Aball is thrown down from a balcony with a vertical velocity (in ft/s) given by v(t)= –32t – 10. chose the inequality that represents the time for which the velocity of the ball will be between –90 and –58 ft/s

Inequalities are used to represent unequal expressions or numbers.

The inequality that represents the time for which the velocity of the ball will be between -90 and -58 ft/s is:

Given

From the numbering system;

-- i.e. -90 is less than -58.

This means that:

Substitute

Hence, the inequality that represents the scenario is:

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∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.