Miguel wrote the predicted and residual values for a data set using the line of best fit y = 1.82x – 4.3. he left out two of the values.

a=1.16 and b=0.12

Step-by-step explanation:

We know that the residual value= given - predicted

For x=3

The given value =1.1

The residual value=-0.06

Thus

The predicted value (a)= given- residual

For x=4

The given value =3.1

The predicted value = 2.98

Thus

The residual value (b) = given - predicted

-18

step-by-step explanation:

because mean value defines that total sum value over total number of set

∠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.