At a restaurant you only have $20 to spend on dinner. In addition to the cost of the meal you must pay a 5% sales tax andleave a 15% tip. What is the most expensive item you can order?

$16.67

Step-by-step explanation:

alright so to do this you need some basic algebra

you have to pay an extra 20% of whatever you buy

thus we can make the following equation

.2x+x=20  (since 20 is the amount of money you have)

combining the like terms,

1.2x=20

and finally, dividing both sides by 1.2

x=$16.67

don't forget to check!

.05*16.67=.83 (sales tax makes the total $17.5)

.15*16.67=2.5 (tip makes the total $20)

whaddya you know, it works!

most expensive item you can buy will cost $16.67

∠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.

step-by-step explanation: