You receive a gift certificate for a clothing store and plan to use it to buy T-shirts and sweatshirts. Choose a situation in which you can buy 9 T-shirts and 1 sweatshirt, but you cannot buy 3 T-shirts and 9 sweatshirts. T-shirts cost $5, sweatshirts cost $10, the gift certificate is worth $120, and you want to buy at least 6 shirts total.

T-shirts cost $5, sweatshirts cost $20, the gift certificate is worth $80, and you want to buy at least 6 shirts total.

T-shirts cost $5, sweatshirts cost $10, the gift certificate is worth $120, and you want to buy no more than 10 shirts total.

T-shirts cost $5, sweatshirts cost $20, the gift certificate is worth $80, and you want to buy no more than 12 shirts total.

Write a system of inequalities that represents the situation chosen above. Let x be the number of T-shirts and y be the number of sweatshirts.

f

step-by-step explanation:

f

∠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.