Answer:
Part 1) Option C. Same side interior angles
Part 2) Option A. 
Part 3) Option B. 
Step-by-step explanation:
Part 1) we know that
If p and q are parallel
then
m<3 and m<5 are consecutive interior angles or Same side interior angles
and

Part 2) we know that
-----> by consecutive interior angles (supplementary angles)
we have that


so
substitute

Part 3) Find the measure of angle 5
we know that

Solve for x




substitute the value of x

14/3 simplified is 4 and 2/3 because 3 goes into 14 a total of 4 times with remainder 2. Therefore, 14/3 simplified is 4 and 2/3 or 4 2/3.
Answer:
10 ( 12p - 6k)
Step-by-step explanation:
4p x 3 = 12p
2k x 3 = 6k
you cannot subtract 12p and 6k bcuz they do not have the same variables.
<h3>
Answer: Independent</h3>
For two events A and B, if the occurrence of either event in no way affects the probability of the occurrence of the other event, then the two events are considered to be <u> independent </u> events.
=========================================================
Explanation:
Consider the idea of flipping a coin and rolling a dice. If these actions are separate (i.e. they don't bump into each other), then one object won't affect the other. Hence, one probability won't change the other. We consider these events to be independent.
In contrast, let's say we're pulling out cards from a deck. If we don't put the first card back, then the future probabilities of other cards will change. This is considered dependent.
Answer:

Step-by-step explanation:
We are asked to find the length of a segment or the <em>distance</em> between the 2 points. The formula for distance is:

where (x₁ y₁) and (x₂, y₂) are the points. We are given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:
- x₁= -5
- y₁= 4
- x₂= 6
- y₂ = -3
Substitute the values into the formula.

Solve inside the parentheses.
- 6--5 (Back to back negative signs become a positive)= 6+5 =11
- -3-4= -7

Solve the exponents.
- (11)²= 11*11= 121
- (-7)²= -7*-7= 49

Add.


Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.

The length of the segment is <u>√170</u> or approximately <u>13.04. </u>