Ethan is saving money in his piggy bank for his upcoming trip to disney world. on the first day, he put in $12 and plans to add seven more dollars each day.
part a: write an explicit formula that can be used to find the amount of money saved on any given day.
part b: how much money will he have on the 18th day?
part c: the disney trip is in 187 days from the day he started saving. how much money will he have on the 187th day?

Part A:

Part B: $131

Part C: $1314

Step-by-step explanation:

Ethan is saving money in his piggy bank for his upcoming trip to Disney World. On the first day, he put in $12 and plans to add seven more dollars each day.

Part A:

On the first day, he puts $12 in the piggy bank.

On the second day, he deposited $7 in it. So, after second day he has (12 + 7) = $19.

On the third day, he deposited $7 more in it. So, after third day he has (19 + 7) = $26.

In this way, the savings in the piggy bank are growing in an arithmetic sequence with first term $12 and a common difference $7.

Therefore, the explicit formula that can be used to find the amount of money saved on any given day is given by  

Part B:

Putting n = 18, we get the money that he will have on the 18th day, is given by dollars.

Part C:  

The Disney trip is in 187 days from the day he started saving. Then he will have after 187 days dollars. (Answer)

312312

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.