Simplify: $$(3x^8y^{-4})(4x^{-2}y^{-9})$$

Using the laws of exponents, we combine the coefficients and add the exponents: 3 * 4 = 12, x^{8-2} = x^6, y^{-4-9} = y^{-13}. Thus, the result is $$\frac{12x^6}{y^{13}}$$ .

Definition: Inequality

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other, using symbols like >,

Definition: Distributive Property

The distributive property states that $$a(b + c) = ab + ac$$ . It allows you to multiply a single term by two or more terms inside a parenthesis.

Definition: Exponent Rules

When multiplying like bases, add the exponents: $$a^m * a^n = a^{m+n}$$ . When dividing, subtract the exponents: $$a^m / a^n = a^{m-n}$$ .

Definition: Function Notation

Function notation is a way to represent functions. If f is a function, then f(x) represents the output of the function f for the input x.

Definition: Slope of a Line

The slope of a line measures its steepness and is calculated as the change in y over the change in x, often represented as $$m = \frac{\Delta y}{\Delta x}$$ .

Definition: Y-Intercept

The y-intercept is the point where a line crosses the y-axis, represented as (0, b) in the equation of a line $$y = mx + b$$ .

Definition: Polynomial

A polynomial is a mathematical expression that consists of variables raised to whole number exponents and coefficients, such as $$2x^3 + 3x^2 - x + 5$$ .

Definition: Coefficient

A coefficient is a numerical or constant quantity placed before a variable in an algebraic expression, such as 5 in $$5x$$ .

NC Math 1 EOC Review Packet #1 Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Back

To solve for x, first isolate x on one side of the inequality. Subtract 2x from both sides: 3 > 2x - 3. Then add 3 to both sides: 6 > 2x. Finally, divide by 2: 3 > x or x < 3.

2.

FLASHCARD QUESTION

Front

Back

Using the distributive property (FOIL), we get: 5x * 3x + 5x * (-1) + 2 * 3x + 2 * (-1) = 15x^2 - 5x + 6x - 2 = 15x^2 + x - 2.

3.

FLASHCARD QUESTION

Front

Back

Substituting -3 into the function: f(-3) = -2(-3)^2 + 5(-3) + 4 = -2(9) - 15 + 4 = -18 - 15 + 4 = -29.

4.

FLASHCARD QUESTION

Front

Back

First, add 7x to both sides: 5 = 5x + 15. Then, subtract 15 from both sides: -10 = 5x. Finally, divide by 5: x = -2.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Definition: Linear Equation

Back

7.

FLASHCARD QUESTION

Front

Definition: Quadratic Function

Back

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