I need help with math

Mathematics

1 answer:

Keith_Richards [23]3 years ago

4 0

$\frac{1}{5} + \frac{3}{4} \times \frac{3}{5} = \\$

$\frac{1}{5} + \frac{9}{20} = \\$

$\frac{4}{20} + \frac{9}{20} = \\$

$\frac{13}{20} \\$

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Lines MN and PQ are parallel. Lines RS and TV intersect them. Which statements are true about these lines? Check all that apply.

Maru [420]

The correct answer is: 
RS is perpendicular to MN and PQ.

Explanation: 
We can use the slopes of these lines to determine the answer.
Slope is given by the formula 
m= $\frac{y_{2}- y_{1} }{ x_{2} - x_{1} }$ .

Using the coordinates for M and N, we have: 
m= $\frac{3--1}{3--3} = \frac{4}{6} = \frac{2}{3}$ .

Since PQ is parallel to MN, its slope will be $\frac{2}{3}$ as well, since parallel lines have the same slope.

Using the coordinates for points T and V in the slope formula, we have 
m= $\frac{-4-1}{0--4} =- \frac{5}{4}$ .

This is not parallel to MN or PQ, since the slopes are not the same.
We can also say that it is not perpendicular to these lines; perpendicular lines have slopes that are negative reciprocals (they are opposite signs and are flipped). This is not true of TV either.

Using the coordinates for R and S in the slope formula, we have 
m= $\frac{-2-1}{2-0} =- \frac{3}{2}$ . Comparing this to the slope of RS, it is flipped and the sign is opposite; they are negative reciprocals, so they are perpendicular.