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krok68 [10]
3 years ago
13

1. 40° 2. 65° 3.75° 4.90°

Mathematics
1 answer:
nataly862011 [7]3 years ago
4 0

Answer:

option 3.75°

Step-by-step explanation:

we know that

If two triangles are similar, then the corresponding angles are congruent

so

In this problem

The corresponding angles are

m∠A and m∠D, m∠B and m∠E, m∠C and m∠F

so

m∠A=m∠D

m∠B=m∠E

m∠C=m∠F

therefore

m∠F=75°

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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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So, how much acid is there in 6 gallons?  well is 20% acid or (20/100), so the amount of acid in it just (20/100) * 6 or 1.2, the rest is say water.

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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}
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