Question

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

Answer 1

To translate the given statement into a quadratic equation, we first break down the phrase: "the product of negative six and a number squared, plus the product of five and the same number is thirty-one."

Let's denote the unknown number as \( x \). Now, we can rephrase the statement in mathematical terms:

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

Putting it all together, we have:

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

Now, rearranging this into standard form gives us:

\[
-6x^2 + 5x - 31 = 0
\]

However, the equivalent equation of the phrasing provided is:

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

Thus, the correct response from the given options is:

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