The perimeter of square is 24 meters. What is the length of one side of the square. Show your work
2 answers:
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Answer:
a) The table of values represents the ordered pairs formed by the elements of the sequence () (range) and their respective indexes (
) (domain):
1 6
2 11
3 16
4 21
5 26
b) The algebraic expression for the general term of the sequence is .
c) The 25th term in the sequence is 126.
Step-by-step explanation:
a) Make a table of values for the sequence 6, 11, 16, 21, 26, ...
The table of values represents the ordered pairs formed by the elements of the sequence () (range) and their respective indexes (
) (domain):
1 6
2 11
3 16
4 21
5 26
b) Based on the table of values, we notice a constant difference between two consecutive elements of the sequence, a characteristic of arithmetic series, whose form is:
(1)
Where:
- First element of the sequence.
- Arithmetic difference.
- Index.
If we know that and
, then the algebraic expression for the general term of the sequence is:
c) If we know that and
, then the 25th term in the sequence is:
The 25th term in the sequence is 126.
The given function is:
The parents functions of g(x) will be:
The domain of g(x) and its parent function is the same i.e. Set of all Real numbers except 0.
The range of g(x) and its parent function is the same i.e. set of all real numbers except 0.
g(x) and its parent function only decrease. They do not increase over any interval. However, the interval in which they decrease is the same for both.
So, the correct answers are:
The domain of g(x) is the same as the domain of the parent function.
<span>The range is the same as the range of the parent function.
</span><span>The function g(x) decreases over the same x-values as the parent function.</span>
The parents functions of g(x) will be:
The domain of g(x) and its parent function is the same i.e. Set of all Real numbers except 0.
The range of g(x) and its parent function is the same i.e. set of all real numbers except 0.
g(x) and its parent function only decrease. They do not increase over any interval. However, the interval in which they decrease is the same for both.
So, the correct answers are:
The domain of g(x) is the same as the domain of the parent function.
<span>The range is the same as the range of the parent function.
</span><span>The function g(x) decreases over the same x-values as the parent function.</span>
Answer:
1. 7 outcomes.
2. 64 outcomes.
3. D and H
Step-by-step explanation:
1. The experimenter will record the total number of heads after flipping the coin 6 times, therefore, the possible outcomes are: the experimenter got 0 heads, the experimenter got 1 head,..., the experimenter got 6 heads. Therefore there are 7 possible outcomes: (0, 1, 2, 3, 4, 5, 6).
2. If the experimenter records the result after each flip (H or T), for the first flip she has 2 results (heads or tails), for the second one she has 2 results, same for the third, fourth, fifth and sixth flip.
Therefore the possible outcomes are: .
3. Now the experimenter will end up the experiment earlier if she gets two tails or two heads in a row.
A.TTHTT is not possible because in this case she would've ended up the experiment after the second flip since she got two tails.
B.TTH is not possible either for the same reason.
C. HT is not possible because she still needs to get another T or two H in a row.
D. This is a possible outcome because in this one she flipped the coin 6 times and she didn't get two heads or two tails in a row so she didn't finish it earlier.
E. Is not possible because she should've stopped after the second flip.
F. Is not possible because it has 7 letters, therefore, 7 flips.
G. Is not possible because she should've stopped once she got heads in the fourth and fifth flip.
H. Is possible because she got heads in the second and third flip.