A roofer throws a group of shingles into the trash bin on the ground below. The height of the shingles can be modelled by the function \( h(t)=-5 t^{2}+11 t+12 \), where \( h(t) \) is the height in metres, and \( t \) is the time in seconds. How long will it take the shingles to hit the bottom of the trash bin?

3. (*) Dado los vectores \( \vec{a}=\left(1,2 x_{1}, 3\right) \), \( \vec{b}=\left(-1,3 x_{2},-2 x_{1}\right), \vec{c}=\left(2,2,-3 x_{2}\right) \) los valores de \( x_{1} \quad y x_{2} \) para los cuales se cumple que \( 2 \vec{a}-3 \vec{b}+\vec{c}=(7,15,21) \) es respectivamente: a. \( (2,-1) \) b. \( (-1,2) \) c. \( (2,-3) \) d. \( (-3,1) \)

7. \( 2 x^{2}+x-4=0 \) \( \begin{array}{ll}\text { a. }-\frac{1}{2} \pm \frac{\sqrt{33}}{4} & \text { c. }-\frac{1}{4} \pm \frac{\sqrt{33}}{4} \\ \text { b. }-4 \pm \frac{\sqrt{66}}{4} & \text { d. }-\frac{1}{2} \pm \frac{\sqrt{33}}{2}\end{array} \)

Solve the inequality. Express the solution set in set-builder notation and interval notation. Graph the solution set on a real number line. \( \frac{1}{2}(n-4)>n+5 \)

Graph the parabola. \[ y=(x+2)^{2}+4 \] Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.

Solve the inequality. Express the solution set in set-builder notation and interval notation. Graph the solution set on a real number line. \[ 5(x-6)>4(x-6)+x \]