Select the quadratic equation that is equivalent to: the product of six and a number squared, minus the product of five and the same number is thirteen.

Question

Responses

6 x squared plus 5 x is equal to 13

5 x squared minus 6 x is equal to 13

6 x squared minus 5 x is equal to 13

Answer 1

To convert the verbal statement into an equation, let's break it down step by step.

1. "The product of six and a number squared" translates to \(6x^2\).
2. "The product of five and the same number" translates to \(5x\).
3. The phrase "minus" indicates subtraction.
4. Therefore, we can combine these parts: \(6x^2 - 5x\).
5. The statement ends with "is thirteen," which means we set the equation equal to 13.

Putting it all together, we have the equation:

\[ 6x^2 - 5x = 13 \]

To express this as equivalent to a standard form quadratic equation, we can rearrange it as:

\[ 6x^2 - 5x - 13 = 0 \]

However, from the given response options, the one that matches our formulation before rearranging is:

6 x squared minus 5 x is equal to 13.

So the correct choice is:

6 x squared minus 5 x is equal to 13.