Answer:C
Step-by-step explanation:
The common difference is 19-7 = 31-19 = 12, so this is an arithmetic sequence. The initial term (when n=1) is 7.
The explicit formula for the terms of an arithmetic sequence is
an = a1 + d(n-1)
where "a1" is the first term and "d" is the common difference. The formula that matches a1=7 and d=12 is
B. a(n) = 7+(n-1)·12
A translation is a transformation in which every point moves the same distance in the same direction
Answer:
Time taken by Franklin to shovel alone is 65.5 minutes.
Step-by-step explanation:
Let the time taken by Franklin to shovel alone = x minutes.
Since, the time taken by Angela to shovel = 180 minutes and the time taken by both = 48 minutes.
Then, we have,
Amount of shoveling done in 1 minute by Angela = ![\frac{1}{180}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B180%7D)
Amount of shoveling done in 1 minute by both = ![\frac{1}{48}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B48%7D)
Amount of shoveling done in 1 minute by Franklin= ![\frac{1}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D)
So, we have,
![\frac{1}{180}+\frac{1}{x}=\frac{1}{48}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B180%7D%2B%5Cfrac%7B1%7D%7Bx%7D%3D%5Cfrac%7B1%7D%7B48%7D)
i.e. ![\frac{x+180}{180x}=\frac{1}{48}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B180%7D%7B180x%7D%3D%5Cfrac%7B1%7D%7B48%7D)
i.e. ![48(x+180)=180x](https://tex.z-dn.net/?f=48%28x%2B180%29%3D180x)
i.e. ![48x+8640=180x](https://tex.z-dn.net/?f=48x%2B8640%3D180x)
i.e. ![132x=8640](https://tex.z-dn.net/?f=132x%3D8640)
i.e. x= 65.5 minutes
Thus, the time taken by Franklin to shovel alone is 65.5 minutes.