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4 years ago

Factor polynomials 12x2+4x

Mathematics

1 answer:

DiKsa [7]4 years ago

4 0

Assuming this is supposed to be 12x^2+4x, you would pull out what you can to get 4x(3x+1)

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Find the sum \[\sum_{k = 1}^{2004} \frac{1}{1 + \tan^2 (\frac{k \pi}{2 \cdot 2005})}.\]

vampirchik [111]

Answer:1002

Step-by-step explanation:

$\Rightarrow \sum_{k=1}^{2004}\left ( \frac{1}{1+\tan ^2\left ( \frac{k\pi }{2\cdot 2005}\right )}\right )$

and $1+\tan ^2\theta =\sec^2\theta$

and $\cos \theta =\frac{1}{\sec \theta }$

$\Rightarrow \sum_{k=1}^{2004}\left ( \cos^2\frac{k\pi }{2\cdot 2005}\right )$

as $\cos ^2\theta =\cos ^2(\pi -\theta )$

Applying this we get

$\Rightarrow \sum_{1}^{1002}\left [ \cos^2\left ( \frac{k\pi }{2\cdot 2005}\right )+\cos^2\left ( \frac{(2005-k)\pi }{2\cdot 2005}\right )\right ]$

every $\theta$ there exist $\pi -\theta$

such that $\sin^2\theta +\cos^2\theta =1$

therefore

$\Rightarrow \sum_{1}^{1002}\left [ \cos^2\left ( \frac{k\pi }{2\cdot 2005}\right )+\cos^2\left ( \frac{(2005-k)\pi }{2\cdot 2005}\right )\right ]=1002$

6 0

3 years ago

At one point in history, the NBA finals required that one of the two teams win at least three of five games in order to win the

Galina-37 [17]

Answer:

50% i believe

Step-by-step explanation:

because in every scenario theres 2 teams and if they are well matched it be half and half on every game assuming they're the same level of comp

5 0

3 years ago

5TH GRADE MATH TESTING PEOPLE

Leviafan [203]

It is 23.917 because 51.92-28.003= to that number

6 0

3 years ago

Read 2 more answers

The function P(x) = 3x2 + 4x + 5,is dilated by the function I(x) = P(2x). Write the new function I(x).

kow [346]

Answer:

I(x) = 12x² + 8x + 5

Step-by-step explanation:

* Lets talk about the solution

- P(x) is a quadratic function represented graphically by a parabola

- The general form of the quadratic function is f(x) = ax² + bx + c,

where a is the coefficient of x² and b is the coefficient of x and c is

the y-intercept

- To find I(x) from P(x) change each x in P by 2x

∵ P(x) is dilated to I(x) by change x by 2x

∵ I(x) = P(2x)

∵ P(x) = 3x² + 4x + 5

∴ I(x) = 3(2x)² + 4(2x) + 5 ⇒ simplify

∵ (2x)² = (2)² × (x)² = 4 × x² = 4x²

∵ 4(2x) = 8x

∴ I(x) = 3(4x²) + 8x + 5

∵ 3(4x²) = 12x²

∴ I(x) = 12x² + 8x + 5

6 0

3 years ago

A given line has the equation 2x + 12y = −1.

balu736 [363]

Answer:

Step-by-step explanation:

Perpendicular lines have slopes that are opposite reciprocals of each other. In order to write the equation of a line perpendicular to the one given, we need to find the slope of the given line and then take the opposite reciprocal of it. The current form the line is in does not give us a clear idea of what the slope is. We will first put the given line into slope-intercept form (right now it's in standard form, which is not helpful for anything at all!). Solving the given equation for y:

12y = -2x - 1 and

$y=-\frac{1}{6}x-\frac{1}{12}$ (notice I reduced the slope's fraction from -2/12)

That means that the slope of the given line is -1/6. So the perpendicular slope is positive 6/1 or just 6.

Using that slope and the given point in point-slope form to write the equation:

y - 9 = 6(x - 0) and

y - 9 = 6x - 0 and

y = 6x + 9

There you go!

6 0

3 years ago