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
6 x squared minus 5 x is equal to 31

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

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

−6x2−5x+31

Answer 1

To write the quadratic equation based on the given statement, we start by translating it into mathematical expressions:

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 this all together, we have:

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

Thus, the equivalent quadratic equation is:

\(-6x^2 + 5x = 31\)

So the correct response is:

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