Select the quadratic equation that is equivalent to: The product of 4 and a number squared, minus the product of 8 and that same number is 7(1 point)

Question

Responses

4x2−8x+7
4 x squared minus 8 x plus 7

−4x2+8x=7
negative 4 x squared plus 8 x is equal to 7

4x2−8x=7
4 x squared minus 8 x is equal to 7

−4x2−8x+7

Answer 1

Let's analyze the problem step by step.

The problem states: "The product of 4 and a number squared, minus the product of 8 and that same number is 7."

1. Let the number be represented by \(x\).
2. The product of 4 and a number squared can be expressed as \(4x^2\).
3. The product of 8 and that same number is represented as \(8x\).
4. Therefore, we can combine these ideas into the equation:

\[ 4x^2 - 8x = 7 \]

This equation states that 4 times the square of the number minus 8 times the number equals 7.

So, the equivalent quadratic equation is:

4x² - 8x = 7

This corresponds to the option:

4x² - 8x = 7 (4 x squared minus 8 x is equal to 7).