Salut! :)
10. f)
[tex]\dfrac{x}{ \dfrac{1}{3} } = \dfrac{0.(7)}{ 2\dfrac{2}{3} } \\ \\ x = \dfrac{ \dfrac{1}{3} \times 0.(7)}{2 \dfrac{2}{3} } = \dfrac{ \dfrac{1}{3} \times \dfrac{7}{9} }{ \dfrac{2 \times 3 + 2}{3} } = \dfrac{ \dfrac{7}{27} }{ \dfrac{8}{3} } = \dfrac{7}{27} \times \dfrac{3}{8} = \dfrac{7}{72} [/tex]
g)
[tex] \dfrac{ ^{4)} \dfrac{1}{5} + ^{5)} \dfrac{3}{4} }{x} = \dfrac{3}{20} \\ \\ \dfrac{ \dfrac{4}{20} + \dfrac{15}{20} }{x} = \dfrac{3}{20} \\ \\ x = \dfrac{20 \times \dfrac{19}{20} }{3} = \dfrac{19}{3} [/tex]
11. a)
[tex] 15a \: este \: divizibil \: cu \: 9 = > 1 + 5 + a \: este \: divizibil \: cu \: 9 = > a = 3 = > 15a = 153 \\ \\ \dfrac{x}{6} = \dfrac{15a}{27} = > \dfrac{x}{6} = \dfrac{153}{27} = > x = \dfrac{6 \times 153}{27} = 34[/tex]
b)
[tex]2a = nr \: prim \leqslant 25= > 2a = 23 \\ \\ \dfrac{3}{46} = \dfrac{x}{23} = > x = \dfrac{23 \times 3}{46} = \dfrac{3}{2} [/tex]
