Final answer:
The correct answer for YZ using the provided equations is 'YZ = 9' after substituting the value of x calculated from the equations into the expression for YZ.
Step-by-step explanation:
The correct answer is option 'YZ = 9'. To solve for YZ using the given information RY = 2x + 9, YZ = 4x + 1, and RZ = 3x + 16, one must understand that in a geometric line segment, the sum of two smaller segments equals the larger segment when the smaller segments are consecutive and span the larger segment.
Hence, RY + YZ = RZ. Substituting the given expressions gives us (2x + 9) + (4x + 1) = (3x + 16). Simplifying this equation yields 6x + 10 = 3x + 16. Solving for x, we subtract 3x from both sides to get 3x + 10 = 16. Subtracting 10 from both sides, yields 3x = 6, and dividing by 3 gives us x = 2. Substituting x = 2 into the expression for YZ, we have YZ = 4(2) + 1 = 8 + 1 = 9.