Review Questions

Front

What is the formula to find the center of a circle given its diameter endpoints?

Back

The center of a circle can be found using the formula: \( C = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \) where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the endpoints of the diameter.

Front

How do you calculate the area of a rectangle?

Back

The area of a rectangle is calculated using the formula: \( A = \text{length} \times \text{width} \).

Front

What is the formula for the area of a rectangle with variable dimensions?

Back

For a rectangle with dimensions \( (10x + 4) \) ft long and \( (7x) \) ft wide, the area is: \( A = (10x + 4)(7x) = 70x^2 + 28x \) square feet.

Front

What is a linear sequence?

Back

A linear sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

How do you find the nth term of a linear sequence?

Back

The nth term of a linear sequence can be found using the formula: \( a_n = a_1 + (n - 1)d \) where \( d \) is the common difference.

Front

What is the formula for the nth term of Becky's earnings?

Back

Becky's earnings can be modeled by the formula: \( a_n = 42.5n + 307.5 \).

Front

What is function subtraction?

Back

Function subtraction involves subtracting the output of one function from another, represented as: \( h(x) = f(x) - g(x) \).

Front

How do you subtract two quadratic functions?

Back

To subtract two quadratic functions, combine like terms after substituting the functions into the subtraction formula.

Front

What is the significance of parallel lines in a system of equations?

Back

Parallel lines in a system of equations indicate that there are no solutions, as they never intersect.

Front

What does it mean if two lines in a system of equations are the same?

Back

If two lines in a system of equations are the same, it means there are infinitely many solutions, as every point on the line is a solution.