12 at a walkathon, each participant completed either a 3-km route, a 5-km route or an 8-km route. - of the participants completed the 3-km route, as of the 20 participants completed the 5-km route and the rest completed the 8-km route. for every 1 km a participant walked, $4 was donated to charity. a total of $8208 was donated to charity. (a) what is the ratio of the number of participants who completed the 3-km route to the number who completed the 5-km route to the number who completed the 8-km route? (b) what is the total number of participants at the walkathon? complete

a) 5:9:6, b) 380

Step-by-step explanation:

Let the number of participant be 'x'.

Let the number of participant of 3-km route be

Let the number of participants of 5-km route be

Let the number of participants of 8-km route be

According to question, we get that

Therefore, the number of participants is 380.

Number of participants of 3 km route

Number of participants of 5 km route  

Number of participants of 8 km route  

Ratio of the number of participants completed 3 km to 5 km to 8 km is given by

95:171:114

=5:9:6

Hence, a) 5:9:6, b) 380

over the argument its not good to fight.

∠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.