Answer:
7/10, because the 7 - (0.7) is on the tenths column, and the 10 - (7/10) represents tenths.
Step-by-step explanation:
or -7/10 if that is a negative sign
angle x would end up being equal to 71 degrees.
Constant rates are used to illustrate linear functions.
- The average rate of change is $9.0 per hour
- The function that models the table is:
![\mathbf{f(x) = 9x }](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%209x%20%7D)
- The amount earned in 7.5 hours is $67.5
<u>(a) The average rate of change</u>
This is calculated using:
![\mathbf{Rate = \frac{y_2 -y_1}{x_2 -x_1}}](https://tex.z-dn.net/?f=%5Cmathbf%7BRate%20%3D%20%5Cfrac%7By_2%20-y_1%7D%7Bx_2%20-x_1%7D%7D)
So, we have:
![\mathbf{Rate = \frac{31.5-22.50}{3.5 - 2.5}}](https://tex.z-dn.net/?f=%5Cmathbf%7BRate%20%3D%20%5Cfrac%7B31.5-22.50%7D%7B3.5%20-%202.5%7D%7D)
![\mathbf{Rate = \frac{9}{1.0}}](https://tex.z-dn.net/?f=%5Cmathbf%7BRate%20%3D%20%5Cfrac%7B9%7D%7B1.0%7D%7D)
![\mathbf{Rate = 9.0}](https://tex.z-dn.net/?f=%5Cmathbf%7BRate%20%3D%209.0%7D)
Hence, the average rate of change is $9.0 per hour
<u>(b) A function that models the table of values</u>
Let x represent hours, and y represent the earnings.
So, we have:
![\mathbf{y =m (x - x_1) + y_1}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3Dm%20%28x%20-%20x_1%29%20%2B%20y_1%7D)
Where:
m =Rate = 9.0
So, we have:
![\mathbf{y = 9(x - 2.5) + 22.5}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%209%28x%20-%202.5%29%20%2B%2022.5%7D)
Expand
![\mathbf{y = 9x - 22.5 + 22.5}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%209x%20-%2022.5%20%2B%2022.5%7D)
![\mathbf{y = 9x }](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%209x%20%7D)
Represent as a function
![\mathbf{f(x) = 9x }](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%209x%20%7D)
Hence, the function that models the table is: ![\mathbf{f(x) = 9x }](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%209x%20%7D)
<u>(c) Amount earned for 7.5 hours</u>
This means that x = 7.5
So, we have:
![\mathbf{f(7.5) = 9 \times 7.5 }](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%287.5%29%20%3D%209%20%5Ctimes%207.5%20%7D)
![\mathbf{f(7.5) = 67.5}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%287.5%29%20%3D%2067.5%7D)
Hence, the amount earned in 7.5 hours is $67.5
Read more about constant rates at:
brainly.com/question/23184115
Answer:
.5 of a minute
Step-by-step explanation: