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Nadusha1986 [10]
3 years ago
11

Find the slope of a line perpendicular to y=⅖x+⅘​

Mathematics
2 answers:
Yakvenalex [24]3 years ago
6 0
To find the slope perpendicular we will take our original slope (2/5) and find the reciprocal.
To do this, we will flip the slope (so we get 5/2) and make it negative so we get our final perpendicular slope of -5/2
zloy xaker [14]3 years ago
4 0

Answer:

-2.5

Step-by-step explanation:

The perpendicular slope will be the opposite reciprocal of the original slope.
So the slope of the perpendicular will be:

\frac{-1}{0.4} = -2.5

If we were asked to give the equation of the perpendicular it would be:

-2.5x+ 4/5

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notice, we get the next term by simply adding 4 to the current term, thus "4" is the "common difference, and we know that 10 is the first term.

\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}\\
----------\\
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\end{cases}
\\\\\\
a_{17}=10+(17-1)(4)\implies a_{17}=10+(16)(4)
\\\\\\
a_{17}=10+64\implies a_{17}=74\\\\
-------------------------------

\bf \textit{ sum of a finite arithmetic sequence}
\\\\
S_n=\cfrac{n(a_1+a_n)}{2}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
----------\\
a_1=10\\
a_{17}=74\\
n=17
\end{cases}
\\\\\\
S_{17}=\cfrac{17(10+74)}{2}\implies S_{17}=\cfrac{17(84)}{2}\implies S_{17}=714
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