8. Identify which equation is a graph of a vertical line.

Mathematics

1 answer:

Y_Kistochka [10]2 years ago

4 0

Answer:

10x = 10.

Step-by-step explanation:

The equation will contain the x variable only.

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What is the sum of a 12-term arithmetic sequence where the last term is 13 and the common difference is -10?

Y_Kistochka [10]

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=12\\
d=-10\\
a_{12}=13
\end{cases}
\\\\\\
a_{12}=a_1+(12-1)d\implies 13=a_1+(12-1)(-10)
\\\\\\
13=a_1-110\implies \boxed{123=a_1}$

$\bf \\\\
-------------------------------\\\\
\textit{sum of a finite arithmetic sequence}\\\\
S_n=\cfrac{n}{2}(a_1+a_n)\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
a_n=\textit{value of the }n^{th}\ term\\
------------\\
n=12\\
a_1=123\\
a_{12}=13
\end{cases}
\\\\\\
S_{12}=\cfrac{12}{2}(a_1+a_{12})\implies S_{12}=\cfrac{12}{2}(123+13)$

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