John thunderhawk is making furniture. he finds that to design a particular cabinet and set up his shop to produce it costs $1,400. then the labor and supplies to build each one are $400. so his cost, y, for x items is represented by y=1,400 + 400x. he can sell the cabinets for $600. so his revenue, y, is represented by y=600x. the solution to this system of equations is his break-even point, the point beyond which he starts making a profit. how many cabinets must he sell to break-even?

x=7

Explanation:

1. y=y so 1,400+400x=600x

2. combine like term by subtracting 400x from both sides giving you 1,400=200x

3. isolate the variable by dividing 1,400/200 giving you 7=x, x=7

x = 12

y = 15

step-by-step explanation:

∠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.