Question

Determine os valores de x e y nos feixes de retas paralelas cortados pelas transversais r e s dados em cada item. PF mande os cálculos

Answer 1

$\tt c)~\sf\dfrac{x}{10}=\dfrac{9\div3}{12\div3}\\\sf\dfrac{x}{10}=\dfrac{3}{4}\\\sf4x=30\\\sf x=\dfrac{30\div2}{4\div2}\\\sf x=\dfrac{15}{2}$

$\tt d)~\sf\dfrac{x+1}{x-1}=\dfrac{12}{x+2}\\\sf(x+1)\cdot(x+2)=12(x-1)\\\sf x^2+2x+x+2=12x-12\\\sf x^2+3x-12x+2+12=0\\\sf x^2-9x+14=0\\\sf\Delta=(-9)^2-4\cdot1\cdot14\\\sf\Delta=81-56\\\sf\Delta= 25\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-(-9)\pm\sqrt{25}}{2\cdot1}\\\sf x=\dfrac{9\pm5}{2}\begin{cases}\sf x_1=\dfrac{9+5}{2}=\dfrac{14}{2}=7\\\sf x_2=\dfrac{9-5}{2}=\dfrac{4}{2}=2\end{cases}$

$\tt e)~\sf\dfrac{2x}{\diagdown\!\!\!\!\!\!15_3}=\dfrac{x+1}{\diagdown\!\!\!\!\!\!10_2}\\\sf\dfrac{2x}{3}=\dfrac{x+1}{2}\\\sf 4x=3x+3\\\sf 4x-3x=3\\\sf x=3$