Q: When I google a dominant chord it's always represented to be  structured like a major chord. But the way I'm always forced to encounter it is as the 1st, 3rd, b7th. Why is that?
A: well if it has a 3rd it's the major 3rd. but honestly the core of a dom7 chord is the tritone in it. really that's the core of what the harmony needs to be doing. the bass will play the bass note. but the 5th note is really not useful. so if the 5th is not there, don't be surprised. the 5th will be there in the schools, but usually not in actual real life