If Joseph was Jesus's adoptive father then did Jesus really have David's blood?

I'm new to this site, but I'm as well searching for answers of several questions I've been facing. Last Monday, I had a question involving the relationship of Jesus and Joseph. So far I know, Joseph has been a long-descendant of David. and I believe Jesus was also supposed to have David's blood, because that was the reason why Joseph became his 'mortal father' But since Maria was pregnant without involving intercourse with Joseph, then Joseph would theoretically have adopted Jesus as his son, breaking the connection of David's blood. So, to repeat my question again, Is it true that Jesus has the blood from Joseph and finally, also David?