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 plus 5 x plus 31

−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

Answer 1

To find the quadratic equation that matches the given problem, let's break down 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. The equation states that this sum is equal to thirty-one, so we set up the equation:

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

This matches the option:

−6x² + 5x = 31

So the correct response is:

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