Please help with this math question (photo)

Complete the missing parts of the paragraph proof.

Vika [28.1K]

Answers:

1) Given

2) angle 2 ** see note below

3) angle 3 ** see note below

4) converse of alternate exterior angle theorem

note: you can swap the answers for 2 and 3 and it doesn't matter

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Explanations:

1) This is given so we just simply state "given". It seems silly to repeat what is given, but this is how you start any geometry proof.

2 & 3) The answers here are angle 2 and angle 3 because they are both interior angles (on the inside of the parallel lines m and L) and they are on alternate sides of the transversal line q. So they are both alternate interior angles and are congruent due to line L parallel to line m (alternate interior angle theorem)

4) If you have a pair of parallel lines, then the alternate exterior angle theorem says that alternate exterior angles are congruent. Going in reverse, the converse of this theorem says that having a pair of congruent alternate exterior angles (angle 1, angle 2) leads to the lines being parallel (p and q).

5 0

3 years ago

Construct an augmented matrix for this linear system: x − y − 4z = 5 2x 2z = 0 4x y z = 3.

Crazy boy [7]

The augmented matrix is,

$\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)$

We have given system of linear equation is,

$x - y - 4z = 5,2x + 2z = 0 ,4x +y +z = 3.$

<h3>What is the meaning of augmented matrix?</h3>

In an augmented matrix, each row represents one equation in the system and each column represents coefficients (with signs) of variables or the constant terms.

So, the first row is

$1\ -1\ -4\ 5$