Math Math Algebra and Functions 3

Question 1

What is the value of x in the proportion 4/x = 8/20?

Accepted Answer

10

Answer

Cross-multiply: 4 × 20 = 8 × x → 80 = 8x → x = 10.

Question 2

Simplify the expression: (2x³)(3x²)

Accepted Answer

6x⁵

Answer

Multiply coefficients and add exponents: 2 × 3 = 6 and x³ × x² = x⁵, giving 6x⁵.

Question 3

If y varies directly with x and y = 15 when x = 3, what is y when x = 7?

Accepted Answer

35

Answer

k = y/x = 15/3 = 5; so y = 5 × 7 = 35.

Question 4

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

Accepted Answer

x ≥ 4

Answer

The expression under the square root must be ≥ 0: x − 4 ≥ 0, so x ≥ 4.

Question 5

Which of the following represents an exponential function?

Accepted Answer

y = 3 × 2ˣ

Answer

y = 3 × 2ˣ is exponential because the variable x is in the exponent.

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