Amerchant has coffee worth $20 a pound that she wishes to mix with 30 pounds of coffee with $60 a pound to get a mixture that is worth $30 a pound. how many pounds of the $20 coffee should be used?

  90 pounds

Step-by-step explanation:

Let x represent the number of pounds of $20 coffee in the mix. Then the cost of the mix is ...

  20x + 60·30 = 30(30+x)

  20x + 1800 = 900 +30x . . . . . eliminate parentheses

  900 = 10x . . . . . . . . . . . . . . . . . subtract 900+20x

  90 = x . . . . . . . . . . . . . . . . . . . . divide by 10

90 pounds of $20 coffee should be used.

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.

∠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.