ALEKS Algebra Fundamentals 3

Question 1

Simplify: (3x²y)(4xy³)

Accepted Answer

12x³y⁴

Answer

Multiply coefficients and add exponents: 3×4 = 12, x^(2+1) = x³, y^(1+3) = y⁴.

Question 2

What is the domain of f(x) = √(x - 4)?

Accepted Answer

x ≥ 4

Answer

The expression under a square root must be non-negative: x - 4 ≥ 0, so x ≥ 4.

Question 3

Solve: |2x - 6| = 10

Accepted Answer

x = 8 or x = -2

Answer

Set 2x - 6 = 10 (x = 8) and 2x - 6 = -10 (x = -2).

Question 4

What is the y-intercept of the line 4x - 2y = 8?

Accepted Answer

-4

Answer

Set x = 0: -2y = 8, so y = -4; the y-intercept is -4.

Question 5

Simplify: (x³)⁴

Accepted Answer

x¹²

Answer

When raising a power to a power, multiply the exponents: (x³)⁴ = x^(3×4) = x¹².

ALEKS - Assessment and Learning in Knowledge Spaces Practice Test