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Answer:
Step-by-step explanation:
I've seen this before... I'm assuming your questions are the following:
A) How many gallons are there in the tub after 5 minutes?
To answer this, you need to know how many additional gallons of water there will be after 5 minutes. So if for every minute, a 1/2 gallon is added, then after 5 minutes, there will be how many gallons added?
Then, add the amount of gallons that were initially in the tub in order to get the total amount of water after 5 minutes.
You should get 8 1/2 gallons.
B) Write an equation using y as gallons and x as minutes.
For this problem, it is useful to utilize the equation of a line:
y=mx + b
Where m is the rate of change (slope), and b is where the water level is at when time begins "begins" (y-intercept).
We know the water level increases by 1/2 gallon every minute. So that is our m value. We also know that the tube starts at 6 gallons, so that is our b value. Therefore, we get:
Y = (1/2)x +6
C) Using part b, find how many minutes have passed for there to be exactly 23 3/4 gallons.
For this, we use our equation and solve for the number of minutes (x). This means we want to isolate x out get it all by itself. First, we subtract 6 from both sides:
y-6 = (1/2)x
Then, we need to get rid of the 1/2. So we multiply both sides by 2:
2(y-6) = x
Now, we plug in 23 3/4 for y and solve.
2(23 3/4 - 6) = x
2(17 3/4) = x
35 1/2 = x
So after 35 1/2 minutes, there will be 23 3/4 gallons in the tub.
Does that helpI've seen this before... I'm assuming your questions are the following:
A) How many gallons are there in the tub after 5 minutes?
To answer this, you need to know how many additional gallons of water there will be after 5 minutes. So if for every minute, a 1/2 gallon is added, then after 5 minutes, there will be how many gallons added?
Then, add the amount of gallons that were initially in the tub in order to get the total amount of water after 5 minutes.
You should get 8 1/2 gallons.
B) Write an equation using y as gallons and x as minutes.
For this problem, it is useful to utilize the equation of a line:
y=mx + b
Where m is the rate of change (slope), and b is where the water level is at when time begins "begins" (y-intercept).
We know the water level increases by 1/2 gallon every minute. So that is our m value. We also know that the tube starts at 6 gallons, so that is our b value. Therefore, we get:
Y = (1/2)x +6
C) Using part b, find how many minutes have passed for there to be exactly 23 3/4 gallons.
For this, we use our equation and solve for the number of minutes (x). This means we want to isolate x out get it all by itself. First, we subtract 6 from both sides:
y-6 = (1/2)x
Then, we need to get rid of the 1/2. So we multiply both sides by 2:
2(y-6) = x
Now, we plug in 23 3/4 for y and solve.
2(23 3/4 - 6) = x
2(17 3/4) = x
35 1/2 = x
So after 35 1/2 minutes, there will be 23 3/4 gallons in the tub.
Does that help
The equation that relates the number of gallons g to t minutes is [tex]\rm y = 2.2x[/tex].
Given that
Max puts a stopper in the bathtub and turns on the faucet at time t =0.
After 5 minutes there are 11 gallons of water in the tub and after 10 minutes there are 22 gallons in the tub.
We have to determine
Write an equation that relates the number of gallons g to t minutes.
According to the question
Let y is the change in the quantity of water in gallons.
And x is the change in the time in minutes.
Max puts a stopper in the bathtub and turns on the faucet at time t =0.
After 5 minutes there are 11 gallons of water in the tub and after 10 minutes there are 22 gallons in the tub.
The standard form linear function is;
[tex]\rm y = mx+c[/tex]
Where c = intercept, m = Slope, y, and x are dependent and independent variables.
Then,
[tex]\rm Slope = \dfrac{Change\ in \ y}{Chnage \ in \ x}\\ \\ Slope = \dfrac{22-11}{10-5}\\ \\ Slope = \dfrac{11}{5}\\ \\ Slope = 2.2[/tex]
Therefore,
The equation that relates the number of gallons g to t minutes is;
[tex]\rm y = mx+c\\\\ y = 2.2x + 0\\\\ y = 2.2x[/tex]
Hence, The equation that relates the number of gallons g to t minutes is [tex]\rm y = 2.2x[/tex].
To know more about the Linear function click the link given below.
https://brainly.com/question/1231262
