Multiple choice

y = x2 − 4x + 4 and y = 2x − 5 Quantity A The value of x that satisfies both the equations Quantity B 6

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

x^2 - 4x + 4 = 2x - 5. x^2 - 6x + 9 = 0. (x-3)^2 = 0. x = 3. Quantity A = 3. Quantity B = 6. Since 6 > 3, Quantity B is greater.

AI explanation

To find the value of x that satisfies both equations, substitute 2x - 5 for y in the first equation to get 2x - 5 = x^2 - 4x + 4. Rearranging this gives the quadratic equation x^2 - 6x + 9 = 0, which factors into the perfect square (x - 3)^2 = 0. Solving this yields a single value for Quantity A of x = 3. Since Quantity B is 6, Quantity B is greater.

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