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Helga [31]
2 years ago
14

You are playing a video game. For each diamonds you collect, you earn 50 points. You need to earn 2000 points or more to continu

e to the next level. The variable d represents the number of diamonds your collect
Mathematics
1 answer:
Brrunno [24]2 years ago
4 0
40 diamonds x 50 point (each diamond) = 2000 points
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Classify each pair of numbered angles.
kifflom [539]
Adjacent angles are angles with a common side and vertex, linear pairs are adjacent angles that are supplementary, and vertical angles are angles made by the same two lines but on opposite sides.

For the first one, 5 and 6 clearly do not share a side but they are made up by the same 2 lines and are opposite of each other, making them vertical.

For the next one, since the angles only share 1 line (and not a side) they can't be any of the above. 
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Help for brainliest answer
guajiro [1.7K]

Step-by-step explanation:

SA=ph+2A, that is, perimeter × height+ twice area

p=21+20+29=70cm

h=22cm

70×22=1540cm

A=1/2 ×20×21=210×2=420

1540+420=1960cm2

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Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator
SpyIntel [72]
\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}
\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)

When x=3, you're left with

147=49a_1\implies a_1=\dfrac{147}{49}=3

When x=\sqrt2 or x=-\sqrt2, you're left with

\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}

Adding the two equations together gives -10=2a_5, or a_5=-5. Subtracting them gives 2\sqrt2=2\sqrt2a_4, a_4=1.

Now, you have

5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)
5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)
2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that a_2x^4=2x^4 and a_3(-3)(-2)=6a_3=-6. These alone tell you that you must have a_2=2 and a_3=-1.

So the partial fraction decomposition is

\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}
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3 years ago
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