The height of the barrel is 6 feet.
The thirty-second term is 143
Further explanation:
As it is already given that the given sequence is an arithmetic sequence
We have to find the common difference first
So,
![a_1=-12\\a_2=-7\\a_3=-2\\a_4=3](https://tex.z-dn.net/?f=a_1%3D-12%5C%5Ca_2%3D-7%5C%5Ca_3%3D-2%5C%5Ca_4%3D3)
![d=a_2-a_1=-7-(-12)=-7+12=5\\a_3-a_2=-2-(-7)=-2+7=5](https://tex.z-dn.net/?f=d%3Da_2-a_1%3D-7-%28-12%29%3D-7%2B12%3D5%5C%5Ca_3-a_2%3D-2-%28-7%29%3D-2%2B7%3D5)
The common difference is 5.
And first term is -12
The explicit formula for arithmetic sequence is:
![a_n=a_1+(n-1)d\\Here,\\a_n\ is\ nth\ term\\a_1\ is\ first\ term\\d\ is\ common\ difference](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d%5C%5CHere%2C%5C%5Ca_n%5C%20is%5C%20nth%5C%20term%5C%5Ca_1%5C%20is%5C%20first%5C%20term%5C%5Cd%5C%20is%5C%20common%5C%20difference)
Putting the values in the formula
![a_n=-12+(n-1)(5)\\a_n=-12+5n-5\\a_n=-17+5n](https://tex.z-dn.net/?f=a_n%3D-12%2B%28n-1%29%285%29%5C%5Ca_n%3D-12%2B5n-5%5C%5Ca_n%3D-17%2B5n)
Putting n=32 in explicit formula
![a_{32}=-17+5(32)\\=-17+160\\=143](https://tex.z-dn.net/?f=a_%7B32%7D%3D-17%2B5%2832%29%5C%5C%3D-17%2B160%5C%5C%3D143)
The thirty-second term is 143
Keywords: Common difference, Arithmetic Sequence
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Answer:
D.) SSS
Step-by-step explanation:
Considering the proof tells us that many sides seem congruent to each other, I am led to believe these triangles are congruent due to SSS.
Answer:
Step-by-step explanation:
the first one
Answer:
2 units
Step-by-step explanation:
Since EFG and XYZ are congruent, we can write it like this:
E = X
F = Y
G = Z
Due to E and F being two units apart on the coordinate plane, we can conclude X and Y are also at a measurement of 2 units! Hope this helps!