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)

Question

Responses

−6x2−5x+31
negative 6 x squared minus 5 x plus 31

6x2−5x=31
6 x squared minus 5 x is equal to 31

−6x2+5x=31
negative 6 x squared plus 5 x is equal to 31

−6x2+5x+31

Answer 1

To translate the given statement into a quadratic equation, we can break down the components of the statement:

1. "The product of negative six and a number squared" translates to \(-6x^2\).
2. "The product of five and the same number" translates to \(5x\).
3. "Is thirty-one" translates to \(= 31\).

Putting it all together, we get the equation:

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

Thus, the correct response is: −6x² + 5x = 31 (negative 6 x squared plus 5 x is equal to 31).