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4 years ago

What is the prime factorization of the number 45

Mathematics

2 answers:

Ilya [14]4 years ago

8 0

5*3*3 five times 3 times 3

ohaa [14]4 years ago

7 0

..........................

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What is 65% of 65? Please help

NARA [144]

I believe the correct answer is 42.25%

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4 years ago

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If cos() = − 2 3 and is in Quadrant III, find tan() cot() + csc(). Incorrect: Your answer is incorrect.

nydimaria [60]

Answer:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

Step-by-step explanation:

Given

$\cos(\theta) = -\frac{2}{3}$

$\theta \to$ Quadrant III

Required

Determine $\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

We have:

$\cos(\theta) = -\frac{2}{3}$

We know that:

$\sin^2(\theta) + \cos^2(\theta) = 1$

This gives:

$\sin^2(\theta) + (-\frac{2}{3})^2 = 1$

$\sin^2(\theta) + (\frac{4}{9}) = 1$

Collect like terms

$\sin^2(\theta) = 1 - \frac{4}{9}$

Take LCM and solve

$\sin^2(\theta) = \frac{9 -4}{9}$

$\sin^2(\theta) = \frac{5}{9}$

Take the square roots of both sides

$\sin(\theta) = \±\frac{\sqrt 5}{3}$

Sin is negative in quadrant III. So:

$\sin(\theta) = -\frac{\sqrt 5}{3}$

Calculate $\csc(\theta)$

$\csc(\theta) = \frac{1}{\sin(\theta)}$

We have: $\sin(\theta) = -\frac{\sqrt 5}{3}$

So:

$\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}$

$\csc(\theta) = \frac{-3}{\sqrt 5}$

Rationalize

$\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}$

$\csc(\theta) = \frac{-3\sqrt 5}{5}$

So, we have:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)$

Substitute: $\csc(\theta) = \frac{-3\sqrt 5}{5}$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}$

Take LCM

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

6 0

3 years ago

Add: 3x(x-y+z) and 2y (x+y-z)

hodyreva [135]

Answer:

3x^2 + 3xz + 2y^2 - 2yz - xy

Step-by-step explanation:

(1) multiply it to get

3x^2 - 3xy + 3xz and 2yx + 2y^2 - 2yz

add similar variables (-3xy + 2yx)

( the order of the variables doesn't matter xy or yx is the same)

we get -xy

and then after that simplifying we get 3x^2 + 3xz + 2y^2 - 2yz - xy

3 0

3 years ago

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I DON'T KNOW HOW TO DO THIS!! PLZZ HELPPPP

motikmotik

The answer is C hope this helped:)

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4 years ago

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Explain how you would use addition to find the product of -2 and 5

Ipatiy [6.2K]

-2+5=3
And is a word used for addition. For example 20 and 6 is 26.

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2 years ago