Step-by-step explanation:
Vertical Angles: Angles facing each other.
Example: 6 & 7
Complementary Angles: Angles adding up to 90 degrees / making a right angle.
Example: 9 & 10
Supplementary Angles: Angles adding up to 180 degrees / making a straight line.
Example: 7 & 8
<u>Answer:</u>
<u>Distance:</u> 6x + 15.5y > 55.5
<u>Time:</u> x + y > 4.5
<u>Step-by-step explanation:</u>
We are given that Martha is training for a duathlon and she covered a total distance of over 55.5 miles in more than than 4.5 hours of training.
Also, she runs at a speed of 6 mph and bikes at a rate of 15.5 mph.
We are to write inequalities representing the distance she traveled and the total time she spent training.
<u>Distance:</u> 6x + 15.5y > 55.5
(formula for distance = speed x time so speeds for running and biking are multiplied by their number of hours)
<u>Time:</u> x + y > 4.5
(she trained for more than 4.5 hours, x hours for running and y hours for biking.
<span>The number can be 102, 108, or 114. They can all be formed that way.
32 + 34 + 36 = 102
34 + 36 + 38 = 108
36 + 38 + 40 = 114
</span>The n<span>ext one is 120 . . . . . 38 + 40 + 42</span>
Answer:
-3
Step-by-step explanation:
The common ratio of a geometric sequence is the number that each term of the sequence is multiplied by. This means that the the previous term is multiplied by the common ratio to get the current term. The common ratio can also be used to create a function that can predict future terms.
To find the common ratio of this sequence, divide a term by the previous term. For example, -15/5. This gives the answer, -3. Dividing the terms allows us to figure out what factor is being multiplied by in the sequence.
ANSWER

EXPLANATION
The given function is

According to the remainder theorem,

where R is the remainder when

is divided by

We therefore substitute the value of x and evaluate to obtain,



This will evaluate to,

Hence the value of the function when

is

According to the remainder theorem,

is the remainder when

is divided by