A candidate received 15,450 more then her opponent who received 79,000. How many votes were cast for each candidate?

94450 for the first candidate

173450 votes in total

Step-by-step explanation:

79000 + 15450= 94450

First candidate: 94450

Second candidate: 79000

94450 + 79000 = 173450 votes in total

are you sure that's how the question reads? If so, then if one candidate received 79,000 and the other received 15,450 more, then the other candidate received 79,000 + 15,450 = 94,450

Step-by-step explanation:

Or is it that one received 15,450 more than the other and the total votes were 79,000? if so, then x + x + 15,450 = 79,000

2x = 79,000 - 15,450

2x = 63,550

x = 63,350 / 2

x = 31,775

so one candidate received 31,775 and the other received 31,775 + 15,450, or 47,225

so 31,775 + 47,225 = the total of 79,000

Hope this helps...

2

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.