5. Considerar los subespacios vectoriales: \( \mathrm{S}=\left\{(x ; y ; z) \in \mathrm{R}^{3} / x+y=z\right\} \) y \( \mathrm{W}=\left\{(x ; y ; z) \in \mathrm{R}^{3} / 2 x-y+z=0\right\} \) a) Calcular \( S+W \), indicando si la suma es directa. Interpretar geométricamente.

Solve the equation by factoring. Select the correct solution. \( 6 x^{2}-5 x-4=0 \) \( \begin{array}{ll}\text { O } & \text { A) } x=-\frac{4}{3},-\frac{1}{2} \\ \text { O } & \text { B) } x=-\frac{1}{2}, \frac{4}{3} \\ \text { O } & \text { C) } x=-\frac{4}{3}, \frac{1}{2} \\ \text { - } & \text { D) } x=\frac{1}{2}, \frac{4}{3}\end{array} \)

1. Louls owns his own orchard. He plants 5 fruit trees for every 5 nut tiees. The equation \( f=\frac{9}{5} n \) models the relationship between the number of nut trees planted and the number of fruit trees planted. Determine the number of nut trees planted if 135 fruit trees were planted.

Write in exponential form. \[ \log _{6} 216=3 \] Write the equivalent exponential equation. \( \square \) (Type an equation. Type your answer using expc

b. \( -0.5 p+\frac{1}{2} p-2.75+\frac{2}{3} \)

Use the distributive property to fill in the blanks below. \( 6 \times(9-4)=(\llbracket \times 9)-(\square \times 4) \) Introduction to the distributive property