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To find the value of the length X of the base of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is given by:
Volume = length x width x height
Given that the volume is 945 cm^3, the height is 15 cm, and the width is 7 cm, we can plug these values into the formula and solve for the length X:
945 = X * 7 * 15
945 = 105X
X = 945 / 105
X = 9
Therefore, the value of the length X of the base is 9 cm.