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solmaris [256]
1 year ago
11

What is the slope of the line passing through the points (0, 4) and (6, 13)

Mathematics
1 answer:
skelet666 [1.2K]1 year ago
3 0

Answer:

The slope is \frac{3}{2}

Step-by-step explanation:

Hi there!

We are given the points (0, 4) and (6, 13)

We want to find the slope of the line containing these two points

Slope (m) is the steepness of the line. When calculating from two points, you use the equation \frac{y_2-y_1}{x_2-x_1}, where (x_1, y_1) and (x_2, y_2) are points

Although we have what we need to find the slope, let's label the values of the points to avoid confusion and mistakes.

x_1=0\\y_1=4\\x_2=6\\y_2=13

Substitute these values into the equation

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{13-4}{6-0}

Subtract

m=\frac{9}{6}

Simplify

m=\frac{3}{2}

The slope of the line is 3/2

Hope this helps!

See more on calculating slopes from 2 points here: brainly.com/question/26738734

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victus00 [196]

Answer:

B

Step-by-step explanation:

It's a right triangle, so the pythagorean theorem will be used a lot.

First, find the side length on the left.

25^2 = 7^2 + y

y = 24

Now, knowing that 7 - 3 = 4 (the smaller side length), I can use this theorem again to find x.

4^2 + 24^2 = x^2

x = \sqrt{592}

Just need to simplify it a little farther...

592 / 16 = 37, so B must be the answer.

3 0
2 years ago
Solve the equation!3 tan^3θ = tan θ
andreev551 [17]
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3 tan³ t - tan t = 0
tan t ( 3 tan² t - 1 ) = 0
tan t = 0
t 1 = k π ,  k ∈ Z
3 tan ² t - 1 = 0
3 tan ² t = 1
tan ² t = 1/3
tan t = +/- √3/3
t 2 = π / 6 + k π
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8 0
3 years ago
Solve the given system of equations using either Gaussian or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTI
cricket20 [7]

Answer:

The system has infinitely many solutions

\begin{array}{ccc}x_1&=&-x_3\\x_2&=&-x_3\\x_3&=&arbitrary\end{array}

Step-by-step explanation:

Gauss–Jordan elimination is a method of solving a linear system of equations. This is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.

An Augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

There are three elementary matrix row operations:

  1. Switch any two rows
  2. Multiply a row by a nonzero constant
  3. Add one row to another

To solve the following system

\begin{array}{ccccc}x_1&-3x_2&-2x_3&=&0\\-x_1&2x_2&x_3&=&0\\2x_1&+3x_2&+5x_3&=&0\end{array}

Step 1: Transform the augmented matrix to the reduced row echelon form

\left[ \begin{array}{cccc} 1 & -3 & -2 & 0 \\\\ -1 & 2 & 1 & 0 \\\\ 2 & 3 & 5 & 0 \end{array} \right]

This matrix can be transformed by a sequence of elementary row operations

Row Operation 1: add 1 times the 1st row to the 2nd row

Row Operation 2: add -2 times the 1st row to the 3rd row

Row Operation 3: multiply the 2nd row by -1

Row Operation 4: add -9 times the 2nd row to the 3rd row

Row Operation 5: add 3 times the 2nd row to the 1st row

to the matrix

\left[ \begin{array}{cccc} 1 & 0 & 1 & 0 \\\\ 0 & 1 & 1 & 0 \\\\ 0 & 0 & 0 & 0 \end{array} \right]

The reduced row echelon form of the augmented matrix is

\left[ \begin{array}{cccc} 1 & 0 & 1 & 0 \\\\ 0 & 1 & 1 & 0 \\\\ 0 & 0 & 0 & 0 \end{array} \right]

which corresponds to the system

\begin{array}{ccccc}x_1&&-x_3&=&0\\&x_2&+x_3&=&0\\&&0&=&0\end{array}

The system has infinitely many solutions.

\begin{array}{ccc}x_1&=&-x_3\\x_2&=&-x_3\\x_3&=&arbitrary\end{array}

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telo118 [61]

Answer:

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Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees.

So we know that 40+3x+x=180.

First step is to combine the like  terms on the left hand side:

40+4x=180

Second step is to subtract 40 on both sides.

4x=140

Third step is to divide both sides by 4:

x=35

The angle that is given is the one that is 40 degrees.

So the angle whose measurement is x is really 35 degrees.

The angle whose measurement is 3x is real 3(35)=105 degrees.

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