Question

determine o valor de x e y​

Answer 1

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a) Temos que nos atentar que as retas estão cruzadas, então a relação é:

$\frac{x}{18} =\frac{9}{15} = \frac{3}{5}\\\\\\x = \frac{3*18}{5} = \frac{54}{5} = 10.8$

x = 10.8

b)

$\frac{3x+1}{5x-1} = \frac{4}{6} = \frac{2}{3}\\\\3(3x + 1) = 2(5x - 1)\\9x +3 = 10x - 2\\9x - 10x = -2 -3\\-x = -5\\x = 5$

x = 5

c)

$\frac{18}{20} = \frac{9}{10} = \frac{15}{x-5}\\\\9(x - 5) = 10 * 15\\9x - 45 = 150\\9x = 195\\x = \frac{195}{9} = \frac{65}{3} = 21,66...$

x = 21,66...

d)

$\frac{2x-2}{3x+1} = \frac{4}{7}\\\\7(2x-2) = 4(3x+1)\\14x - 14 = 12x + 4\\14x - 12x = 4 + 14\\2x = 18\\x = 9$

x = 9

e) Vamos achar primeiro o y:

$\frac{3}{6} = \frac{1}{2} = \frac{y}{8}\\\\2y = 8\\y = 4$

Com y = 4 podemos fazer:

$\frac{x}{3} = \frac{10}{y} = \frac{10}{4}\\\\4x = 3 * 10\\x = \frac{30}{4} = \frac{15}{2} = 7,5$

x = 7,5    y = 4