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6. If M is replaced by one of the following numbers, the product \( (M-10)(M+14) \) becomes a perfect square. A. 0 B. 12 C. 14 D. 16 E. 18

Ask by Riley Potter. in South Africa
Mar 14,2025

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\( M = 18 \) makes \( (M-10)(M+14) \) a perfect square.

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To determine which value of \( M \) makes \( (M - 10)(M + 14) \) a perfect square, we can evaluate each option: A. \( M = 0 \): \[ (0 - 10)(0 + 14) = (-10)(14) = -140 \] (not a perfect square) B. \( M = 12 \): \[ (12 - 10)(12 + 14) = (2)(26) = 52 \] (not a perfect square) C. \( M = 14 \): \[ (14 - 10)(14 + 14) = (4)(28) = 112 \] (not a perfect square) D. \( M = 16 \): \[ (16 - 10)(16 + 14) = (6)(30) = 180 \] (not a perfect square) E. \( M = 18 \): \[ (18 - 10)(18 + 14) = (8)(32) = 256 \] (which is \( 16^2 \), a perfect square) Thus, the answer is **E. 18**.

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