Answer: $5000 - $250x = y (Benjamin)
$2000 + $100x = y (Corrado)
Step-by-step explanation: Benjamin is spending $250 per month. So if number of given months is x his total spending in x number of months will be $250x. Whereas his initial amount in bank was $5000 and he is withdrawing $250 each month. So the remaining amount y spent on car expenses can be calculated with the equation as follows:
$5000 - $250x = y
Benjamin's friend Corrado is depositing $100 per month. So if number of given months is x his total deposits in x number of months will be $100x. Whereas his initial amount in bank was $2000 and he is depositing $100 each month which will add in initial amount to find y the current amount of money in bank. So the total amount y saved for college fund, can be calculated with the equation as follows:
$5000 - $250x = y
Answer:
She spends:
2980.83 hours reading in a year,
3406.67 hours listening to music in a year,
and 3650 hours listening to podcasts in a year.
Step-by-step explanation:
Let's multiply each activity she does by 14 and take it to a year:
-Reading
![R = 14*35 \frac{min}{d} = 490 \frac{min}{d}*\frac{365 d}{1 y}*\frac{1 h}{60 min} = 2980.83 \frac{h}{y}](https://tex.z-dn.net/?f=%20R%20%3D%2014%2A35%20%5Cfrac%7Bmin%7D%7Bd%7D%20%3D%20490%20%5Cfrac%7Bmin%7D%7Bd%7D%2A%5Cfrac%7B365%20d%7D%7B1%20y%7D%2A%5Cfrac%7B1%20h%7D%7B60%20min%7D%20%3D%202980.83%20%5Cfrac%7Bh%7D%7By%7D%20)
She spends 2980.83 hours reading in a year.
-Listenign to music:
She spends 3406.67 hours listening to music in a year.
-Listenign to podcasts:
She spends 3650 hours listening to podcasts in a year.
I hope it helps you!
Neato
assuming you mean
![g(x)=-1(x-2)^2-3](https://tex.z-dn.net/?f=g%28x%29%3D-1%28x-2%29%5E2-3)
remember
in form
![f(x)=a(x-h)^2+k](https://tex.z-dn.net/?f=f%28x%29%3Da%28x-h%29%5E2%2Bk)
a is leading coficient
(h,k) is vertex
k will be the minimum or max value of the function
if a is positive, then the parabola opens up and k is minimum
if a is negative, then the parabola opens down and k is max
given
a is negative
the parabola opens down and k is the max value
it is -3
the max value is -3, which occors at x=2
g(2)=-3 is max
g(2x) is ![g(2x)=12x^2-6](https://tex.z-dn.net/?f=g%282x%29%3D12x%5E2-6)
Step-by-step explanation:
We are given ![g(x)=3x^2-6](https://tex.z-dn.net/?f=g%28x%29%3D3x%5E2-6)
We need to find g(2x)
Solving:
![g(x)=3x^2-6\\g(2x)=3(2x)^2-6\\g(2x)=3(4x^2)-6\\g(2x)=12x^2-6](https://tex.z-dn.net/?f=g%28x%29%3D3x%5E2-6%5C%5Cg%282x%29%3D3%282x%29%5E2-6%5C%5Cg%282x%29%3D3%284x%5E2%29-6%5C%5Cg%282x%29%3D12x%5E2-6)
So, g(2x) is ![g(2x)=12x^2-6](https://tex.z-dn.net/?f=g%282x%29%3D12x%5E2-6)
Keywords: Composite Functions
Learn more about Composite Functions at:
#learnwithBrainly