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Nadya [2.5K]
3 years ago
6

Which of the following is a factor of 3x^3+18x^2+27x? A. 9x B. x^3 C. x+3 D. x-3

Mathematics
1 answer:
Tju [1.3M]3 years ago
3 0
3x³ + 18x² + 27x = 3x(x² + 6x + 9) = 3x(x+3)²

Answer: <span>C. x+3</span>
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Prove that tan60+tan70-tan50+tan10=2sqrt3?
LiRa [457]
{tan(60) + tan(10)}/{1 - tan(60)*tan(10)} - {tan(60) - tan(10)}/{1 + tan(10)*tan(60)} 

<span>ii) Taking LCM & simplifying with applying tan(60) = √3, the above simplifies to: </span>

<span>= 8*tan(10)/{1 - 3*tan²(10)} </span>

<span>iii) So tan(70) - tan(50) + tan(10) = 8*tan(10)/{1 - 3*tan²(10)} + tan(10) </span>

<span>= [8*tan(10) + tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)} </span>

<span>= [9*tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)} </span>

<span>= 3 [3*tan(10) - tan³(10)]/{1 - 3*tan²(10)} </span>

<span>= 3*tan(30) = 3*(1/√3) = √3 [Proved] </span>

<span>[Since tan(3A) = {3*tan(A) - tan³(A)}/{1 - 3*tan²(A)}, </span>
<span>{3*tan(10) - tan³(10)}/{1 - 3*tan²(10)} = tan(3*10) = tan(30)]</span>
8 0
3 years ago
Name the adjacent angles in the diagram below:​
harkovskaia [24]

Hey there!

In this picture, we have many pairs of adjacent angles:

1 and 2

2 and 4

4 and 3

3 and 1

This is because these pairs are being connected by a vertex and a side.

Hope it helps and have a great day!!!

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Therefore B is the correct answer.
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Answer:

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12 equal sections means probability is 1 in 12 of landing on any one numbered section.

2 in 12 or 1 in 6 chance of landing on either of two numbered sections in one attempt.

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