Gianna and her children went into a movie theater and she bought $77.50 worth of bags of popcorn and pretzels. each bag of popcorn costs $6.50 and each pretzel costs $4.75. she bought a total of 13 bags of popcorn and pretzels altogether. determine the number of bags of popcorn and the number of pretzels that gianna bought.

4 pretzels and 9 popcorn

Step-by-step explanation:

x=popcorn and y=pretzels

x+y=13 solve for x

x=13-y

6.5x+4.75y=77.5 plug 13-y in for x

6.5(13-y)+4.75y=77.5 distribute

84.5-6.5y+4.75=77.5 combine like terms

84.5-1.75y=77.5

-84.5          -84.5

-1.75y=-7 divide both sides by -1.75

*y=4* plug into x+y=13

x+4=13 subtract 4 from each side

*x=9*

∠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.