Answer:
In 4 months the cost of both gyms will be the same.
Step-by-step explanation:
At first we need to model the function to calculate the cost of the 2 gyms.
Slope-intercept equation of linear function
![f(x)=mx+b](https://tex.z-dn.net/?f=f%28x%29%3Dmx%2Bb)
where
slope of line
y-intercept
Let linear function to calculate total cost of gym be:
![c(n)=mn+b](https://tex.z-dn.net/?f=c%28n%29%3Dmn%2Bb)
where
total cost of gym
cost per month (slope)
number of months
start-up fee (y-intercept)
For Gym 1
,
![c(n)=20n+12](https://tex.z-dn.net/?f=c%28n%29%3D20n%2B12)
For Gym 2
,
![c(n)=22n+4](https://tex.z-dn.net/?f=c%28n%29%3D22n%2B4)
In order to find the number of months the cost of both gyms will be the same, we need to equate both functions and solve for number of months ![(n)](https://tex.z-dn.net/?f=%28n%29)
![20n+12=22n+4](https://tex.z-dn.net/?f=20n%2B12%3D22n%2B4)
![\\\textrm{Subtracting 22n from both sides}\\20n-22n+12=22n-22n+4\\-2n+12=4\\\textrm{Subtracting 12 from both sides}\\-2n+12-12=4-12\\-2n=-8\\\textrm{Dividing both sides by -2}\\\frac{-2}{-2}n=\frac{-8}{-2}\\n=4\textrm{ months}](https://tex.z-dn.net/?f=%5C%5C%5Ctextrm%7BSubtracting%2022n%20from%20both%20sides%7D%5C%5C20n-22n%2B12%3D22n-22n%2B4%5C%5C-2n%2B12%3D4%5C%5C%5Ctextrm%7BSubtracting%2012%20from%20both%20sides%7D%5C%5C-2n%2B12-12%3D4-12%5C%5C-2n%3D-8%5C%5C%5Ctextrm%7BDividing%20both%20sides%20by%20-2%7D%5C%5C%5Cfrac%7B-2%7D%7B-2%7Dn%3D%5Cfrac%7B-8%7D%7B-2%7D%5C%5Cn%3D4%5Ctextrm%7B%20months%7D)
So,
In 4 months the cost of both gyms will be the same.
Answer:
Step-by-step explanation:
The correct answer is D. If we are multiplying by 10 we would move the decimal place one place to the right to show that the number is now 10 times bigger. If we multiply by one hundred. We are getting 100 times bigger, so we would move the decimal place 2 places to the right.
The opposite is true if we are dividing. Instead of moving the decimal to the right to show that the number is getting bigger, we move to the left to show that the number is getting smaller. If we are getting smaller by 10, we would move the decimal one place to the left. In this case, we are getting 100 times smaller so we move the decimal two places to the left.
The answer is 100 if you want to get it correct
1. vertex is -4 because:
x^2-8x-20,
a=1, b=-8 , c=-20
use vertex form! -b/2a = -8/2(1) = -8/2 = -4.
2. axis of symmatry is the x which is also -4. The same steps go for the second one.
3. y intercept, I think the answer is -20. Im not sure for this one.
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