Final answer:
Option (d) (3a + 2b) is the algebraic expression. It contains variables and coefficients being added together, without an equals sign. The other options are either arithmetic expressions or equations.
Step-by-step explanation:
An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y), and operators (like add, subtract, multiply, and divide). The question asks which of the provided options is an algebraic expression.
- (0 - 1 + 5(4)) is an arithmetic expression, as it only contains numbers and operations.
- (x + 3 = 4) is an equation, not a simple expression, because it includes an equals sign.
- (x + 2y = 6) is also an equation, for the same reason as above.
- (3a + 2b) is the correct answer; this is an algebraic expression, because it only contains variables and coefficients being added together, with no equals sign present.
A quadratic equation is a specific type of algebraic equation which can be of the form at² + bt + c = 0. To solve a quadratic equation like x² + 1.2 x 10⁻²x - 6.0 × 10⁻³ = 0, one can utilize the quadratic formula where a, b, and c are constants in the quadratic equation's standard form.
In practice tests or exercises where you need to identify linear vs. quadratic equations, remember that linear equations take the form y = mx + b and do not have any variables raised to the power higher than one. Equations like y = 10 + 5x − 3x² are not linear due to the term -3x², indicating it's a quadratic equation.