The correct answer is D

Explanation

Roman Numeral Answer Format

Roman Numeral roman numeral 1: Can the value of x be negative 1 over 3?

You could test this answer by substituting negative 1 over 3 for x in the equation and seeing whether the result is true. But you can also reason this question out without substituting numbers:

If x = negative 1 over 3, then (negative (1 over 3))^2 is a positive number, because any nonzero number squared is positive.

If x = negative 1 over 3, then x over 3 is negative.

So x over 3 is negative and x^2 is positive.

Therefore, x cannot be negative 1 over 3.

Mark Roman numeral roman numeral 1 with an “F” for false.

Roman Numeral roman numeral 2: Can the value of x be 0?

This is a very easy substitution to make:

x over 3 = x^2

0 over 3 = 0^2 = 0

Roman numeral roman numeral 2 is true, so mark it with a “T” for true.

Roman Numeral roman numeral 3: Can the value of x be 1 over 3?

Substitute 1 over 3 for x:

If x = 1 over 3, then x over 3 = 1 over 9.

Also, x^2 = (1 over 3)^2 = 1 over 9.

Roman numeral roman numeral 3 is true, so mark it with a “T” for true.

Check the Answers:

You now know whether each of the Roman numeral statements is true or false:

roman numeral 1 is false.
roman numeral 2 is true.
roman numeral 3 is true.

Find the choice that says only roman numeral 2 and roman numeral 3 are true.