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# 1. Use a counter example to disprove this statement X < 3 implies x^2 < 9

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1. Use a counter example to disprove this statement X < 3 implies x^2 < 9

2.prove that n^2 + n + 41 does not take prime values for all positive integers

3. Are any two straight lines that never meet necessarily parallel

Oct 31, 2018

#1
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well I can't answer the other two but I can answer the last one

if two lines are not parallel they will meet at some point because a line goes at both directions at an infinite scale and sooner or later they will meet the only exception is when your dealing with a ray a line that starts at a point and goes on in one direction at an infinite scale

I hope this was helpful

Oct 31, 2018
edited by DarkCalculis  Oct 31, 2018
#2
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The first one is UNtrue because, what if x is less than negative three?

Oct 31, 2018
#3
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First one

Let x  = -4

So  (-4)^2  =  16

So....x^2 > 9

Second one

Let n = 41

So

41^2 + 41 + 41      =  41 ( 41 + 1 + 1)   =   43 *41  so...it is not prime

Last one

In "three-space," we can have two lines that never meet but are not parallel....these are known as "skew" lines   Oct 31, 2018