Start by adding the whole part of the numbers
[tex]4+5=9[/tex]then add the fractions
[tex]\frac{1}{2}+\frac{3}{4}=\frac{4+6}{8}=\frac{10}{8}=\frac{5}{4}=1\frac{1}{4}[/tex]since the fraction also gave a mixed number it can be added to the whole part we already had
[tex]9+1\frac{1}{4}=10\frac{1}{4}[/tex]The correct answer option is the fourth one.