Algebra Fundamentals Flashcards

Which equation represents a line perpendicular to y = 3x + 2?

Answer: y = -(1/3)x + 6

A perpendicular line has a slope that is the negative reciprocal of 3, which is -1/3.

Simplify: (2x³)⁴

Answer: 16x¹²

Apply the power rule: 2⁴ = 16 and (x³)⁴ = x¹², giving 16x¹².

Two trains leave a station simultaneously in opposite directions. One travels at 60 mph and the other at 80 mph. After how many hours are they 420 miles apart?

Answer: 3 hours

Combined speed = 140 mph; 420 ÷ 140 = 3 hours.

What are the roots of the equation x² - 6x + 9 = 0?

Answer: x = 3 only

x² - 6x + 9 = (x - 3)² = 0, so x = 3 is a double root.

Which expression represents 'the square of the sum of x and 4'?

Answer: (x + 4)²

'The square of the sum of x and 4' means (x + 4)².

If the equation 2x + ky = 8 has a solution at (4, 0), what is k?

Answer: k can be any value

At (4, 0): 2(4) + k(0) = 8 → 8 = 8, which is true for any value of k.

What is the value of x in the proportion 5/8 = x/40?

Answer: x = 25

Cross-multiplying: 8x = 200, so x = 25.