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) - 6x ^ 2 + 5x = 31; 6x ^ 2 - 5x = 31; - 6x ^ 2 - 5x + 31; - 6x ^ 2 + 5x + 31

Answer 1

To form the quadratic equation from the given statement, let's break it down 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."

Let the variable \( x \) represent "the number."

1. Product of negative six and a number squared: This translates to \( -6x^2 \).
2. Product of five and the same number: This translates to \( 5x \).
3. The equation states this total is equal to thirty-one: So we have: \[ -6x^2 + 5x = 31 \]

Now, rearranging this equation to standard form: \[ -6x^2 + 5x - 31 = 0 \]

However, this is not one of the options provided. But the equivalent expression in terms of equality to \( 31 \) would be \( -6x^2 + 5x - 31 = 0 \).

The closest form among the given choices that reflects this equation accurately is:

-6x² + 5x = 31.

Hence, the equivalent quadratic equation is: -6x² + 5x = 31.