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3 years ago

ALGEBRA 1:

Mathematics

2 answers:

SCORPION-xisa [38]3 years ago

7 0

(2x+1)^2
=(2x+1)(2x+1)
=4x^2+2x+2x+1
=4x^2+4x+1

erastova [34]3 years ago

6 0

Answer:

Step-by-step explanation:

(2x-1)(2x-1) Work outside then inside

4x^2 and +1 are the outside terms

-2x and -2x are the inside terms

so the answer will be

4x^2 - 4x +1

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3 years ago

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Solution:

The permutation formula is expressed as

$\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}$

The combination formula is expressed as

$\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}$

where

$\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}$

Given that 6 objects are taken at a time from 8, this implies that

$\begin{gathered} n=8 \\ r=6 \end{gathered}$

Thus,

Number of permuations:

$\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}$

Number of combinations:

$\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}$

Hence, there are 28 combinations and 20160 permutations.

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1 year ago

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2 years ago

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In this (assumed) geometry, corresponding angles are congruent, so the angle of interest has measure 105°.

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