The sum of the exterior angles of a polygon is always 180 degrees. True False
2 answers:
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Answer:
103, 776
Step-by-step explanation:
There are 48 possibilities, and you are picking 3.
Now, the order does matter (aka, if the same 3 athletes won but got different places, we would still consider it to be a separate possibility)
(this is considered "without repetitions")
the number of permutations (arrangement combinations where the order does matter) without repetitions formula:
Number of permutations
without <em>repetitions </em>= nPr
=
(
[the P is for combinations [where the order does matter, if the order didn't matter then it would be C, and it would be a different formula.]
n is the total number of objects.
r is the number of objects selected]
<em>(a repetition would be like two versions of the same person competing, which doesn't make sense)</em>
{the ! means factorial:
5! = 5 x 4 x 3 x 2 x 1}
{for example, if there are 5 people to give a presentation, and they can go in any order [but cannot repeat their presentation], so they all must fill 5 slots}
{for the first slot there are 5 choices, the second slot there are 4 choices...}
)
So, if we follow this formula:
n: 48
r: 3
=
=
(the 45! cancel out)
= 48 * 47 * 46
= 103, 776
(or, without the formula:
for the first choice (lets say of gold), there are 48 options
for the second choice (lets say silver), there are 47 options left to choose from
for the third choice (lets say bronze), there are 46 options left to choose from
)
<h3>Answer: </h3>
The GCF is 4
The polynomial factors to
==========================================================
Further explanation:
Ignore the x terms
We're looking for the GCF of 12, 4 and 20
Factor each to their prime factorization. It might help to do a factor tree, but this is optional.
- 12 = 2*2*3
- 4 = 2*2
- 20 = 2*2*5
Each factorization involves "2*2", which means 2*2 = 4 is the GCF here.
We can then factor like so
The distributive property pulls out that common 4. We can verify this by distributing the 4 back in, so we get the original expression back again.
The polynomial inside the parenthesis cannot be factored further. Proof of this can be found by looking at the roots and noticing that they aren't rational numbers (use the quadratic formula).