$\bf ~~~~~~~~~~~~\textit{internal division of a line segment}
\\\\\\
A(-4,-8)\qquad B(11,7)\qquad
\qquad \stackrel{\textit{ratio from A to B}}{3:7}
\\\\\\
\cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{7}\implies \cfrac{A}{B} = \cfrac{3}{7}\implies 7A=3B\implies 7(-4,-8)=3(11,7)\\\\[-0.35em]
~\dotfill\\\\
C=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em]
~\dotfill$

$\bf C=\left(\cfrac{(7\cdot -4)+(3\cdot 11)}{3+7}\quad ,\quad \cfrac{(7\cdot -8)+(3\cdot 7)}{3+7}\right)
\\\\\\
C=\left( \cfrac{-28+33}{10}~~,~~\cfrac{-56+21}{10} \right)\implies C=\left( \cfrac{5}{10}~~,~~\cfrac{-35}{10} \right)
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
~\hfill C=\left( \frac{1}{2}~,~-\frac{7}{2} \right)~\hfill$

4 0

3 years ago

A rectangular garage is 12 yards long and 8 yards wide. It costs $1.00 per square yard to put in a new concrete floor. How much

Sav [38]

<h3>Answer: 96 dollars</h3>

===========================================================

Explanation:

Compute the area to get 12*8 = 96 square yards

We can think of it like having 96 squares and each square costs $1. So naturally the total cost is 96*1 = 96 dollars.

4 0

3 years ago