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4 years ago

15

Rachel can make 3 bracelets in an hour. Oliver can make only 2 bracelets in an hour, but he already has 5 completed bracelets. E

xplain to Rachel how she can use a system of equations to determine when she will have the same number of bracelets as Oliver. Use complete sentences.

2 answers:

bagirrra123 [75]4 years ago

6 0

Answer:

X=5

Step-by-step explanation:

the Hours will be said as X. So after X amount of hours rachel will have 3x bracelets. Oliver will have 5+2x bracelets. once they have the same number of bracelets the equation will be 3x=5+2x. X=5

Lyrx [107]4 years ago

4 0

If you use the equation for Rachel it would be
y=3x and for oliver it would be y=2x+5

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What is the equation of a line that is perpendicular to −x+3y=9 and passes through the point (−3, 2) ?

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The equation of line that is perpendicular to the line $-x+3y =9$ and passes through the point $\left({-3,2}\right)$ is $\boxed{{\mathbf{y=-3x-7}}}$ .

Further explanation:

It is given that the equation of line is $-x+3y =9$ and passes through point $\left({-3,2}\right)$ .

Rewrite the given equation $-x+3y =9$ as follows:

$\begin{aligned}-x+3y&=9\\3y&=9+x\\y&=\frac{9}{3}+\frac{1}{3}x\\y&=\frac{1}{3}x+3\\\end{aligned}$

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Therefore, the slope is $\frac{1}{3}$ .

It is given that both lines are perpendicular to each other so the product of slope must be equal to $-1$ .

${m_1}\cdot {m_2}=-1$ …… (1)

Substitute $\frac{1}{3}$ for ${m_1}$ in equation (1) to obtain the value of slope ${m_2}$ .

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Therefore, the slope is $-3$ .

It is given that the line passes through point $\left({-3,2}\right)$ .

The point-slope form of the equation of a line with slope $m$ passes through point $\left({{x_1},{y_1}}\right)$ is represented as follows:

$y-{y_1}=m\left({x-{x_1}}\right)$ …… (2)

Substitute $-3$ for ${x_1}$ , $2$ for ${y_1}$ and $-3$ for $m$ in equation (2) to obtain the equation of line.

$\begin{aligned}y-2&=-3\left({x-\left({-3}\right)}\right)\\y-2&=-3\left({x+3}\right)\\y&=-3x-9+2\\y&=-3x-7\\\end{aligned}$

Therefore, the equation of line is $y=-3x-7$ .

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, equation of line, line, passes through point.

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Step-by-step explanation:

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