Rewrite the equation below so that it does not have fractions.

Mathematics

1 answer:

Leviafan [203]3 years ago

5 0

9514 1404 393

Answer:

8x -24 = 9y

Step-by-step explanation:

We assume your equation is ...

2/3x -2 = 3/4y

Fractions can be eliminated by multiplying the equation by the least common denominator of the fractions.

LCM(3, 4) = 12

Multiplying the equation by 12 gives you ...

12(2/3x -2) = 12(3/4y)

8x -24 = 9y

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A segment with endpoints A (2, 1) and C (4, 7) is partitioned by a point B such that AB and BC form a 3:2 ratio. Find B.

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$\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(2,1)\qquad C(4,7)\qquad \qquad \stackrel{\textit{ratio from A to C}}{3:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{3}{2}\implies \cfrac{A}{C} = \cfrac{3}{2}\implies 2A=3C\implies 2(2,1)=3(4,7)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill$

$\bf B=\left(\cfrac{(2\cdot 2)+(3\cdot 4)}{3+2}\quad ,\quad \cfrac{(2\cdot 1)+(3\cdot 7)}{3+2}\right)\implies B=\left( \cfrac{4+12}{5}~,~\cfrac{2+21}{5} \right) \\\\\\ B=\left(\cfrac{16}{5}~~,~~\cfrac{23}{5} \right)\implies B=\left( 3\frac{1}{5}~~,~~4\frac{3}{5} \right)$