Can someone please help me this problem? Thanks :)

 B) 2/3

Work Shown:

Method 1

Apply the slope formula

m = (y2-y1)/(x2 - x1)

m = (3-1)/(-1 - (-4)) using the first two rows as points

m = (3-1)/(-1 + 4)

m = 2/3 is the slope

Method 2

Each time y goes up by 2, x goes up by 3.

For instance, the jump from y = 1 to y = 3 is "plus 2". At the same time, the jump from x = -4 to x = -1 is "plus 3".

We can then say

slope = (rise)/(run)

slope = (change in y)/(change in x)

slope = (y increase by 2)/(x increase by 3)

slope = 2/3

∠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.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.