Final answer:
Upon examining each pair from the list provided, none of them satisfy the condition where one factor is 11 less than half of the other factor. Therefore, there are no correct options from the given list.
Step-by-step explanation:
To find the pairs of factors of -36 that satisfy the given condition where one factor is 11 less than half of the other factor, we can setup the following equation for each pair:
Let x be one factor, then the other factor, y, satisfies the condition y = (1/2)x - 11. Since the factors of -36 multiply to give -36, we have the equation xy = -36.
Substituting y into the equation gives us x((1/2)x - 11) = -36, which simplifies to (1/2)x² - 11x + 36 = 0. This is a quadratic equation, which can be solved for x, and subsequently for y, to find the pairs of factors. However, since we are provided with a list of possible answers, we can test each pair directly:
- A. -2 and 18: -2 = (1/2)(18) - 11 (-2 does NOT equal 9 - 11)
- B. 4 and -9: 4 = (1/2)(-9) - 11 (4 does NOT equal -4.5 - 11)
- C. -6 and 6: -6 = (1/2)(6) - 11 (-6 does NOT equal 3 - 11)
- D. 3 and -12: 3 = (1/2)(-12) - 11 (3 does NOT equal -6 - 11)
None of the provided pairs satisfies the condition. Therefore, there are no correct options from the given list.