vincent has model trains. he made these tables to compare the time during which each train moves with the distance it moves.

for which train do the numbers in the table form a proportional relationship?
a. is the 1st pic
b. is the 2nd pic
c. is the 3rd pic
d. is the 4th pic

Option B. is the 2nd pic (Train 2)

Step-by-step explanation:

Let

x ----> the time in seconds

y ----> the distance in centimeters

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each table

Train 1

Find the value of k

For x=5, y=10 ---->

For x=10, y=15 ---->

For x=20, y=20 ---->

The values of k are different

therefore

The numbers in the table not form a proportional relationship

Train 2

Find the value of k

For x=5, y=20 ---->

For x=10, y=40 ---->

For x=20, y=80 ---->

The values of k are the same

therefore

The numbers in the table form a proportional relationship

Train 3

Find the value of k

For x=5, y=10 ---->

For x=10, y=15 ---->

For x=20, y=30 ---->

The values of k are different

therefore

The numbers in the table not form a proportional relationship

Train 4

Find the value of k

For x=5, y=20 ---->

For x=10, y=25 ---->

For x=20, y=30 ---->

The values of k are different

therefore

The numbers in the table not form a proportional relationship

b.

Step-by-step explanation:

the 2nd picture

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x

∠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.