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Select the quadratic equation that is equivalent to: the product of negative six and a number squared, plus the product of five and the same number is thirty-one.(1 point) Responses −6x2−5x+31−6x2−5x+31negative 6 x squared minus 5 x plus 31 −6x2+5x=31−6x2+5x=31negative 6 x squared plus 5 x is equal to 31 6x2−5x=316x2−5x=316 x squared minus 5 x is equal to 31 −6x2+5x+31

1 answer

To translate the statement "the product of negative six and a number squared, plus the product of five and the same number is thirty-one" into a quadratic equation, we can follow these steps:

  1. Let the unknown number be represented by \( x \).
  2. "The product of negative six and a number squared" translates to \( -6x^2 \).
  3. "The product of five and the same number" translates to \( 5x \).
  4. Combine these to get the left-hand side of the equation: \( -6x^2 + 5x \).
  5. Setting this equal to thirty-one gives us the equation:

\[ -6x^2 + 5x = 31. \]

Now, compare this with the given options:

  • \( -6x^2 - 5x + 31 \) (not equivalent)
  • \( -6x^2 + 5x = 31 \) (this is the correct one)
  • \( 6x^2 - 5x = 31 \) (not equivalent)
  • \( -6x^2 + 5x + 31 \) (not equivalent)

The correct response is:

−6x² + 5x = 31.