Final answer:
The statement is false. When y varies directly as the square of x and given that Y = -54 when x = 9, the correct value of Y when x = 6 is calculated to be -24 not -15.
Step-by-step explanation:
If y varies directly as the square of x, then there exists a constant k such that
y = kx2. Given that y = -54 when x = 9, we can find the constant k by substituting these values into the direct variation equation: y = kx2, which gives us -54 = k × 92, or -54 = k × 81. Solving for k yields
k = -54/81 = -2/3. To check if Y = -15 when x = 6, we substitute these values into the direct variation equation with our found constant k: Y = (-2/3) × 62 equals
Y = (-2/3) × 36, which simplifies to Y = -24.
Therefore, the statement Y = -15 when x = 6 is false because when we substitute x = 6 into our direct variation equation, we get Y = -24, not Y = -15.