Numbers & Expressions
Let A = (-4, 3] and B = [1, 7). Find A ∩ B.
[1, 3]
Solve 3x - 7 = 11.
x = 6
Find the midpoint of the segment with endpoints (-2, 5) and (6, -1).
(2, 2)
Find the slope of the line through (1, 2) and (3, 8).
3
A rectangle has perimeter 54 ft. Its length is 3 ft more than twice its width. Find its dimensions.
Width = 8 ft; length = 19 ft
Assume x > 0. Simplify (27x⁶)^(1/3).
3x²
Solve |2x - 3| > 5. Give the answer in interval notation.
(-∞, -1) ∪ (4, ∞)
Find the distance between (-1, 2) and (5, 10).
10
Find an equation in slope-intercept form of the line through (3, -2) parallel to 4x - 2y = 7.
y = 2x - 8
y varies directly as x. If y = 12 when x = 3, find y when x = 8.
32
Factor completely: 6x³ - 15x² - 36x.
3x(2x + 3)(x - 4)
Solve √(2x + 3) = x and reject any extraneous solution.
x = 3
Write the equation of the circle with center (-3, 4) and radius 6.
(x + 3)² + (y - 4)² = 36
Find an equation in slope-intercept form of the line through (4, 1) perpendicular to 4x - 2y = 7.
y = -(1/2)x + 3
F varies inversely as the square of d. If F = 20 when d = 2, find F when d = 5.
16/5, or 3.2
Simplify and state restrictions: [(x² - 9)/(x² - x - 6)] · [(x + 2)²/(x + 3)].
x + 2, where x ≠ -3, -2, 3
Solve 1/(x - 1) = 2/(x + 2).
x = 4
A diameter of a circle has endpoints (-2, 5) and (6, -1). Find the center, radius, and equation.
Center (2, 2); radius 5; (x - 2)² + (y - 2)² = 25
Find both intercepts of 3x + 2y = 12.
x-intercept (4, 0); y-intercept (0, 6)
y varies directly as x² and inversely as z. If y = 18 when x = 3 and z = 2, find y when x = 5 and z = 10.
10
Assume x, y > 0. Simplify (16x⁸y⁻⁴)^(3/4).
8x⁶/y³
Solve x² - 5 = 2x. Give both solutions to the nearest hundredth.
x ≈ -1.45 and 3.45
Rewrite x² + y² - 6x + 4y - 12 = 0 in standard form; give the center and radius.
(x - 3)² + (y + 2)² = 25; center (3, -2); radius 5
Find the line through the intersection of y = 2x - 5 and y = -x + 4 that is perpendicular to 3x - y = 7.
y = -(1/3)x + 2
A school sold 240 tickets. Adult tickets cost $8 and student tickets cost $5. Total revenue was $1,530. How many of each were sold?
110 adult tickets and 130 student tickets