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3 years ago

What is the length of DE ?

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

4 0

Answer:

A. 6

Step-by-step explanation:

On triangle ZYX divide each side by 3 to get 4-4-3. Then multiple each side by 2, to get 8-8-6. That would mean DE is 6.

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Convert the following systems of equations to an augmented matrix and use Gauss-Jordan reduction to convert to an equilivalent m

Rasek [7]

Answer:

System of equations:

$x_1+2x_2+2x_3=6\\2x_1+x_2+x_3=6\\x_1+x_2+3x_3=6$

Augmented matrix:

$\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right]$

Reduced Row Echelon matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right]$

Step-by-step explanation:

Convert the system into an augmented matrix:

$\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right]$

For notation, R_n is the new nth row and r_n the unchanged one.

1. Operations:

$R_2=-2r_1+r_2\\R_3=-r_1+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&-3&-3&-6\\0&-1&1&0\end{array}\right]$

2. Operations:

$R_2=-\frac{1}{3}r_2$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&-1&1&0\end{array}\right]$

3. Operations:

$R_3=r_2+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&2&2\end{array}\right]$

4. Operations:

$R_3=\frac{1}{2}r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right]$

4 0

3 years ago

Jordan has 28 golf balls. 28 golf balls in 4 rows and 7 columns. Of the 28 golf balls, 17 are yellow. How many golf balls are ye

crimeas [40]

The distribution of the balls is an illustration of proportions, and 4 of the golf balls are yellow

<h3>How to determine the number of yellow golf balls?</h3>

The distribution of the balls are given as:

Total = 28

Yellow = 1/7

The number of yellow balls is given as:

Yellow = 1/7 * Total

This gives

Yellow = 1/7 * 28

Evaluate the product

Yellow = 4

Hence, 4 of the golf balls are yellow

Read more about proportion at:

brainly.com/question/1781657

#SPJ1

7 0

1 year ago

Solve for x. Round to the nearest hundredth

PIT_PIT [208]

Given that the length of one leg is 6 and the angle is 40°

The hypotenuse is x.

We need to determine the value of x.

<u>Value of x:</u>

The value of x can be determined using the trigonometric ratio.

Thus, we have;

$cos \ \theta=\frac{adj}{hyp}$

Substituting the values, we get;

$cos \ 45^{\circ}=\frac{6}{x}$

Simplifying, we have;

$x=\frac{6}{cos \ 45^{\circ}}$

$x=\frac{6}{0.766}$

Dividing, we get;

$x\approx7.83$

Therefore, the value of x is 7.83(app.)

Hence, Option A is the correct answer.

3 0

3 years ago

If the perimeter of a rectangle is 318 inches, find the width and length. what's the answer?

Igoryamba

Is there any other known values?

7 0

3 years ago

Read 2 more answers

What is the standard form equation of the line shown below? Graph of a line going through negative 2, 3 and 1, negative 3

V125BC [204]

Answer:

3. 2x + y = −1

Step-by-step explanation:

To find the equation of the line, we write it first in the slope-intercept form:

$y=mx+q$

where

m is the slope

q is the y-intercept

From the graph, we see that the line crosses the y-axis at y = -1, so the y-intercept is -1:

$q=-1$

Now we have to find the slope, by calculating the rate of change of the line through 2 points:

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

Taking the two points at (-2,3) and (1,-3), we find:

$m=\frac{-3-3}{1-(-2)}=\frac{-6}{3}=-2$

So the equation of the line is

$y=-2x-1$

Now we have to re-arrange it in the standard form, so in the form

$ax+bx=c$

where a, b and c are integer numbers.

To do that, we simply add +2x on both sides of the equation of the line in the slope-intercept form, and we get:

$y+2x=-1$

So, option 3).

6 0

3 years ago