$\textit{internal division of a line segment using ratios} \\\\\\ A(1,-5)\qquad B(10,1)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:5} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{5}\implies \cfrac{A}{B} = \cfrac{1}{5}\implies 5A=1B\implies 5(1,-5)=1(10,1)$

$(\stackrel{x}{5}~~,~~ \stackrel{y}{-25})=(\stackrel{x}{10}~~,~~ \stackrel{y}{1})\implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{5+10}}{1+5}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-25+1}}{1+5} \right)} \\\\\\ C=\left( \cfrac{15}{6}~~,~~\cfrac{-24}{6} \right)\implies C=\left(\cfrac{5}{2}~~,~~-4 \right)$

5 0

2 years ago

Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 centimeters longer than twice the

aksik [14]

<span>there are 100 centimeters in a meter.

therefore 2.5 meters = 2.5 * 100 = 250 centimeters.

x = the length of the first board.
2x + 18 = the length of the second board.
x - 12 = the length of the third board.
x + 4 = the length of the fourth board.

the total length of all the boards is equal to 5x + 10,

since the total length of the board is 250 centimeters, then you get:

5x + 10 = 250

</span><span>solve for x to get x = 48 centimeters.

the 4 board lengths are:

x = 48
2x + 18 = 114
x - 12 = 36
x + 4 = 52

add them up and you get a total of 250 centimeters.

250 centimeters / 100 = 2.5 meters.

this confirms the solution is good.
</span>

3 0

3 years ago