[tex] \displaystyle\\
1)\\
x=0,6=\frac{6}{10}\\\\
y=0,(6)=\frac{6}{9}\\\\
a)~~\frac{x}{y} =\frac{\dfrac{6}{10}}{\dfrac{6}{9}}= \frac{6}{10}\cdot \frac{9}{6}=\boxed{\frac{9}{10}}\\\\
b)~~\frac{x^2}{y^2} =\frac{\left(\dfrac{6}{10}\right)^2}{\left(\dfrac{6}{9}\right)^2}= \frac{\dfrac{6^2}{10^2}}{\dfrac{6^2}{9^2}}= \frac{6^2}{10^2}\cdot \frac{9^2}{6^2}= \frac{9^2}{10^2}= \boxed{\frac{81}{100}} [/tex]
.
[tex] \displaystyle\\
2)\\
\text{Avem proportia:}\\\\
\frac{x}{3}=\frac{15}{y}\\\\
a)~~xy=3\cdot 15=45~\Longrightarrow~30-\frac{45}{xy}=30-\frac{45}{45}=30-1=\boxed{29}\\\\
b)~~y = \frac{3\cdot 15}{x}= \frac{45}{10}= \boxed{\frac{9}{2}}=\boxed{4,5}
[/tex]
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[tex] \displaystyle\\
3)\\
\text{Se da:}\\\\
\frac{x}{y}=4\\\\
x-y=18\\\\
a)\\
x=4y~~~\text{Din prima ecuatie}\\\\
4y-y=18\\\\
3y=18\\\\
y=\frac{18}{3}=\boxed{6}\\\\
x=4y=4\cdot6=\boxed{24}\\\\
b)\\\\
m_a = \frac{6+24}{2}= \frac{30}{2}=\boxed{15} [/tex]
