Mixed Review #1

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

How do you write an equation in slope-intercept form?

Back

Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the y-intercept represent in a graph?

Back

The y-intercept is the point where the graph crosses the y-axis, representing the value of y when x is 0.

Front

How do you solve the equation 3x + 2(4x - 4) = 3?

Back

First, distribute: 3x + 8x - 8 = 3. Combine like terms: 11x - 8 = 3. Add 8 to both sides: 11x = 11. Divide by 11: x = 1.

Front

What is the process to simplify an expression like (144k²r⁷)¹.⁵?

Back

Use the power of a power property: (a^m)^n = a^(m*n). So, (144k²r⁷)¹.⁵ = 144^1.5 * k^(2*1.5) * r^(7*1.5) = 12k³r¹⁴.

Front

What is the formula for finding the slope of a line?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1) between two points (x1, y1) and (x2, y2).

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What is the definition of a variable in mathematics?

Back

A variable is a symbol, often a letter, that represents a number in mathematical expressions or equations.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you multiply a by each term inside the parentheses.

Front

How do you find the value of y in the equation y = (5/3)x + 3 when x = 6?

Back

Substitute x with 6: y = (5/3)(6) + 3 = 10 + 3 = 13.