If I was asked to think of a number and multiply it by 2,1 cou write this algebraically as \( 2 x \). Write the following algebraically, using \( x \) as your unknown. "I think of a number, multiply it by 3 and add 1 to the result."

IV. Encuentra la solución de las siguientes ecuaciones cuadráticas. (Valor: 15 Puntos) 1. \( 2 x^{2}+5 x+3=0 \) 2. \( x^{2}=3 x-1 \) 3. \( k(10 k-1)=2 \)

shane Athat \( (f \cdot 5)^{-1}=g^{-1} \cdot f^{-1} \) givonthat \( f(x)=\frac{x-1}{x+2} \) \( g(x)=\frac{5}{x-5} \)

1. \( \frac{x}{3}=\frac{2}{3} \) \( x=3(2)(3) \)

2 Find, in the form \( y=a x^{2}+b x+c \), the equation of the quadratic whose graph: a touches the \( x \)-axis at 4 and passes through \( (2,12) \) b has vertex \( (-4,1) \) and passes through \( (1,11) \)

If \( 25 \% \) of two-thirds of a number is 10 , find the number. \( \begin{array}{ll}\text { A) } 75 & \text { B) } 120 \\ \text { C) } 60 & \text { D) } 30\end{array} \)