Self Practice 2024-12-27 P1: Answer Only

Front

What is a ratio?

Back

A ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, a ratio of 4:5 means for every 4 of the first item, there are 5 of the second.

Front

How do you find the number of girls in a group if the ratio of boys to girls is given?

Back

To find the number of girls, set up the equation based on the ratio. If the ratio of boys to girls is 4:5 and there are 3 more girls than boys, let the number of boys be 4x and girls be 5x. Then, solve for x using the equation 5x = 4x + 3.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if they intersect at a right angle (90 degrees). The slopes of perpendicular lines are negative reciprocals of each other.

Front

How do you find the x- and y-intercepts of a line?

Back

To find the x-intercept, set y = 0 in the equation and solve for x. To find the y-intercept, set x = 0 and solve for y.

Front

What is the relationship between the sum and difference of two numbers?

Back

The sum of two numbers is the result of adding them together, while the difference is the result of subtracting one from the other. If the sum is 99 and the difference is 9, you can set up the equations: x + y = 99 and x - y = 9.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees. The side opposite the right angle is called the hypotenuse.

Front

How do you express a ratio in simplest form?

Back

To express a ratio in simplest form, divide both terms of the ratio by their greatest common divisor (GCD). For example, the ratio 4:8 can be simplified to 1:2.

Front

What is the Pythagorean theorem?

Back

Front

How do you solve a system of equations?

Back

To solve a system of equations, you can use methods such as substitution, elimination, or graphing. The goal is to find the values of the variables that satisfy all equations in the system.

Front

What is a variable in mathematics?

Back

A variable is a symbol, often a letter, that represents a number in mathematical expressions or equations. For example, in the equation x + 2 = 5, x is the variable.