Given that p = (-2/5) and q = (-6/5), evaluate |p + 2q| giving the answer to two decimal places.

Given vector $q = \begin{pmatrix} -6 \\ 5 \end{pmatrix}$, multiply each component by 2:

$$2q = 2 \begin{pmatrix} -6 \\ 5 \end{pmatrix} = \begin{pmatrix} 2 \times (-6) \\ 2 \times 5 \end{pmatrix} = \begin{pmatrix} -12 \\ 10 \end{pmatrix}$$

Given vector $p = \begin{pmatrix} -2 \\ 5 \end{pmatrix}$ and $2q = \begin{pmatrix} -12 \\ 10 \end{pmatrix}$, add the corresponding components:

$$p + 2q = \begin{pmatrix} -2 \\ 5 \end{pmatrix} + \begin{pmatrix} -12 \\ 10 \end{pmatrix} = \begin{pmatrix} -2 + (-12) \\ 5 + 10 \end{pmatrix} = \begin{pmatrix} -14 \\ 15 \end{pmatrix}$$

The magnitude of a vector $\begin{pmatrix} x \\ y \end{pmatrix}$ is given by $\sqrt{x^2 + y^2}$.
For $p + 2q = \begin{pmatrix} -14 \\ 15 \end{pmatrix}$:

$$|p + 2q| = \sqrt{(-14)^2 + (15)^2}$$ $$|p + 2q| = \sqrt{196 + 225}$$ $$|p + 2q| = \sqrt{421}$$

$$\sqrt{421} \approx 20.5182845$$

Rounding to two decimal places:

$$|p + 2q| \approx 20.52$$

The value of $|p + 2q|$ to two decimal places is:

$$20.52$$