Multiple choice

Directions: Solve the given equations and identify the correct answer. 10x2 - 20x - 80 = 0 y2 + 13y - 68 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or relation cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving 10x^2 - 20x - 80 = 0 gives x^2 - 2x - 8 = 0, so (x-4)(x+2)=0, x=4 or -2. Solving y^2 + 13y - 68 = 0 gives (y+17)(y-4)=0, y=-17 or 4. Comparing the sets, x >= y is true because the maximum value of x is 4 and the maximum value of y is 4, and all other combinations satisfy the inequality.

AI explanation

Dividing the first equation by 10 gives x^2 - 2x - 8 = 0, which factors into (x - 4)(x + 2) = 0 to yield x = 4 or x = -2. Factoring the second equation y^2 + 13y - 68 = 0 gives (y + 17)(y - 4) = 0, yielding y = 4 or y = -17. Since x equals or exceeds the values of y, x >= y.

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