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Point P is on line segment bar (OQ). Given OP=x-3,PQ=1, and OQ=3x-10, determine the numerical length of bar (OP).

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Final answer:

To find the length of bar (OP), we use the formula for the length of a line segment and solve an equation to determine the value of x. Substituting the value of x back into the equation gives us the numerical length of bar (OP), which is 1.

Step-by-step explanation:

To find the length of bar (OP), we can use the formula for the length of a line segment, which is the difference between the coordinates of the two endpoints. In this case, the coordinates of O and P are given by OQ = OP + PQ. So, we can substitute the given values into the equation and solve for OP.

Given OQ = 3x - 10, OP = x - 3, and PQ = 1, we can write the equation:

3x - 10 = (x - 3) + 1

Now, we can solve the equation to find the value of x:

3x - 10 = x - 2

2x = 8

x = 4

Substituting the value of x back into the equation for OP:

OP = 4 - 3 = 1

Therefore, the numerical length of bar (OP) is 1.

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