Explicație pas cu pas:
a)
[tex]\overline {15a} : 9 \iff (1 + 5 + a) : 9 \\ \iff (6 + a) : 9 \implies a = 3[/tex]
[tex]\frac{x}{6} = \frac{153}{27} \iff x = \frac{6 \cdot 153}{27} \\ \implies x = \bf 34[/tex]
b)
[tex]\overline {2a}\leqslant 25 \implies \overline {2a} = 23[/tex]
[tex]\frac{3}{46} = \frac{x}{23} \iff x = \frac{3 \cdot 23}{46} \\ \implies x = \bf \frac{3}{2} [/tex]
c)
[tex]\overline {2a5} : 9 \iff (2 + a + 5) : 9 \\ \iff (7 + a) : 9 \implies a = 2[/tex]
[tex]\frac{225}{35} = \frac{36}{x} \iff x = \frac{35 \cdot 36}{225} \\ \implies x = \bf \frac{28}{5} [/tex]
d)
[tex]{2}^{2019} + {2}^{2020} + {2}^{2021} = {2}^{2019}(1 + 2 + 4) = 7 \cdot {2}^{2019} \\ [/tex]
[tex]\frac{{32}^{404}}{0.5} = \frac{{( {2}^{5} )}^{404}}{ \frac{1}{2} } = 2 \cdot {2}^{2020} = {2}^{2021} \\ [/tex]
(unde este x??)
e)
[tex]\frac{x}{1 + 2 + 3 + ... + 102} = \frac{0.3}{103} \\ \frac{x}{ \frac{102 \cdot 103}{2} } = \frac{ \frac{3}{9} }{103} \iff \frac{2x}{102 \cdot 103} = \frac{1}{3 \cdot 103} \\ x = \frac{102}{2 \cdot 3} \implies x = \bf 17[/tex]
