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

−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.