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Oksi-84 [34.3K]
3 years ago
8

Determine if the conditional and its converse are true. If they are both true, select which biconditional correctly represents t

hem. If either the conditional or the converse is false, select the counterexample which disproves the statement:
If four points are non-coplanar, then they are non-collinear.
If four points are non-collinear, then they are non-coplanar.
Mathematics
1 answer:
Ugo [173]3 years ago
3 0
The conditional,  <span>If four points are non-coplanar, then they are non-collinear, </span>is true:

This is, coplanarity is a necessary condition to be collinear.

The converse, <span>If four points are non-collinear, then they are non-coplanar, is false.

A counterexample that disproves this statement is the 4 vertices of a paralelogram, of course they are in a same plane and are not collinear.
</span> 


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The table lists how poverty level income cutoffs​ (in dollars) for a family of four have changed over time. Use the midpoint for
frez [133]

The poverty level cutoff in 1987 to the nearest dollar  was $10787.

<h3>How to find a midpoint?</h3>

The midpoint as the point that divides the line segment exactly in half having two equal segments. Therefore, the midpoint presents the same distance between the endpoints for the line segment. The midpoint formula is: \mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right).

For solving this exercise, first you need plot the points in a chart. See the image.

Your question asks to approximate the poverty level cutoff in 1987 to the nearest dollar using the midpoint formula. Note that the year 1987 is between 1980 and 1990, thus you should apply the midpoint formula from data for this year (1987).

\mathrm{Midpoint\:of\:}\left(1980,8429),\:\left(1990,13145):\quad \left(\frac{1990+1980}{2},\:\:\frac{13145+8429}{2}\right)\\\\ \\

\mathrm{Midpoint\:of\:}\left(1980,8429)\:=\left(\frac{1990+1987}{2},\:\frac{13145+3843}{2}\right)\\ \\ =\left(\frac{3977}{2},\:\frac{21574}{2}\right)

\mathrm{Midpoint\:of\:}\left(1980,8429)\:=\=(\frac{3977}{2},10787)

The answer for your question will be the value that you calculated for the y-coordinate. Then, the poverty level cutoff in 1987 to the nearest dollar  was $10787.

Read more about the midpoint segment here:

brainly.com/question/11408596

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2xsquare+12x+19<br> Find the minimum value of f (x)
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Converting to vertex form is one way of doing this
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