What is the equation of the line that passes through the point (-6,4) and has a slope of -5/6

Mathematics

1 answer:

irakobra [83]3 years ago

7 0

Answer: y = -5/6 x - 1

Step-by-step explanation:

The slope is -5/6, which is why x = -5/6. The - 1 is so the line on the graph will pass through (0,-1) and (-6,4).

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Use the formula to evaluate the series -3+6-12+24-...-a7

vichka [17]

-3+6-12+24 <---- notice the terms firstly, they go as

-3 , +6 , -12 , +24 ,.... <---- to get the next term's value, you multiply it by -2

thus, is a geometric sequence, and -2 is the "common difference", and the first term is -3 of course.

so... what's the sum of the first 7 terms?

 $\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=-3\\
r=-2\\
n=7
\end{cases}$

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S_7=-3\left( \cfrac{1-(-2)^7}{1-(-2)} \right)
\\\\\\
S_7=-3\left( \cfrac{1-(-128)}{1+2}\right)\implies S_7=-3\left( \cfrac{129}{3} \right)\implies S_7=-3(43)
\\\\\\
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8 0

4 years ago

Find the value of x. x√5=x^4

Kaylis [27]

Answer:

x=0, $\sqrt[6]{5}$