How many solutions does this equation have? 2n–142=n–7

Mathematics

1 answer:

Molodets [167]4 years ago

5 0

2n-142 = n-7

2n-n = 142-7

n = 135

It has only one solution

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There are two factors of -36 such that one factor is 11 less than half of the other factor choose all the pairs of these factors

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Answer with explanation:

Factors of -36 are

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If you will take, $=\pm 1,\pm 3,\pm 4, \pm 9,$ , then you can find such pairs.

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likewise, how many liters are there in the 40% solution? well, (40/100) * y, or 0.4y, that many.

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$\bf \begin{array}{lccclll}
&\stackrel{liters}{amount}&\stackrel{alcohol~\%}{quantity}&\stackrel{liters}{alcohol}\\
&------&------&------\\
\textit{18\% solution}&x&0.18&0.18x\\
\textit{40\% solution}&y&0.40&0.4y\\
------&------&------&------\\
mixture&10&0.20&2
\end{array}$

$\bf \begin{cases}
x+y=10\implies \boxed{y}=10-x\\
0.18x+0.4y=2\\
----------\\
0.18x+0.4\left( \boxed{10-x} \right)=2
\end{cases}
\\\\\\
0.18x-0.4x+4=2\implies -0.22x=-2
\\\\\\
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The graph is shown below.
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Note that y = f(x).
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