Mathematics, 04.02.2020 09:52 mmoore36

The sum of two numbers is 17, and their difference is 29. what are the two numbers?

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X + y = 17
x - y = 29

x = 17 - y
x - y = 29

x = 17 - y
17 - y - y = 29

x = 17 - y
17 - 2y = 29

x = 17 - y
- 2y = 29 - 17

x = 17 - y
-2y = 12

x = 17 - y
y = -6

x = 17 - (-6)
y = -6

x = 17 + 6
y = -6

x = 23
y = -6

Answer from: samreitz1147

X + y = 17
x - y = 29

We're going to do substitution.

1. We first put one of these in terms of x or y. Either are fine, but I'm going to do x, and any of the equations are fine, but I'm going to do the first one.

x + y = 17 >> x = -y + 17

2. We plug in this x-value into the other equation, and solve for the variable.

(-y+17) - y = 29
-2y + 17 = 29
-2y = 12
y = -6

3. We now plug the variable we found (y in this case) into the first equation to find the other variable (x).

x + -6 = 17 >> x = 23

In conclusion, the two numbers are 23 and -6.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

∠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.

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