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
X, y - the numbers
The sum of the two numbers is 50.
![x+y=50 \\ x=50-y](https://tex.z-dn.net/?f=x%2By%3D50%20%5C%5C%0Ax%3D50-y)
The first number is 43 less than twice the second number.
![x=2y-43 \\ \\ 50-y=2y-43 \\ -y-2y=-43-50 \\ -3y=-93 \\ y=31 \\ \\ x=50-y=50-31=19](https://tex.z-dn.net/?f=x%3D2y-43%20%5C%5C%20%5C%5C%0A50-y%3D2y-43%20%5C%5C%0A-y-2y%3D-43-50%20%5C%5C%0A-3y%3D-93%20%5C%5C%0Ay%3D31%20%5C%5C%20%5C%5C%0Ax%3D50-y%3D50-31%3D19)
The numbers are 19 and 31.
Answer: all my caculations are leading me to B
9514 1404 393
Answer:
21 September
Step-by-step explanation:
Since Alicia is 12 days older, her birthday was 12 days before October 3rd. If we think of October 3rd as equivalent to September 33rd, then 12 days previous is the 33 -12 = 21st day of September.
Alicia's birthday is September 21st.
Answer: 9.7ft
Step-by-step explanation: