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Answer:
The given expression can't be expressed in polynomial form. Hence, it is not a polynomial.
Step-by-step explanation:
P(x,n) is a polynomial of nth degree if it is of the form,
P(x,n) = ![a_{0} + a_{1}x + a_{2}x^{2} + a_{3}x^{3} + ......... +a_{n}x^{n}](https://tex.z-dn.net/?f=a_%7B0%7D%20%2B%20a_%7B1%7Dx%20%2B%20a_%7B2%7Dx%5E%7B2%7D%20%2B%20a_%7B3%7Dx%5E%7B3%7D%20%2B%20.........%20%2Ba_%7Bn%7Dx%5E%7Bn%7D)
where n is a finite positive integer and n ∈ N
and '
's are fixed but otherwise arbitrary constants ∀ i = 0(1)n .
Now, the given expression is,
![9x^{3} + \frac {1}{2x^{2}} + 3x^{-1}](https://tex.z-dn.net/?f=9x%5E%7B3%7D%20%2B%20%5Cfrac%20%7B1%7D%7B2x%5E%7B2%7D%7D%20%2B%203x%5E%7B-1%7D)
which doesn't fit in the above form. Hence, it is not a polynomial.
Answer:
Abel to Ben: 6
Abel to Carl: 3
Ben to Carl: 0.5
Step-by-step explanation:
First we formulate the problem in equations:
Abel = 6 * Ben
Cale = Abel / 3
If Cale's score is Abel's score over 3, so Abel's score is 3 times Cale's score.
If Abel's score is 6 times Ben's score, and 3 times Cale's score, then Cale's score is 2 times Ben's score (so Ben's score is 0.5 times Cale's score)
So, the ratio between all scores are the following:
Abel to Ben: 6
Abel to Carl: 3
Ben to Carl: 0.5
Answer:
Yes, by SSS Similarity Theorem
Step-by-step explanation:
If you observe each corresponding line segment (e.g. AB to DE), triangle DEF is basically triangle ABC but it's dilated by a scale factor 2, meaning that the line segments become 2 times as big. Since this holds true for all corresponding line segments, the triangles are similar by the SSS Similarity Theorem.