Remark
Perpendicular slopes are found by using the formula m1*m2 = - 1. That is followed by using the given point to determine the y intercept.
Solution
<em><u>Step One</u></em>
Find the slope of the new line
m1 = - 1/3
m2 = ??
m1 * m2 = - 1
(-1/3) * m2 = - 1
You could continue by changing (-1/3) to a decimal.
(-0.3333333333) * m2 = -1 Now divide by the decimal
m2 = - 1/ (-0.3333333333)
m2 = 3 which is what my calculator tells me the answer is.
<u>Step Two</u>
So far what you have is
y = 3x + b
Use the point (-3, -7) to get the y intercept.
-7 = 3(-3) + b
b - 9 = - 7
b = -7 + 9
b = 2
y = 3x + 2 Answer
Graph
The graph shown below is both lines plotted in desmos. The red line is y = 3x + 2 which is perpendicular to the given graph y = (-1/3)x +5 which is in blue.
The green dot is the point (-3 , - 7)
We have been given that Lori runs 3 miles in 30 minutes.
First of all, we will find rate at which Lori runs per minute as:
![\text{Speed}=\frac{\text{Distance}}{\text{Time}}](https://tex.z-dn.net/?f=%5Ctext%7BSpeed%7D%3D%5Cfrac%7B%5Ctext%7BDistance%7D%7D%7B%5Ctext%7BTime%7D%7D)
![\text{Lori's speed}=\frac{\text{3 miles}}{\text{30 min}}](https://tex.z-dn.net/?f=%5Ctext%7BLori%27s%20speed%7D%3D%5Cfrac%7B%5Ctext%7B3%20miles%7D%7D%7B%5Ctext%7B30%20min%7D%7D)
![\text{Lori's speed}=\frac{\text{0.1 miles}}{\text{ min}}](https://tex.z-dn.net/?f=%5Ctext%7BLori%27s%20speed%7D%3D%5Cfrac%7B%5Ctext%7B0.1%20miles%7D%7D%7B%5Ctext%7B%20min%7D%7D)
We know that 1 minute equal 60 minutes. Let us convert speed into miles per hour as:
![\text{Lori's speed}=\frac{\text{0.1 miles}}{\text{ min}}\times \frac{\text{60 min}}{\text{1 hour}}](https://tex.z-dn.net/?f=%5Ctext%7BLori%27s%20speed%7D%3D%5Cfrac%7B%5Ctext%7B0.1%20miles%7D%7D%7B%5Ctext%7B%20min%7D%7D%5Ctimes%20%5Cfrac%7B%5Ctext%7B60%20min%7D%7D%7B%5Ctext%7B1%20hour%7D%7D)
![\text{Lori's speed}=\frac{\text{6 miles}}{\text{hour}}](https://tex.z-dn.net/?f=%5Ctext%7BLori%27s%20speed%7D%3D%5Cfrac%7B%5Ctext%7B6%20miles%7D%7D%7B%5Ctext%7Bhour%7D%7D)
Therefore, Lori runs 6 miles per hour.
We have been given that Alexis runs 2 kilometers in 15 minutes.
We will find rate at which Alexis runs per minute as:
![\text{Alexis's speed}=\frac{\text{2 km}}{\text{15 min}}](https://tex.z-dn.net/?f=%5Ctext%7BAlexis%27s%20speed%7D%3D%5Cfrac%7B%5Ctext%7B2%20km%7D%7D%7B%5Ctext%7B15%20min%7D%7D)
![\text{Alexis's speed}=\frac{\text{2 km}}{\text{15 min}}\times \frac{\text{60 min}}{\text{1 hour}}](https://tex.z-dn.net/?f=%5Ctext%7BAlexis%27s%20speed%7D%3D%5Cfrac%7B%5Ctext%7B2%20km%7D%7D%7B%5Ctext%7B15%20min%7D%7D%5Ctimes%20%5Cfrac%7B%5Ctext%7B60%20min%7D%7D%7B%5Ctext%7B1%20hour%7D%7D)
![\text{Alexis's speed}=\frac{\text{2 km}}{1}\times \frac{4}{\text{1 hour}}](https://tex.z-dn.net/?f=%5Ctext%7BAlexis%27s%20speed%7D%3D%5Cfrac%7B%5Ctext%7B2%20km%7D%7D%7B1%7D%5Ctimes%20%5Cfrac%7B4%7D%7B%5Ctext%7B1%20hour%7D%7D)
![\text{Alexis's speed}=\frac{\text{8 km}}{\text{1 hour}}](https://tex.z-dn.net/?f=%5Ctext%7BAlexis%27s%20speed%7D%3D%5Cfrac%7B%5Ctext%7B8%20km%7D%7D%7B%5Ctext%7B1%20hour%7D%7D)
1 km = 0.621371 miles.
8 km =
miles.
Therefore, Alexis runs 5 miles per hour.
Since Lori' speed is greater than Alexis's, therefore, Lori ran the fastest.
I wasn't sure what properties the assignment was looking for... Let me know if you have any other questions!
Answer:
the answer is true hope it helps
Step-by-step explanation:
The correct answer is A: 24-8x. To solve this all you need to do it distribute the 4 to the 6 and -2x. Once you do that you get your answer of 24-8x. Hope this helped!