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The variables x and y are connected by the equation y = x³ − 5x² − x + 5 as shown in the table. Calculate the value of q.

Mathematics

ScanSolve AI Answer

Answer

-15
Graph of y = x³ − 5x² − x + 5

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Key points of y = x³ − 5x² − x + 5
Pointxy
x-intercept−10
Maximum−0.15.05
y-intercept05
x-intercept10
Minimum3.43−16.9
x-intercept50

Step-by-step solution

4 steps

To calculate the value of qq, we need to substitute the corresponding xx value into the given equation.

  1. Identify the equation and the value of xx for qq.

    The given equation is y=x3−5x2−x+5y = x^3 - 5x^2 - x + 5.
    From the table, when x=4x=4, y=qy=q.

  2. Substitute x=4x=4 into the equation.

    q=(4)3−5(4)2−(4)+5q = (4)^3 - 5(4)^2 - (4) + 5

  3. Calculate the terms.

    q=64−5(16)−4+5q = 64 - 5(16) - 4 + 5 q=64−80−4+5q = 64 - 80 - 4 + 5

  4. Perform the arithmetic operations.

    q=−16−4+5q = -16 - 4 + 5 q=−20+5q = -20 + 5 q=−15q = -15

    The value of qq is −15\boxed{-15}.

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