9th Grade Math Practice

Front

What happens to the mean of a set of numbers if a constant is added to each number in the set?

Back

The mean increases by that constant.

Front

How do you solve the equation 3(x+2)-6x=12?

Back

First, distribute: 3x + 6 - 6x = 12. Combine like terms: -3x + 6 = 12. Subtract 6 from both sides: -3x = 6. Divide by -3: x = -2.

Front

What is the range of the function y = -2x + 3 if the domain is {0, 2, -6}?

Back

The range is {3, -1, -15}.

Front

How can you model the sum of three consecutive numbers?

Back

Let the first number be x. The consecutive numbers are x, x+1, and x+2. The equation is x + (x+1) + (x+2) = 123, which simplifies to 3x + 3 = 123.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and there are an infinite number of points that satisfy both equations.

Front

What is the formula for calculating the mean of a set of numbers?

Back

The mean is calculated by adding all the numbers together and dividing by the count of numbers.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

Front

What does it mean for two lines to be parallel in the context of a system of equations?

Back

Parallel lines have no points in common, meaning the system has no solutions.

Front

How do you find the x-intercept of a linear equation?

Back

Set y to 0 and solve for x.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes (positive or negative).