Final answer:
The question pertains to the Segment Addition Postulate in geometry, but the given expression for segment QO seems to contain a typo. As written, with QO equating to a constant negative value, we cannot apply the postulate. Correct segment length expressions are needed to verify the equations.
Step-by-step explanation:
The question refers to the Segment Addition Postulate, which states that if B is between A and C, then AB + BC = AC. To check if the given equations meet this postulate for segment QO, we must verify if the lengths QA + AO equal QO. Starting with the given equations: QA = 4x+9, AO = 2x+4, and QO = 20-50. It seems there might be a typo in the expression for QO, assuming it should be a linear expression involving x, similar to the other two. However, as written, QO is not dependent on x and is a constant value, which doesn't align with the premise of the postulate when we have expressions for QA and AO that are dependent on x. Moreover, the expression 20-50 yields a negative value, which does not make sense in the context of a segment length. To correct this and proceed with the application of the postulate, we would need a valid expression for QO in terms of x.
Without the correct expressions, we cannot check the Segment Addition Postulate. The given reference information regarding quadratic equations and vector components does not directly apply to solving this geometry question. Therefore, without the correct information for segment QO, we cannot verify the equations in question.