Question

Which explains one way in which the Byzantine Empire continued the cultural traditions of the Romans?
by adapting some ancient Greek ideas
by using Latin as the primary written language
by restricting women to the inside of the home
by distracting the people with gladiatorial contests

Answer 1

Golly, who writes these questions? All of these have difficulties. The first is odd, because adapting ideas from some other culture is hardly continuing your own traditions. The second is true for the very early Eastern Empire, but the official language changed to Greek in the 7th century. The third is false (and even insulting), while the fourth seems silly, in part because gladiatorial combat is hardly an important or even unique aspect of Imperial Roman culture.

If I were forced to choose, I'd pick the second option (Latin).

Answer 2

The empire preserved Roman culture by creating a uniform code of law based on Roman law. These experts dropped outdated laws and rewrote others to make
them clearer. The new code was called the Justinian Code. The
code included laws on marriage, slavery, property ownership,
women’s rights, and criminal justice.
Although they spoke Greek, Byzantines thought of themselves
as part of the Roman cultural tradition. Byzantine students
studied Latin and Greek, and Roman literature and history. In
this way, the east preserved Greek and Roman culture. In the
former Western Empire, the Germanic peoples blended Roman
culture with their own. However, they lost much of the scientific
and philosophical knowledge of the Greeks and Romans. So overall your answer would be b. Using latin as a primary language.