Question

Encontre o valor das incógnitas:

Answer 1

Resposta:

a) x = 2; y = 2

b) x = 5; y = 11

c) x = 0,25 ou $\frac{1}{4}$

d) x = 2

Explicação passo-a-passo:

Deve-se aplicar teorema de tales em todas as imagens:

a)

$\frac{10}{13} = \frac{y}{y+6} \\\\13y= 10y+6$

$3y = 6\\y = \frac{6}{3}\\y = 2\\\\\frac{3}{3+x} = \frac{6}{10} \\\\\frac{3}{3+x} = \frac{3}{5}\\\\15 = 9+3x\\3x = 6\\x = \frac{6}{3}\\\\x = 2$

b)

$\frac{4}{14} = \frac{2}{2+x}\\\\28 = 8+4x\\4x = 20\\x = \frac{20}{4}\\\\x = 5\\\\\frac{10}{22} = \frac{5}{y} \\\\10y = 110\\y = \frac{110}{10}\\\\y = 11$

c)

$\frac{4x+1}{5x+3} = \frac{16}{34}$

$\frac{4x+1}{5x+3} = \frac{8}{17} \\\\68x + 17 = 40x + 24\\68x-40x = 24-17\\28x = 7\\x = \frac{7}{28} \\\\x = \frac{1}{4}\ ou\ 0,25$

d)

$\frac{4}{5} = \frac{x - 2}{x+2} \\\\4x + 8 = 5x - 10\\-x = -2\\x = 2$

Espero ter ajudado :)