Part A: Sydney made $18.50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0.50 and received a $3 tip from a neighbor. Write an equation to represent this situation. (4 points) Part B: Daria made a profit of $21.00 selling lemonade. She sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbor, but also had to buy each plastic cup she used for $0.10 per cup. Write an equation to represent this situation. (4 points) Part C: Explain how the equations from Part A and Part B differ. (2 points)

see below

Step-by-step explanation:

Part A:

18.50 = .50c +3  where c is the number of cups

Part B

Profit = income - expenses

21 = .75c +3 - .10c

21 = .65c+3

Part C

Daria in part B makes more per cup ( the slope) as she makes .65 per cup and Sydney only make .50 per cup.  They both get the same amount in tip, but Daria will get more money overall ( 21 dollars versus 18.50)

∠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.

believe it or not anna is correct good job anna give me a fist bump there u go gal