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)
Answer:
Rule: Output = 2 * input + 1
Right blank: Output = - 1
Left blank: Input = 4
Step-by-step explanation:
Rule
Start with the rule
Output = 2 * input + 1
Let the output = y
Let the input = x
y = 2x + 1
Now
Right Blank
x = - 1
y = 2*-1 + 1
y = -2 + 1
y = - 1
That's the output for -2
Left Blank
The second blank asks you to solve for the input (x) The output (y) is 9
9 = 2x + 1 Subtract 1 from both sides
9-1 = 2x Combine
8 = 2x Divide by 2
8/2 = 2x/2
x = 4
Slope is 2 because it goes up by two and over by one
Answer:
C
Step-by-step explanation:
(2x+3)(x+4) = 2x² + 8x + 3x + 12
= 2x² + 11x + 12 ≠ 2x² + 10x + 12
-6.5(n-5)=18.2
Use Distributive Property:
-6.5n + 32.5 = 18.2
Subtract 32.5 from both sides:
-6.5n = -14.3
Divide both sides by -6.5
n = -14.3 / -6.5
n = 2.2