Question

Identify the following as an expression or an equation. (4 points)
2x^2+3x+5
7x+3=1
24x^3=18
44•-2^x

Answer 1

Select the quadratic equation that is equivalent to: the product of eight and a number squared, minus the product of three and the same number is twenty-six. (1 point)

Answer 2

In mathematics, an **expression** is a combination of numbers, variables, and operations without an equality sign, while an **equation** is a statement that two expressions are equal, indicated by an equality sign (=).

1. **2x^2 + 3x + 5** - **Expression**
2. **7x + 3 = 1** - **Equation**
3. **24x^3 = 18** - **Equation**
4. **44 • -2^x** - **Expression**

So, the classifications are:
- Expression: 2x^2 + 3x + 5
- Equation: 7x + 3 = 1
- Equation: 24x^3 = 18
- Expression: 44 • -2^x

Answer 3

To express the given statement as a quadratic equation, we start by defining the unknown number as \( x \).

The phrase "the product of eight and a number squared" can be expressed mathematically as \( 8x^2 \).

The phrase "the product of three and the same number" can be written as \( 3x \).

Putting it all together, the entire statement reads:

\[ 8x^2 - 3x = 26. \]

To rearrange this into standard quadratic form (where one side equals zero), we subtract 26 from both sides:

\[ 8x^2 - 3x - 26 = 0. \]

Thus, the equivalent quadratic equation is:

\[ 8x^2 - 3x - 26 = 0. \]