\[ f(x)=|-11+6 x| \quad g(x)=\frac{x^{2}+4}{x+4} \quad h(x)=-4+\sqrt{x-5} \] Find \( f\left(\frac{2}{3}\right), g(2) \), and \( h(8) \). Simplify your answers as much as possible. \[ \begin{array}{l}f\left(\frac{2}{3}\right)=7 \\ g(2)=\frac{4}{3} \\ h(8)=\square\end{array} \]

To find the values of \( f\left(\frac{2}{3}\right) \), \( g(2) \), and \( h(8) \), let's start by evaluating each function one by one: 1. **Calculating \( f\left(\frac{2}{3}\right) \)**: \[ f(x) = |-11 + 6x| \] Substituting \( x = \frac{2}{3} \): \[ f\left(\frac{2}{3}\right) = |-11 + 6 \cdot \frac{2}{3}| \] \[ = |-11 + 4| = |-7| = 7 \] 2. **Calculating \( g(2) \)**: \[ g(x) = \frac{x^2 + 4}{x + 4} \] Substituting \( x = 2 \): \[ g(2) = \frac{2^2 + 4}{2 + 4} = \frac{4 + 4}{2 + 4} = \frac{8}{6} \] \[ = \frac{4}{3} \] 3. **Calculating \( h(8) \)**: \[ h(x) = -4 + \sqrt{x - 5} \] Substituting \( x = 8 \): \[ h(8) = -4 + \sqrt{8 - 5} = -4 + \sqrt{3} \] Now we put it all together: \[ \begin{array}{l} f\left(\frac{2}{3}\right) = 7 \\ g(2) = \frac{4}{3} \\ h(8) = -4 + \sqrt{3} \end{array} \] Thus, the answer is: \[ h(8) = -4 + \sqrt{3} \]