Answer:
The correct answer is A.; C.; E.
Step-by-step explanation:
A. Negative integers are rational numbers because all integers are rational numbers, i.e. integers are a subset of rational numbers, making the statement correct.
B. Mixed numbers are rational numbers because they can be written in the form of a simple fraction and thus the statement B is wrong.
C. Decimal numbers that terminate, like 0.125, are rational numbers is true as they can be written as a simple fraction making the statement true.
D. Decimal numbers that go on forever with repeating patterns, like 4.272727..... are irrational numbers is false as they can also be represented by a simple function making them rationals.
E. Decimal numbers that go on forever with no repeating patterns are irrational numbers as they can never be written as a simple fraction making the statement E true.