Answer:
5.625
Step-by-step explanation:
This question involves the use of the angle bisector theorem, which states that an angle bisector through an angle in a triangle creates proportionality, that is:
[tex]\frac{AC}{CB}=\frac{AD}{DB}[/tex]
Substituting the given values and solving for x yields:
[tex]\frac{4}{7.5}=\frac{3}{x}\\\text{Cross Multiplying}\\4x = 22.5\\\text{Divide by 4}\\x = 22.5/4 = \textbf{5.625}[/tex]
