Regents Ultimate Regents Algebra 5

Question 1

A store marks up items 40% from cost. If an item costs $80, what is the selling price?

Accepted Answer

$112

Answer

Selling price = 80 + 0.40(80) = 80 + 32 = $112.

Question 2

Which equation represents a line perpendicular to y = (1/3)x + 5?

Accepted Answer

y = -3x + 2

Answer

Perpendicular lines have slopes that are negative reciprocals; the negative reciprocal of 1/3 is -3.

Question 3

Simplify: (4x² - 9) ÷ (2x + 3)

Accepted Answer

2x - 3

Answer

Factor the numerator as a difference of squares: (2x+3)(2x-3); cancel (2x+3) to get 2x - 3.

Question 4

A geometric sequence has first term 4 and common ratio 3. What is the 5th term?

Accepted Answer

324

Answer

aₙ = a₁ · rⁿ⁻¹; a₅ = 4 · 3⁴ = 4 · 81 = 324.

Question 5

Which system of inequalities is graphed by the region below y = x + 2 AND above y = -x?

Accepted Answer

y < x + 2 and y > -x

Answer

Below y = x + 2 means y < x + 2, and above y = -x means y > -x.

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