1) The slope is 2 and the y-int is 4.
2) the slope is 1/3 and the y-int is 4-.
Answer:
k= 5b-3/
4
Step-by-step explanation:
3−3k+7k=5b
(Combine −3k and 7k to get 4k.)
3+4k=5b
(Subtract 3 from both sides)
4k=5b−3
(Divide both sides by 4.)
k= 5b-3/
4
The average rate of change for this function for the interval from x = 1
to x = 3 will be 8. Therefore option B is correct.
<h3>How to find the average rate of change of something?</h3>
Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:
![\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20rate%7D%20%3D%20%5Cdfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
where when
![x = x_1, y = y_1\\and \\x = x_2, y = y_2](https://tex.z-dn.net/?f=x%20%3D%20x_1%2C%20y%20%3D%20y_1%5C%5Cand%20%5C%5Cx%20%3D%20x_2%2C%20y%20%3D%20y_2)
The average rate of change can be calculated as;
From x=1 to x=3,
y = 2 and y = 18
Therefore, based on the table, when:
![x_1 = 1 y_1 = 2 \\and \\x_2 = 3, y_2 = 18](https://tex.z-dn.net/?f=x_1%20%3D%201%20y_1%20%3D%202%20%5C%5Cand%20%5C%5Cx_2%20%3D%203%2C%20y_2%20%3D%2018)
Then:
![\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20rate%7D%20%3D%20%5Cdfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![\text{Average rate} = \dfrac{18 - 2}{3-1}\\\\\text{Average rate} = \dfrac{16}{2}\\\\\text{Average rate} = 8](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20rate%7D%20%3D%20%5Cdfrac%7B18%20-%202%7D%7B3-1%7D%5C%5C%5C%5C%5Ctext%7BAverage%20rate%7D%20%3D%20%5Cdfrac%7B16%7D%7B2%7D%5C%5C%5C%5C%5Ctext%7BAverage%20rate%7D%20%3D%208)
Therefore option B is correct.
Learn more about average;
brainly.com/question/12424098
#SPJ1
Answer:
10.5 hours.
Step-by-step explanation:
Please consider the complete question.
Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 14 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?
Let t represent time taken by newer pump in hours to drain the pool on its own.
So part of pool drained by newer pump in one hour would be
.
We have been given that it takes the older pump 14 hours to drain the pool by itself, so part of pool drained by older pump in one hour would be
.
Part of pool drained by both pumps working together in one hour would be
.
Now, we will equate the sum of part of pool emptied by both pumps with
and solve for t as:
![\frac{1}{14}+\frac{1}{t}=\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B14%7D%2B%5Cfrac%7B1%7D%7Bt%7D%3D%5Cfrac%7B1%7D%7B6%7D)
![\frac{1}{14}\times 42t+\frac{1}{t}\times 42t=\frac{1}{6}\times 42t](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B14%7D%5Ctimes%2042t%2B%5Cfrac%7B1%7D%7Bt%7D%5Ctimes%2042t%3D%5Cfrac%7B1%7D%7B6%7D%5Ctimes%2042t)
![3t+42=7t](https://tex.z-dn.net/?f=3t%2B42%3D7t)
![7t=3t+42](https://tex.z-dn.net/?f=7t%3D3t%2B42)
![7t-3t=3t-3t+42](https://tex.z-dn.net/?f=7t-3t%3D3t-3t%2B42)
![4t=42](https://tex.z-dn.net/?f=4t%3D42)
![\frac{4t}{4}=\frac{42}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4t%7D%7B4%7D%3D%5Cfrac%7B42%7D%7B4%7D)
![t=10.5](https://tex.z-dn.net/?f=t%3D10.5)
Therefore, it will take 10.5 hours for the newer pump to drain the pool on its own.
Answer:14
Step-by-step explanation: