Compare x and y (define the answer codes): I. 17x^2 + 48x = 9 II. 13y^2 = 32y − 12 Choose: A) x > y B) x < y C) x = y D) Relationship cannot be determined

Introduction / Context:
We compare solutions from two quadratic relations. If every possible x is strictly less than every possible y, we can conclude x < y. Compute the roots for both to compare their ranges.

Given Data / Assumptions:

• I: 17x^2 + 48x − 9 = 0.
• II: 13y^2 − 32y + 12 = 0.

Concept / Approach:
Use quadratic formula to get all roots. Compare the largest x to the smallest y; if the largest x is still less than the smallest y, then every x is less than every y.

Step-by-Step Solution:

Verification / Alternative check:
Check all pairings: {−3, 0.17647} versus {0.46154, 2}; all comparisons show x < y.

Why Other Options Are Wrong:

• x > y or x = y: Contradicted by numeric ranges.
• Relationship cannot be determined: Not the case; strict separation exists.

Common Pitfalls:
Not identifying the smallest y and largest x correctly; mixing signs or miscomputing discriminants can flip conclusions.

Final Answer: