emmachiles1006
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Steven conjectures that for |x|>5, it is true that x^3>125. Is his conjecture correct? Why or why not?
PLEASE HELP, IM TAKING A TEST AND THIS THE LAST QUESTION!

Sagot :

MrRoyal

Conjectures are conclusions formed from evidences.

Steven's conjecture that: [tex]x^3 > 125[/tex] is true because: [tex]x > 5[/tex] or [tex]x > -5[/tex] for [tex]|x| > 5[/tex]

The parameter is given as:

[tex]|x| > 5[/tex]

Split the inequality as follows:

[tex]x > 5[/tex] or [tex]x > -5[/tex]

Take the cube of both sides

[tex]x^3 > 5^3[/tex] or [tex]x^3 > -5^3[/tex]

Evaluate all exponents

[tex]x^3 > 125[/tex] or [tex]x^3 > -125[/tex]

[tex]x^3 > 125[/tex] implies that Steven's conjecture is correct.

So:

Steven's conjecture that: [tex]x^3 > 125[/tex] is true because:

[tex]x > 5[/tex] or [tex]x > -5[/tex] for [tex]|x| > 5[/tex]

Read more about absolute inequalities at:

https://brainly.com/question/4688732

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