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

−6x^2+5x+31

6x^2−5x=31


−6x^2+5x=31

−6x^2−5x+31

Answer 1

To determine which option is equivalent to the statement provided, let's break down the statement step by step.

The statement is: "the product of negative six and a number squared, plus the product of five and the same number is thirty-one."

1. "the product of negative six and a number squared" can be expressed as:
\(-6x^2\)

2. "plus the product of five and the same number" can be expressed as:
\(+ 5x\)

3. "is thirty-one" translates to:
\(= 31\)

Putting it all together, we write the equation based on the statement:
\[
-6x^2 + 5x = 31
\]

Now, looking at the provided options, the correct equivalent quadratic equation is:
**−6x^2 + 5x = 31**.