Math Flashcards

Solve the system: x + y = 11 and 2x − y = 7.

Answer: (6, 5)

Adding the equations gives 3x = 18, so x = 6 and y = 5.

Simplify (2x³)² · x⁻⁴.

Answer: 4x²

(2x³)² = 4x⁶, and 4x⁶ · x⁻⁴ = 4x².

A circle has a circumference of 10π inches. What is its area?

Answer: 25π sq in

2πr = 10π gives r = 5, so the area is π(5)² = 25π.

Which inequality is the solution to −3x + 4 > 16?

Answer: x < −4

−3x > 12, and dividing by −3 flips the sign, so x < −4.

If f(x) = x² − 3x + 2, what is f(−2)?

Answer: 12

(−2)² − 3(−2) + 2 = 4 + 6 + 2 = 12.

What is the median of the data set 7, 3, 9, 12, 5, 10?

Answer: 8

In sorted order (3, 5, 7, 9, 10, 12), the middle two values average to (7 + 9)/2 = 8.

A rectangle's length is twice its width, and its perimeter is 36 feet. What is its area?

Answer: 72 sq ft

2(2w + w) = 36 gives w = 6 and l = 12, so the area is 72.