On vacation, Charlie and Gail took turns driving. Together they drove 325 miles. The distance Charlie drove was l15 miles more than the distance Gail drove.

waldo7852p
2022-09-21
Answered

How far did each of them drive IF

On vacation, Charlie and Gail took turns driving. Together they drove 325 miles. The distance Charlie drove was l15 miles more than the distance Gail drove.

On vacation, Charlie and Gail took turns driving. Together they drove 325 miles. The distance Charlie drove was l15 miles more than the distance Gail drove.

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Marley Stone

Answered 2022-09-22
Author has **13** answers

Let x = the distance Gail drove

$x+115$ = the distance Charlie drove

$x+x+115=325$

$2x+115=325$

$2x=210$

$x=105$

Gail drove 105 miles

Charlie drove 105+115=220 miles

$x+115$ = the distance Charlie drove

$x+x+115=325$

$2x+115=325$

$2x=210$

$x=105$

Gail drove 105 miles

Charlie drove 105+115=220 miles

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I am given the following matrix A and I need to find a nullspace of this matrix.

$A=\left(\begin{array}{ccccc}2& 4& 12& -6& 7\\ 0& 0& 2& -3& -4\\ 3& 6& 17& -10& 7\end{array}\right)$

I have found a row reduced form of this matrix, which is:

${A}^{\prime}=\left(\begin{array}{ccccc}1& 2& 0& 0& \frac{23}{10}\\ 0& 0& 1& 0& \frac{13}{10}\\ 0& 0& 0& 1& \frac{22}{10}\end{array}\right)$

And then I used the formula ${A}^{\prime}x=0$, which gave me: A ′ = ( 1 2 0 0 23 10 0 0 1 0 13 10 0 0 0 1 22 10 ) ( x 1 x 2 x 3 x 4 x 5 ) = ( 0 0 0 )

Hence I obtained the following system of linear equations:

$\{\begin{array}{l}{x}_{1}+2{x}_{2}+\frac{23}{10}{x}_{5}=0\\ {x}_{3}+\frac{13}{10}{x}_{5}=0\\ {x}_{4}+\frac{22}{10}{x}_{5}=0\end{array}$

How should I proceed from this point?

Thanks

$A=\left(\begin{array}{ccccc}2& 4& 12& -6& 7\\ 0& 0& 2& -3& -4\\ 3& 6& 17& -10& 7\end{array}\right)$

I have found a row reduced form of this matrix, which is:

${A}^{\prime}=\left(\begin{array}{ccccc}1& 2& 0& 0& \frac{23}{10}\\ 0& 0& 1& 0& \frac{13}{10}\\ 0& 0& 0& 1& \frac{22}{10}\end{array}\right)$

And then I used the formula ${A}^{\prime}x=0$, which gave me:

Hence I obtained the following system of linear equations:

$\{\begin{array}{l}{x}_{1}+2{x}_{2}+\frac{23}{10}{x}_{5}=0\\ {x}_{3}+\frac{13}{10}{x}_{5}=0\\ {x}_{4}+\frac{22}{10}{x}_{5}=0\end{array}$

How should I proceed from this point?

Thanks