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lozanna [386]
2 years ago
8

Simplify 9 - {x - (7 + x)}. (a) 16 (b) -2x + 2 (c) -2x + 16 (d) 2x + 2

Mathematics
2 answers:
Setler79 [48]2 years ago
5 0

Answer:

A

Step-by-step explanation:

To simplify the expression:

  • multiply a negative into the inner parenthesis
  • add like terms inside the outer parenthesis
  • multiply a negative to the terms inside the parenthesis
  • add like terms

9- {x-(7+x)}

9- {x-7-x}

9- {-7}

9+7

16

Arisa [49]2 years ago
3 0

Answer:

The correct answer is a) 16

Step-by-step explanation:

To find this first distribute the interior negative to both terms in the parenthesis.

9 - {x - (7 + x)}

9 - {x - 7 - x}

Now simplify the like terms.

9 - {-7}

Now distribute the negative once again.

9 + 7

And complete the indicated operation.

16

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How much pure acid should be mixed with 6 gallons of a 20% acid solution in order to get a 90% acid solution?
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now, if we want a 90% solution, and say we add "y" gallons, how much acid is in it?  well (90/100) * y, or 0.9y.

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we know whatever "x" and "y" amounts are, they -> x + 6 = y

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\bf \begin{array}{lccclll}
&\stackrel{gallons}{acid}&\stackrel{acid~\%}{quantity}&\stackrel{acid~gallons}{quantity}\\
&------&------&------\\
\textit{pure acid}&x&1.00&x\\
\textit{20\% sol'n}&6&0.20&1.2\\
------&------&------&------\\\
mixture&y&0.90&0.9y
\end{array}
\\\\\\
\begin{cases}
x+6=\boxed{y}\\
x+1.2=0.9y\\
----------\\
x+1.2=0.9\left( \boxed{x+6} \right)
\end{cases}
\\\\\\
x+1.2=0.9x+5.4\implies x-0.9x=5.4-1.2\implies 0.1x=4.2
\\\\\\
x=\cfrac{4.2}{0.1}\implies x=\stackrel{gallons}{42}
3 0
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