Identify the following as an expression or an equation. (4 points)

Question

2x^2+3x+5
7x+3=1
24x^3=18
44•-2^x

Answer 1

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 2

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 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:

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