2 years ago

Follow the process of completing the square to solve x2 - 10x + 8 = 0.

Mathematics

1 answer:

11111nata11111 [884]2 years ago

4 0

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3 years ago

Number 8 please, What are the coordinates of point C below segment AC that is partitioned at point B in a ratio of 2 to 5.

jonny [76]

$\bf \left. \qquad \right.\textit{internal division of a line segment}
\\\\\\
A(5,0)\qquad C(x,y)\qquad
\qquad 2:5
\\\\\\
\cfrac{AB}{BC} = \cfrac{2}{5}\implies \cfrac{A}{C}=\cfrac{2}{5}\implies 5A=2C\implies 5(5,0)=2(x,y)\\\\
-------------------------------\\\\
{ B=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}$

$\bf -------------------------------\\\\
B=\left(\cfrac{(5\cdot 5)+(2\cdot x)}{2+5}\quad ,\quad \cfrac{(5\cdot 0)+(2\cdot y)}{2+5}\right)=\boxed{(8,0)}
\\\\\\
B=\left( \cfrac{25+2x}{7}~~,~~\cfrac{0+2y}{7} \right)=(8,0)\implies 
\begin{cases}
\cfrac{25+2x}{7}=8\\\\
25+2x=56\\
2x=31\\\\
\boxed{x=\cfrac{31}{2}}\\
-------\\
\cfrac{0+2y}{7}=0\\\\
2y=0\\
\boxed{y=0}
\end{cases}$

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