Regents Ultimate Regents Algebra 3

Question 1

The graph of a line passes through (0, -4) and (3, 2). What is the equation of the line?

Accepted Answer

y = 2x - 4

Answer

Slope = (2 - (-4))/(3 - 0) = 6/3 = 2; y-intercept is -4, so y = 2x - 4.

Question 2

What is the solution set of |2x - 3| = 7?

Accepted Answer

x = 5 or x = -2

Answer

2x - 3 = 7 gives x = 5, and 2x - 3 = -7 gives x = -2.

Question 3

A rectangle has length (x + 5) and width (x - 2). Which expression represents its area?

Accepted Answer

x² + 3x - 10

Answer

Using FOIL: (x+5)(x-2) = x² - 2x + 5x - 10 = x² + 3x - 10.

Question 4

What is the value of x in the system: 3x + y = 11 and x - y = 1?

Accepted Answer

3

Answer

Adding the equations: 4x = 12, so x = 3.

Question 5

Which describes an exponential decay function?

Accepted Answer

f(x) = 500(0.85)ˣ

Answer

A base between 0 and 1 (0.85) produces exponential decay.

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