Which of the following statements is a tautology and why is it that right answer a. integers are rational numbers. b. whole numbers are natural numbers. c. rational numbers are irrational. d. irrational numbers are integers.

Well, we know that N ⊂ Z ⊂ Q ⊂ R

This means that the naturals are included in the integers, the integers (and the naturals) are included in the rationals, and the rationals are included in the reals.

Then, A is a tautology.

B is false, because the 0 is not a natural number,

C is false, because the irrational numbers are the complement of the rational numbers.

D you can see that the integers are irrationals, but not all irrationals are integers, so this also is false.

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°