Question 15 7 pts
During a clothing store's Bargain Days, the regular price for T-shirts is discounted by $6. There is a state sales tax of 5%, and the $6 discount is applied before the
sales tax is calculated. A). Write an expression that shows the regular price r of a T-shirt minus the $6 discount. B). Write a rule for the function p(r) that expresses the
final price p of a T-shirt with the discount applied and sales tax added. C). How much would you pay during Bargain Days for a shirt regularly priced at $20.00?

A) The expression that shows the regular price minus the discount is r - 6

B) The function is p(r) = 1.05r - 6.3

C) You would pay $14.7 during Bargain Days

Step-by-step explanation:

∵ The regular price is r

∵ The discount on it is 6%

∴ The price after the discount = r - 6

A) The expression that shows the regular price minus the discount is

     r - 6

∵ The state sales tax is 5% applied after the discount

∴ The sales tax = 5%(r - 6)

→ Change 5% to decimal y dividing it by 100

∵ 5% = = 0.05

∴ The sales tax = 0.05(r - 6) = 0.05(r) - 0.05(6)

∴ The sales tax = 0.05r - 0.3

∵ p is the price of the T-shirt with discount and sales tax

→ Add the sales tax to the regular price minus the discount

∴ p(r) = r - 6 + 0.05r - 0.3

→ Add the like terms

∴ p(r) = (r + 0.05r) + (-6 - 0.3)

∴ p(r) = 1.05r + (-6.3)

∴ p(r) = 1.05r - 6.3

B) The function is p(r) = 1.05r - 6.3

∵ The regular price of a shirt is $20

→ Substitute r by 20 in the function above to find how much you would

   pay during the Bargain Days

∴ p(20) = 1.05(20) - 6.3

∴ p(20) = 21 - 6.3

∴ p(20) = $14.7

C) You would pay $14.7 during Bargain Days

∠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.