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

Question

GPT-4o mini · 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:

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

$- 6 x^{2} + 5 x = 31.$

Now, compare this with the given options:

$- 6 x^{2} - 5 x + 31$ (not equivalent)
$- 6 x^{2} + 5 x = 31$ (this is the correct one)
$6 x^{2} - 5 x = 31$ (not equivalent)
$- 6 x^{2} + 5 x + 31$ (not equivalent)

The correct response is:

−6x² + 5x = 31.