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3 years ago

Given that m∠ABD = 84° and m∠BAC = 37°, what is the m∠ACD?

Mathematics

1 answer:

stich3 [128]3 years ago

7 0

Answer: 84°

Step-by-step explanation:

Pardon my drawing, I know it;s not prefect, and I'm not sure how to draw a figure on Brainly, but this is the best I can do. For this problem, it is easier to draw it out so you can see that the angles look like. Just pretend the lines are filled in, and this is a perfect parallelogram.

A ________________ C

/ /

B /_______________/ D

As you can see, the angles given in the problem gives us a parallelogram. Since we know m∠ABD is 84° and m∠BAC is 37°, we know that m∠ACD is 84°. If you draw diagonal lines, ∠ABD and ∠ACD are vertical angles. Vertical angles are congruent. Therefore, m∠ACD is 84°.

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3 years ago

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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3 years ago

Read 2 more answers