va rog ajutați mă 1,2,3.mersi

[tex]1) \frac{x}{y} = \frac{2}{3} [/tex]

[tex]3x = 2y = > x = \frac{2y}{3} [/tex]

[tex] \frac{6x + y}{9x + 3y} = \frac{6 \times \frac{2y}{3} +y }{9 \times \frac{2y}{3} + 3y } = \frac{4y + y}{6y + 3y} = \frac{5y}{9y} = \frac{5}{9} [/tex]

[tex] = > a) \frac{5}{9} [/tex]

[tex]2) \frac{a}{b} = \frac{c}{d} = \frac{e}{f} = \frac{7}{5} [/tex]

[tex] \frac{e}{f} = \frac{7}{5} [/tex]

[tex]5e = 7f = > e = \frac{7f}{5} [/tex]

[tex] \frac{c}{d} = \frac{e}{f} [/tex]

[tex]cf = de[/tex]

[tex]cf = \frac{7df}{5} [/tex]

[tex]5cf = 7df \: | \div f[/tex]

[tex]5c = 7d = > c = \frac{7d}{5} [/tex]

[tex] \frac{a}{b} = \frac{c}{d} [/tex]

[tex] \frac{a}{b} = \frac{ \frac{7d}{5} }{d} [/tex]

[tex]ad = \frac{7db}{5} [/tex]

[tex]5ad = 7db \: | \div d[/tex]

[tex]5a = 7b = > a = \frac{7b}{5} [/tex]

[tex] \frac{a + c + e}{b + d + f} = \frac{ \frac{7b}{5} + \frac{7d}{5} + \frac{7f}{5} }{b + d + f} = \frac{ \frac{7b + 7d + 7f}{5} }{b + d + f} [/tex]

[tex] = \frac{ \frac{7(b + d + f)}{5} }{b + d + f} = \frac{7(b + d + f)}{5} \times \frac{1}{b + d + f} [/tex]

[tex] = \frac{7(b + d + f)}{5(b + d + f)} = \frac{7}{5} [/tex]

[tex] = > c) \frac{7}{5} [/tex]

[tex]3) \frac{1 + 2 + 3 + ... + 100}{25} = \frac{x}{3} [/tex]

[tex] \frac{ \frac{100(100 + 1)}{2} }{25} = \frac{x}{3} [/tex]

[tex] \frac{ \frac{100 \times 101}{2} }{25} = \frac{x}{3} [/tex]

[tex] \frac{50 \times 101}{25} = \frac{x}{3} [/tex]

[tex]2 \times 101 = \frac{x}{3} [/tex]

[tex]202 = \frac{x}{3} [/tex]

[tex]x = 202 \times 3[/tex]

[tex]x = 606[/tex]

[tex] = > c)606[/tex]