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+31−6x2−5x+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

Answer 1

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:

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

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

Now, compare this with the given options:

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

The correct response is:

**−6x² + 5x = 31**.