Math (Grades 8-12) Flashcards

Which of the following is a solution to the system of equations: y = 2x + 1 and y = -x + 4?

Answer: (1, 3)

Set equal: 2x+1 = -x+4, so 3x=3, meaning x=1. Then y=2(1)+1=3. The solution is (1,3).

What is the complete solution to 2x squared = 50?

Answer: x = 5 or x = -5

2x^2 = 50 → x^2 = 25 → x = plus or minus 5. Both 5 and -5 are valid solutions.

Simplify: (3x squared times y)(4x times y cubed)

Answer: 12x cubed y to the 4th

Multiply coefficients: 3 times 4 = 12. Add exponents of like bases: x^2 times x^1 = x^3, y^1 times y^3 = y^4. Result: 12x^3 y^4.

A function is defined as f(x) = 3x - 7. For what value of x does f(x) = 8?

Answer: x = 5

Set f(x) = 8: 3x - 7 = 8 → 3x = 15 → x = 5.

What is the slope of the line passing through points (1, 2) and (4, 8)?

Answer: 2

Slope = (y2 - y1) divided by (x2 - x1) = (8-2) divided by (4-1) = 6/3 = 2.

Which of the following best describes the graph of an absolute value function like y = |x|?

Answer: A V-shape

The absolute value function y = |x| produces a V-shaped graph because the output is always non-negative.