frac{25}{32}](https://tex.z-dn.net/?f=a_%20%7B10%7D%20%3D%20%5Cfrac%7B25%7D%7B32%7D%20)
EXPLANATION
The given geometric sequence is
400, 200, 100...
The first term is
![a_1=400](https://tex.z-dn.net/?f=a_1%3D400)
The common ratio is
![r = \frac{200}{400} = \frac{1}{2}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7B200%7D%7B400%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20)
The nth term is
![a_n=a_1( {r}^{n - 1} )](https://tex.z-dn.net/?f=a_n%3Da_1%28%20%7Br%7D%5E%7Bn%20-%201%7D%20%29)
We substitute the known values to get;
![a_n=400( \frac{1}{2} )^{n - 1}](https://tex.z-dn.net/?f=a_n%3D400%28%20%20%5Cfrac%7B1%7D%7B2%7D%20%29%5E%7Bn%20-%201%7D%20)
![a_ {10} =400( \frac{1}{2} )^{10 - 1}](https://tex.z-dn.net/?f=a_%20%7B10%7D%20%3D400%28%20%20%5Cfrac%7B1%7D%7B2%7D%20%29%5E%7B10%20-%201%7D%20)
![a_ {10} =400( \frac{1}{2} )^{9}](https://tex.z-dn.net/?f=a_%20%7B10%7D%20%3D400%28%20%20%5Cfrac%7B1%7D%7B2%7D%20%29%5E%7B9%7D%20)
![a_ {10} = \frac{25}{32}](https://tex.z-dn.net/?f=a_%20%7B10%7D%20%3D%20%5Cfrac%7B25%7D%7B32%7D%20)
What are you confused by?