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3 years ago

Fine the slope of the line perpendicular to the line graphed below

Mathematics

1 answer:

goldenfox [79]3 years ago

6 0

Answer:

$-\frac{1}{2}$

Step-by-step explanation:

The slope of this line is 2 because the rise from one point is 2, and the run is 1. The change in y-value is divided by the change in the x-value which is 2/1, hence, the slope of the line being 2.

The slope of the line perpendicular to the one shown below will be $-\frac{1}{2}$ because the slope that will result in a perpendicular line is the negative reciprocal of the original slope.

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Solve the following matrix equations: (matrices)

Masja [62]

Step-by-step explanation:

$3X + \begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix} = \begin{pmatrix} - 1 & 6 \\ 10 & 14 \end{pmatrix} \\ \\ 3X = \begin{pmatrix} - 1 & 6 \\ 10 & 14 \end{pmatrix} - \begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix} \\ \\ 3X = \begin{pmatrix} - 1 - 2 & 6 - 3 \\ 10 - 4 & 14 - 5 \end{pmatrix}\\ \\ 3X = \begin{pmatrix} - 3 & 3 \\ 6 & 9\end{pmatrix}\\ \\ X = \frac{1}{3} \begin{pmatrix} - 3 & 3 \\ 6 & 9\end{pmatrix}\\ \\ X = \begin{pmatrix} \frac{ - 3}{3} & \frac{3}{3} \\ \\ \frac{6}{3} & \frac{9}{3} \end{pmatrix}\\ \\ \huge \red{ X} = \purple{ \begin{pmatrix} - 1 &1 \\ 2 & 3 \end{pmatrix}}$

$3X + 2I_3=\begin{pmatrix} 5 & 0 & -3 \\6 & 5 & 0\\ 9 & 6 & 5\end{pmatrix} \\\\3X + 2\begin{pmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{pmatrix} =\begin{pmatrix} 5 & 0 & - 3\\6 & 5 & 0\\ 9 & 6 & 5 \end{pmatrix} \\\\3X + \begin{pmatrix} 2 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2\end{pmatrix} =\begin{pmatrix} 5 & 0 & - 3\\ 6 & 5 & 0 \\ 9 & 6 & 5 \end{pmatrix} \\\\3X =\begin{pmatrix} 5 & 0 & -3 \\ 6 & 5 & 0 \\ 9 & 6 & 5 \end{pmatrix} - \begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{pmatrix} \\\\3X =\begin{pmatrix} 5-2 & 0-0 & -3-0 \\ 6-0 & 5-2 & 0-0 \\ 9-0 & 6-0 & 5-2 \end{pmatrix} \\\\3X =\begin{pmatrix} 3 & 0 & - 3 \\ 6 & 3 & 0 \\ 9 & 6 & 3 \end{pmatrix} \\\\X =\frac{1}{3} \begin{pmatrix} 3 & 0 & - 3 \\ 6 & 3 & 0 \\ 9 & 6 & 3 \end{pmatrix} \\\\X =\begin{pmatrix} \frac{3}{3} & \frac{0}{3} & \frac{-3}{3} \\\\ \frac{6}{3} & \frac{3}{3} & \frac{0}{3} \\\\ \frac{9}{3} & \frac{6}{3} & \frac{3}{3} \end{pmatrix} \\\\\huge\purple {X} =\orange{\begin{pmatrix} 1 & 0 & - 1\\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{pmatrix}}\\$

8 0

3 years ago

In the school cafeteria there are 20 seats at each table.

Mrac [35]

Answer:

12.5

Step-by-step explanation:

you can solve this by dividing 250/20=12.5

8 0

3 years ago

A rectangular yoga mat has a perimeter of 179 inches. The width of the mat is eight less than half the length. Find the width, i

lianna [129]

Answer:

The width is $24.5in$

Step-by-step explanation:

The perimeter of the rectangular yoga mat can be found using the formula;

$P=2l+2w$ .

$\Rightarrow 179=2l+2w...(1)$ .

It was given that the width of the mat is eight less than half the length.

$w=\frac{1}{2}l-8...(2)$

We put equation (2) into equation (1) to get;

$179=2l+2(\frac{1}{2}l-8)$ .

$\Rightarrow 179=2l+l-16$ .

$\Rightarrow 179+16=2l+l$ .

$\Rightarrow 3l=195$

Divide both sides by 3;

$l=65$

We put $l=65$ into equation 2 to get;

$w=\frac{1}{2}\times65-8$

$w=32.5-8$

$w=24.5in$

4 0

3 years ago

I need answers kind of struggling

SIZIF [17.4K]

Answer:

Step-by-step explanation:

1/200*90=9/20

multiply by 100 because you need to convert to cm and you get 45

5 0

2 years ago

To visit his grandmother, Luis takes a train 6.376.376, point, 37 kilometers and a car 5.455.455, point, 45 kilometers.

murzikaleks [220]

Answer:

Luis traveled 11.82 km in total.

Step-by-step explanation:

<em>The statement should say</em>: To visit his grandmother, Luis takes a train 6.37 kilometers and a car 5.45 kilometers. How many kilometers is Luis's journey in total?

Hence, to find the total distance traveled by Luis we must add the distances of the train (6.37 km) and the car (5.45 km):

$d = d_{t} + d_{c} = 6.37 km + 5.45 km = 11.82 km$

Therefore, Luis traveled 11.82 km in total.

I hope it helps you!

8 0

2 years ago