Math Midterm 2024 individual work

Front

What is the intersection point of the lines described by the equations y = x + 3 and y = \frac{-1}{5}x - 3?

Back

The intersection point is (-5, -2).

Front

How do you calculate the hourly charge of a technician if the total bill is $576.50 and the parts cost $109 for 5.5 hours of work?

Back

The technician charges $85/hour.

Front

Simplify the expression (5^{-2})^{-3}.

Back

The simplified expression is 5^{6}.

Front

Is the number 0.1875 rational or irrational?

Back

0.1875 is rational because it terminates.

Front

Is the number 0.95929409956639… rational or irrational?

Back

0.95929409956639… is irrational.

Front

What is a rational number?

Back

A rational number is any number that can be expressed as a fraction \frac{a}{b}, where a and b are integers and b ≠ 0.

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction; its decimal representation goes on forever without repeating.

Front

How do you find the slope of a line given its equation in the form y = mx + b?

Back

The slope (m) is the coefficient of x in the equation.

Front

What does it mean for a number to terminate?

Back

A terminating number has a decimal representation that ends after a finite number of digits.

Front

What is the formula for finding the intersection of two linear equations?

Back

To find the intersection, solve the equations simultaneously to find the values of x and y.