Question

Atividade de Matemática.Eles são inversamente proporcionais .determine os valores de x e y ​

Answer 1

Devido ser inversamente

invertemos a fração⤴️ $\frac{7}{10}\\\\Fica\:\frac{10}{7}$

a)

$\frac{7}{10} = \frac{5}{x} = \frac{2}{y} \Rightarrow \\ \\ \Large \purple{\frac{10}{7} = \frac{5}{x} = \frac{2}{y} } \\ \\ \frac{10}{7} = \frac{5}{x} \\ \\ 10x = 35 \\ \\ x = \frac{35 \div 5}{10 \div 5} \\ \\ \Large \boxed{ \green{ x = \frac{7}{2} }} \\ \\ \frac{10}{7} = \frac{2}{y} \\ \\ 10y = 14 \\ \\ y = \frac{14 \div 2}{10 \div 2} \\ \\ \Large \boxed{ \green{ y = \frac{7}{5} }}$

b)

$\frac{y}{4} = \frac{12}{8} = \frac{6}{x} \Rightarrow \\ \\ \Large \purple{\frac{y}{4} = \frac{8}{12} }\\ \\ 12y = 32 \\ \\ y = \frac{32 \div 4}{12 \div 4} \\ \\ \Large \boxed{ \green{ y = \frac{8}{3} }} \\ \\ \frac{8}{12} = \frac{6}{x} \\ \\ 8x = 72 \\ \\ x = \frac{72}{8} \\ \\ \Large \boxed{ \green{ x = 9}}$

c)

$\frac{x}{3} = \frac{y}{5} = \frac{15}{9} \Rightarrow \\ \\ \Large\purple{\frac{x}{3} = \frac{y}{5} = \frac{9}{15} } \\ \\ \frac{x}{3} = \frac{9}{15} \\ \\ 15x = 27 \\ \\ x = \frac{27 \div 3}{15 \div 3} \\ \\ \large \boxed{ \green{x = \frac{9}{5} }} \\ \\ \frac{y}{5} = \frac{9}{15} \\ \\ 15y = 45 \\ \\ y = \frac{45}{15} \\ \\ \Large \boxed{ \green{y = 3}}$

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