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Answer :
The best answer that describes the meaning of the multiplicities next to the number 1 in the preceding diagram is: the number 1 represents the solution that repeats thrice.
A multiplicity is a mathematical concept used to describe the number of times a value appears as a root of a polynomial equation. The number of times a specific value appears as a root of a polynomial is referred to as the multiplicity of that value.
In the given diagram, the number 1 represents the solution of the equation x = 1. The multiplicities of the number 1 are represented by the number 3.
Therefore, the number 1 has a multiplicity of 3. This means that the solution of the equation x = 1 repeats thrice. This can be better understood by looking at the graph of the equation.
The graph of the equation x = 1 is a vertical line that intersects the x-axis at 1.
Since the equation has a multiplicity of 3, the vertical line intersects the x-axis three times.
This means that the point (1, 0) occurs three times on the graph. This is shown in the diagram as three dots along the x-axis.
Therefore, the meaning of the multiplicities next to the number 1 in the preceding diagram is that the number 1 represents the solution that repeats thrice.
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