Answer
The required value is $\mathbf{v}\cdot \mathbf{w}=-18$.
Work Step by Step
We need
$\mathbf{v}\cdot \mathbf{w}$
And,
$\begin{align}
& \mathbf{v}=-5\mathbf{i}+2\mathbf{j} \\
& \mathbf{w}=2\mathbf{i}-4\mathbf{j}
\end{align}$
So,
$\begin{align}
& \mathbf{v}\cdot \mathbf{w}=\left( -5\mathbf{i}+2\mathbf{j} \right)\cdot \left( 2\mathbf{i}-4\mathbf{j} \right) \\
& =\left( -5\cdot 2 \right)+\left( 2\cdot -4 \right) \\
& =\left( -10 \right)-8 \\
& \mathbf{v}\cdot \mathbf{w}=-18
\end{align}$
So,
$\mathbf{v}\cdot \mathbf{w}=-18$
Therefore, the required value is
$\mathbf{v}\cdot \mathbf{w}=-18$.
