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3 years ago

1. A line passes through the point (2, k) and (4k, 5) and has a slope of 1/2 . Find the value of k.

1 answer:

5 0

$(\stackrel{x_1}{2}~,~\stackrel{y_1}{k})\qquad (\stackrel{x_2}{4k}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{k}}}{\underset{run} {\underset{x_2}{4k}-\underset{x_1}{2}}}~~= ~~\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}} \\\\\\ 10-2k=4k-2\implies 10=6x-2\implies 12=6k\implies \cfrac{12}{6}=k\implies 2=k$

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Step-by-step explanation:

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The actual length (L) of a rectangle is 27 centimeters. Use the scale drawing of the rectangle to find the actual width (W).

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The ratio of the length to the width is $\rm \dfrac{L}{W}$ .
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$\rm \dfrac{2.4}{3.6}=\dfrac{27}{W}$

I took the L/W of the scale figure
and set it equal to the L/W of the actual figure.

Now we can solve for the unknown width.
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Hope that helps! :)

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The ratio of red to blue marbles in a bag is 2:5. If there are 65 blue marbles in the bag, how many red marbles are there? Let x

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so the fraction of blue marbles is 5/7

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