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nignag [31]
3 years ago
13

Please help me get the right answer?!

Mathematics
2 answers:
il63 [147K]3 years ago
5 0
Hi!

Let's put the value of x into the equation.

f(-2) = 9^{-2}
solve
f(-2) = 0.012345679

Now let's see if this is equal to any of the answers.

1/81 = 0.012345679 c<em>orrect</em>
81 = 0.012345679 <span><em>wrong</em>
</span>1/18 = 0.012345679 <em>wrong</em>
18 = 0.012345679 <em>wrong</em>

The answer is <span>A. 1/81 

Hope this helps! :)
</span>
Aleksandr-060686 [28]3 years ago
4 0
The answer is A, \frac{1}{81}. This is because when plugging in -2 for x, the expression will look like this: 9^{-2}. To make the exponent positive, you have to flip it into a fraction. Then it will be \frac{1}{9^2}. Lastly, you simplify the denominator into 81.
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\bf A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{-3}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of AB}}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{\textit{\underline{negative reciprocal} and slope of the diameter}}{\cfrac{4}{3}}

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\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{5+1}{2}~~,~~\cfrac{1+4}{2} \right)\implies \left(3~~,~~\cfrac{5}{2} \right)

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\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{\frac{5}{2}}) \stackrel{slope}{m}\implies \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\cfrac{5}{2}}=\stackrel{m}{\cfrac{4}{3}}(x-\stackrel{x_1}{3})\implies y-\cfrac{5}{2}=\cfrac{4}{3}x-4 \\\\\\ y=\cfrac{4}{3}x-4+\cfrac{5}{2}\implies y=\cfrac{4}{3}x-\cfrac{3}{2}

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