10
QuizMultiple Choice

Systems of Inequalities

Question 10 • Precalculus

The sum of the squares of two different numbers is less than or equal to 49. Twice one of the numbers squared is less than the other number. Which system of inequalities represents these criteria?

Answer
A
x2 + y2 ≤ 49 and 2x2 < y
B
x2 + y2 ≥ 49 and 2x2 < y
C
x2 + y2 ≤ 49 and x2 < 2y
D
x2 + y2 ≥ 49 and x2 < 2y

Explanation

Let the two numbers be x and y. Their squared values have a sum of at most 49, so x² + y² ≤ 49. “Twice one of the numbers squared is less than the other number” means 2x² < y. Together, these inequalities are choice A.

AI-written and checked against the verified answer.