Mathematics Lecture Notes

Flashcards based on lecture notes covering solving linear equations, quadratic equations, completing the square, and working with complex numbers.

What is the formula to solve for y given 2x + y = 23?

y = -2x + 23

What is the first step in solving the equation 5x + 2x - 23 = 5?

Combine like terms to get 7x - 23 = 5.

What does the quadratic formula x = -b ± √(b² - 4ac) help us solve for in the equation 4x² - x - 3 = 0?

It helps us find the values of x that satisfy the quadratic equation.

How do you complete the square for the equation x² - 1x - 9 = 0?

Rewrite it as (x - 3)² = 0.

What does it mean to express in the form a + bi?

It means to express a complex number where a is the real part and bi is the imaginary part.