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Aleonysh [2.5K]
3 years ago
5

Find the complete factorization of

Mathematics
1 answer:
notsponge [240]3 years ago
5 0
<h3>Option C is correct</h3>

<h3>Let us see the verification;</h3>

6x {}^{3}  - 15x {}^{2}  - 9x \\ 3x(2x {}^{2} - 5x - 3)  \\ 3x( 2x {}^{2}  + x - 6x - 3) \\ 3x(x(2x + 1) - 3(2x - 1) \\ (2x + 1)

<h2>Hence, Proved ✔︎</h2>

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\large\displaystyle\text{$\begin{gathered}\sf 9|x-8| < 36 \end{gathered}$}

\large\displaystyle\text{$\begin{gathered}\sf Divide \ both \ sides \ by \ 9. \end{gathered}$}

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\large\displaystyle\text{$\begin{gathered}\sf Solve \ Absolute \ Value. \end{gathered}$}

  • \large\displaystyle\text{$\begin{gathered}\sf |x-8| < 4 \end{gathered}$}

\large\displaystyle\text{$\begin{gathered}\sf We \ know \ x-8 < 4 \ and \ x-8 > -4 \end{gathered}$}

<u>                                                                                                                             </u>

         \large\displaystyle\text{$\begin{gathered}\sf x-8 < 4 \ (Condition \ 1) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 < 4+8 \ (Add \ 8 \ to \ both \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x < 12 \end{gathered}$}

<u>                                                                                                                             </u>

           \large\displaystyle\text{$\begin{gathered}\sf x-8 > -4 \ (Condition \ 2) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 > -4+8 \ (Add \ 8 \ to \ both \ \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x > 4 \end{gathered}$}

<u>                                                                                                                             </u>

<u />\underline{\boldsymbol{\sf{Answer}}}

\boxed{\large\displaystyle\text{$\begin{gathered}\sf x < 12 \ and \ x > 4 \end{gathered}$} }

\large\displaystyle\text{$\begin{gathered}\sf Therefore,\bf{\underline{the \  correct \ option}} \  \end{gathered}$}\large\displaystyle\text{$\begin{gathered}\sf is \ \bf{\underline{"A"}}. \end{gathered}$}

6 0
2 years ago
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Answer:

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We'll call the 2 numbers x and y. Starting with the last part of that first sentence "one number is 10 times the other number" can be written, in algebraic form:

y = 10x

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x equal to \frac{22}{10}=2.2

So x = 2.2 and y = 22.

7 0
3 years ago
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