Solve the equation for \( k \):

\[
\frac{2}{5} + \frac{k}{4} = \frac{9}{10}
\]

**Solution Steps:**

1. Find a common denominator for the fractions. The least common multiple of 5, 4, and 10 is 20.
2. Rewrite each fraction with a denominator of 20:

\[
\frac{2}{5} = \frac{8}{20}, \quad \frac{9}{10} = \frac{18}{20}
\]

So the equation becomes:

\[
\frac{8}{20} + \frac{k}{4} = \frac{18}{20}
\]

3. Subtract \(\frac{8}{20}\) from both sides:

\[
\frac{k}{4} = \frac{18}{20} - \frac{8}{20} = \frac{10}{20} = \frac{1}{2}
\]

4. Solve for \( k \) by multiplying both sides by 4:

\[
k = \frac{1}{2} \times 4 = 2
\]

Therefore, \( k = 2 \).