The graphs of f(x) and g(x)= f(x)+k are shown below. the value of k is _

The value of k is 2

Step-by-step explanation:

The rule of vertical translation

From the graph

∵ Point (0, 0) ∈ f(x)

∵ Point (0, 2) ∈ g(x)

∵ Point (2, 4) ∈ f(x)

∵ Point (2, 6) ∈ g(x)

∴ Each y-coordinates of the points on f(x) added by 2 on g(x)

→ That means f(x) is translated up 2 units

∴ f(x) is translated up by 2 units

→ By using the first rule above

∴ g(x) = f(x) + 2

∵ g(x) = f(x) + k

∴ k = 2

∴ The value of k is 2

need points to ask question

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.