A railroad track follows a straight path from station A to station B. What is the distance traveled by the railroad track from station A to station B before completing its journey until station C? Distance travelled from station A to station C is 3x+4 and from station B to C is 6x-4.

-3x + 8

Step-by-step explanation:

The railroad track moves in a straight path from station A to station B and then from station B to station C.

Let the distance from station A to station C be AC and the distance from station B to station C as BC while the distance from station A to station B be AB the following equation holds:

AC = AB + BC

Given the distance from station A to station C is 3x + 4 and from station B to C is 6x-4, Hence:

AC = 3x + 4 and BC = 6x - 4.

Using the line segment addition postulate:

AC = AB + BC

3x + 4 = AB + (6x - 4)

AB = 3x + 4 - (6x - 4)

AB = 3x + 4 - 6x + 4

AB = 3x - 6x + 4 + 4

AB = -3x + 8

b. x- 48 =120

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.