Mathematics: How many ways can the letters of the word algebra be arranged?

How many ways can the letters of the word algebra

Ответ:

Ivonne728

04.01.2022

You can choose from the first letter 7 ways. For each of those 7 ways to choose the first letter, you can chose the second letter also. As well as the 3rd, 4th, 5th, 6th, and 7th. So you would multiply or use powers (7x7x7). Which would give you the answer of 343. There is 343 ways that "algebra" can be arranged. (I'm in the 7th grade)

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Ответ:

CobyHageman

17.06.2021

Mathematics

$Let\ k:y=m_1x+b_1\ l:y=m_2x+b_2,\ then\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\\--------------------------------------\\6x-4y=24\qquad\text{subtract 6x from both sides}\\\\-4y=-6x+24\qquad\text{divide both sides by (-4)}\\\\y=\dfrac{-6}{-4}x+\dfrac{24}{-4}\\\\y=\dfrac{3}{2}x-6\to m_1=\dfrac{3}{2}\\----------------------$

$3y+2x=12\qquad\text{subtract 2x from both sides}\\\\3y=-2x+12\qquad\text{divide both sides by 3}\\\\y=\dfrac{-2}{3}x+\dfrac{12}{3}\\\\y=-\dfrac{2}{3}x+4\to m_2=-\dfra\dfrac{2}{3}\\-------------------------------\\\\m_1=\dfrac{3}{2},\ m_2=-\dfrac{2}{3}\to m_1\neq m_2-not\ parallel\\\\m_1m_2=\dfrac{3}{2}\left(-\dfrac{2}{3}\right)=-1\\\\\ The\ lines\ are\ perpendicular$

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How many ways can the letters of the word algebra be arranged?

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