We need to find a polynomial function f(x) with degree 3 and zeros 2 and 2i, such that:

Since 2i is a zero, -2i is also a zero of this function. Thus, we have:

where a is a constant.
Expanding the expression on the right side, we obtain:

Now, using f(-1) = 30, we obtain:

Therefore, the function is:
Answer
Answer: 
Step-by-step explanation:
Given: Emelina wrote the equation of a line in point-slope form as shown below.

To write the equation in intercept form, first we multiply 3 inside the bracket values in the right side , we get

Now, subtract 4 from both sides , we get

Hence, Emelina’s equation in slope-intercept form : 
Answer:
7
Step-by-step explanation:
Answer:

Step-by-step explanation:
step 1
Find the slope of the given line
The formula to calculate the slope between two points is equal to

we have
(-2,5) and (-4,8)
substitute the values in the formula



step 2
Find the slope of the perpendicular line to the given line
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
so

----> slope of the given line
therefore
---> slope of the perpendicular line to the given line
step 2
Find the equation of the line in point slope form

we have


substitute

step 3
Convert to slope intercept form

isolate the variable y



Answer: Vertical angles are congruent.
Step-by-step explanation:
In the given picture, NS and RT are intersecting line segments, intersects at point Q.
We know that when two lines intersect to make an cross, angles on opposite sides of the cross are called vertical angles. These angles are equal by the theorem that says Vertical angles are congruent.
⇒∠NQT ≅ ∠SQR
Therefore, the reason that justifies the step 2 :- ∠NQT ≅ ∠SQR is "Vertical angles are congruent" in the proof.