Explicație pas cu pas:
a) 15a : 9 <=> (1+5+a):9 => (6+a):9 => a = 3 => 15a = 153
[tex]\frac{x}{6} = \frac{153}{27} \iff x = \frac{6 \times 153}{27} \implies x = 34 \\ [/tex]
b) 2a număr prim ≤ 25 => a = 23
[tex]\frac{3}{46} = \frac{x}{23}\iff x = \frac{3 \times 23}{46} \implies x = \frac{3}{2} \\ [/tex]
c) 2a5 : 9 <=> (2+a+5):9 => (7+a):9 => a=2 => 2a5 =225
[tex]\frac{225}{35} = \frac{36}{x}\iff x = \frac{35 \times 36}{225} \implies x = \frac{28}{5} \\ [/tex]
d)
[tex]\frac{ {2}^{2019} + {2}^{2020} + {2}^{2021}}{x} = \frac{ {32}^{404} }{0.5} \\ \frac{ {2}^{2019}(1 + 2 + {2}^{2})}{x} = \frac{ {( {2}^{5} )}^{404} }{ \frac{1}{2} } \\ \frac{ {2}^{2019}(1 + 2 + 4)}{x} = {2}^{2020} \times 2 \\ x = \frac{7 \times {2}^{2019}}{{2}^{2021}} \iff x = \frac{7}{ {2}^{2} } \implies x = \frac{7}{4} [/tex]
e)
[tex] \frac{x}{1 + 2 + 3 + ... + 102} = \frac{0.(3)}{103} \\ \frac{x}{ \frac{102 \times 103}{2} } = \frac{ \frac{3}{9} }{103} \iff \frac{2x}{102 \times 103} = \frac{1}{3 \times 103} \\ \iff x = \frac{102 \times 103}{2 \times 3 \times 103} \implies x = 17[/tex]
