A. 4(-1)-2y=12
-4-2y=12
-2y=16
y=-8
B. 4(4)-2y=12
16-2y=12
-2y=-4
y=2
Answer:
1) c
2) D
3) H
Step-by-step explanation:
Just follow the graph as shown
Answer:
H. 102.05
Step-by-step explanation:
The circumference is 5pi = 15.7
15.7 * 6.5 = 102.05
Answer:
The car uses less gas
They use the same amount of gas after
miles
Step-by-step explanation:
Given
The table represents the car mileage
--- The van
First, calculate the car's slope (m)
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
From the table, we have:
![(x_1,y_1) = (60,13.5);\ \ (x_2,y_2) = (180,10.5)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%2860%2C13.5%29%3B%5C%20%5C%20%28x_2%2Cy_2%29%20%3D%20%28180%2C10.5%29)
So, we have:
![m = \frac{10.5 - 13.5}{180 - 60}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B10.5%20-%2013.5%7D%7B180%20-%2060%7D)
![m = \frac{-3}{120}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-3%7D%7B120%7D)
![m = -\frac{1}{40}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B1%7D%7B40%7D)
Calculate the equation using:
![y = -\frac{1}{40}(x - 60)+13.5](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B40%7D%28x%20-%2060%29%2B13.5)
![y = -\frac{1}{40}x + 1.5+13.5](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B40%7Dx%20%2B%201.5%2B13.5)
![y = -\frac{1}{40}x + 15](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B40%7Dx%20%2B%2015)
implies that for every mile traveled, the car uses 1/40 gallon of gas
Also:
--- The van
By comparison to: ![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
![m = -\frac{1}{5}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B1%7D%7B5%7D)
This implies that for every mile traveled, the van uses 1/5 gallon of gas.
By comparison:
![1/40 < 1/5](https://tex.z-dn.net/?f=1%2F40%20%3C%201%2F5)
This means that the car uses less gas
Solving (b): Distance traveled for them to use the same amount of gas.
We have:
--- The van
--- The car
Equate both
![-\frac{1}{5}x + 31 =-\frac{1}{40}x + 15](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B5%7Dx%20%2B%2031%20%3D-%5Cfrac%7B1%7D%7B40%7Dx%20%2B%2015)
Collect like terms
![\frac{1}{40}x -\frac{1}{5}x =-31 + 15](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B40%7Dx%20-%5Cfrac%7B1%7D%7B5%7Dx%20%20%3D-31%20%2B%2015)
![\frac{1}{40}x -\frac{1}{5}x =-16](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B40%7Dx%20-%5Cfrac%7B1%7D%7B5%7Dx%20%20%3D-16)
Take LCM
![\frac{x - 8x}{40} = -16](https://tex.z-dn.net/?f=%5Cfrac%7Bx%20-%208x%7D%7B40%7D%20%3D%20-16)
![\frac{- 7x}{40} = -16](https://tex.z-dn.net/?f=%5Cfrac%7B-%207x%7D%7B40%7D%20%3D%20-16)
Solve for -7x
![-7x = -640](https://tex.z-dn.net/?f=-7x%20%3D%20-640)
Solve for x
![x = \frac{640}{7}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B640%7D%7B7%7D)
Answer:
1)5/10 or 1/2 2)5 times out of 10 tries or 1 time out of 2 3) 75
Step-by-step explanation: