Sara worked 22 hours last week. joan worked 4 hours less than sara, and erin worked half as many hours as joan. how many hours did sara, joan, and erin work last week?

Explanation:

You may set a numerical equation by translating the word statements into arithmetic expressions in this way:

1) Sara worked 22 hours last week: 22

2) Joan worked 4 hours less than Sara: 22 - 4

3) Erin worked half as many hours as Joan: [22 - 4] / 2

4) How many hours did Sara, Joan, and Erin work last week? : add up every arithmetic expression:

5) Simplify doing the operations:

Conclusion:

SO basically Sara worked for 22 hours and Joan worked for 18 hours and Erin worked for only 9 hours. 22 + 18 + 9 = 49 hours in total.

step-by-step explanation:

∠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.