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3 years ago

Triangle ABC is dilated by a scale factor of 1.5 to form Triangle DEF. Are Triangles ABC and DEF congruent? Why or why not?

Mathematics

1 answer:

Triss [41]3 years ago

6 0

Answer:

Yes, they will be.

Step-by-step explanation:

Congruent means when they are the same shape and same size.

If triangle ABC is dilated to <u><em>form</em></u> triangle DEF, that means that they will have the same shape and the same size.

So yes Triangles ABC and DEF will be congruent to one another because they will be the same shape, and they will have the same size as well.

Hope this helped!

Have a supercalifragilisticexpialidocious day!

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Find the augmented matrix for each of the following systems of linear equations. (a) x₂ - 2x2 = 0 (6) x + x₃ = 1 .3x₂ + 4x2 = -1

Y_Kistochka [10]

Answer:

The augmented matrix for each set of linear equations is:

a) $x_1-2x_2=0\\3x_1+4x_2=-1\\2x_1-x_2=3$

Augmented matrix:

$\left[\begin{array}{ccc}1&-2&0\\3&4&-1\\2&-1&3\end{array}\right]$

b) $x_1+x_3=1\\-x_1+2x_2-x_3=3$

Augmented matrix:

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

c) $x_1+x_3=1\\2x_2-x_3+x_5=2\\2x_3+x_4=3$

Augmented matrix:

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

d) $x_1=1\\x_2=2$

Augmented matrix:

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

Step-by-step explanation:

In order to find the augmented matrix, you have to take the numeric values of each variable and make a matrix with them. For example, in the linear system a) you can make a matrix out of the numeric values accompanying x_1 and x_2, this matrix will be:

$\left[\begin{array}{cc}1&-2\\3&4\\2&-1\end{array}\right]$

Then you have to make a vector with the constants in the linear equations, for the case of system a) the vector will be:

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

To construct the augmented matrix, you append those matrices together and create a new one:

$\left[\begin{array}{ccc}1&-2&0\\3&4&-1\\2&-1&3\end{array}\right]$

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How many 4-character passwords can you generate if the first character can be any letter of the English alphabet, the next two c

Anarel [89]

There are 7,800 different passwords.

<h3>How many different passwords can be generated?</h3>

Here we need to count the number of options for each of the digits of the password.

The first character has 26 options (26 letters in the alphabet).

The second character has 10 options (ditis from 0 to 9), and also does the third character

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The total number of different passwords that can be generated is given by the product between the numbers of options, so we have:

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There are 7,800 different passwords.

If you want to learn more about combinations:

brainly.com/question/11732255

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