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taurus
1 day ago
15

Mrs. Smythe is twice as old as her daughter Samantha. Ten years ago the sum of their ages was 46 years. How old is Mrs. Smythe?

Mathematics
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What is the midpoint of a line segment with the endpoints (-6, -3) and (9, -7)?
PIT_PIT [12445]
The midpoint of the line segment with endpoints (-6, -3) and (9, -7) is (1.5,-5).
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2 months ago
You can upgrade lighting at your factory to LED bulbs that cost $6.95 each and last an average of 5 years. It costs $3 in labor
Inessa [12570]
Each LED bulb, along with installation labor, is priced at
.. $6.95 +$3 = $9.95

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3 0
2 months ago
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What is a3 in an arithmetic sequence in which a10=41 and a15=61
zzz [12365]
\bf \begin{array}{llll}
term&value\\
-----&-----\\
a_{10}&41\\
a_{11}&41+d\\
a_{12}&(41+d)+d\\
&41+2d\\
a_{13}&(41+2d)+d\\
&41+3d\\
a_{14}&(41+3d)+d\\
&41+4d\\
a_{15}&(41+4d)+d\\
&41+5d=61
\end{array}
\\\\\\
41+5d=61\implies 5d=20\implies d=\cfrac{20}{5}\implies \boxed{d=4}\\\\
-------------------------------\\\\

\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}\\
----------\\
d=4\\
n=10\\
a_{10}=41
\end{cases}
\\\\\\
41=a_1+(10-1)4\implies 41=a_1+36\implies \boxed{5=a_1}

therefore

\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}\\
----------\\
d=4\\
n=3\\
a_{1}=5
\end{cases}
\\\\\\
a_3=a_1+(3-1)4\implies a_3=5+(3-1)4

and you are probably aware of the amount.
8 0
1 month ago
Read 2 more answers
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