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ELEN [110]
3 years ago
14

I need help solving this

Mathematics
1 answer:
inessss [21]3 years ago
5 0

Answer:

Base = 18

Height = 9

x = 7

Step-by-step explanation:

A = \frac{1}{2}\cdot b.h \\\\\ \frac{(x + 2)(2x + 4)}{2} = 81 \\\ \frac{2x^2 + 4x + 4x + 8}{2} = 81 \\\\\ 2x^2 + 8x + 8 = 162 \\\ 2x^2 + 8x - 154 = 0 \\\ \Delta = (8)^2 - 4.2.(- 154) \\\ \Delta = 1296 \\\ x = \frac{- 8 + 36}{4} \\\\\ x = \frac{28}{4} \\\\\ x = 7


Base = 2 × 7 + 4 = 18

Height = 7 + 2 = 9


I hope I helped you.

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alexdok [17]
What's the question that needs to be solved and I will help?
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3 years ago
How much pure acid should be mixed with 6 gallons of a 20% acid solution in order to get a 90% acid solution?
beks73 [17]
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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.

now let's add "x" gallons of pure acid, now, pure acid is just pure acid, so is 100% acid, how much acid is there in it?  (100/100) * x, or 1x or just x.

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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}
\\\\\\
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\\\\\\
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