A. Solve each equation.
1) -3(1 + 4k) + 4 = -3(4k - 4) + k
2) - (79/6) = (11/6)m + (19/4)m
Solve each inequality, write its solution set in interval notation, and graph the solution set on a number line.
3) 2(x - 4) ≤ -3(x - 4)
4) ½ - ½n ≤ -(29/20)
Solve each compound inequality, write its solution set in interval notation, and graph the solution set on a number line.
5) -13 ≤ 3 + 4x < 11
6) -(35/12) ≤ -(7/3)n ≤ -(7/3)
Write the equation of the line described in standard form, Ax + By = C, where A, B, and C are integers.
7) through: (5, 3), perpendicular to y = -(5/2)x - 1
Rewrite the equation in slope-intercept form and then use the slope and y-intercept to sketch a fraph of the line with the given equation.
8) 3x + 2y = 8
Show all work as you solve the linear modeling problem below.
9) There were 271 Whole Foods stores worldwide in 2008 and 361 Whole Foods stores worldwide in 2013. Write a linear equation in slope-intercept form that models this growth. Let x stand for the number of years after 2008 and let y stand for the number of Whole Foods stores worldwide.
Simplify. Your answer should contain only positive exponents.
10) 4x4y2 · 5x4y3
11) 3uv-2/2u2v4·-4u3
12) (2x4y-3)4
13) (2x-3y0) · (x3y4)2
Perform the indicated operation and simplify.
14) (k4 + 8k + 2) - (7k4 + 2k - 7)
Multiply as indicated and simplify.
15) (5v - 1)(2v2 + 2v - 7)
Solve the equation by factoring.
16) 3n2 = -15 + 14n
Solve the equation by completing the square.
17) a2 - 10a - 140 = -9
Solve the equation by use of the quadratic formula.
18) 5r2 - 8 = 2r
State the excluded values for the following expression. Then simplify the expression.
19) p2 + 12 p + 32/p2 - 2p - 80
Solve the equation and show the check of the potential answer(s). If any answers are excluded values, state this on your answer sheet.
20) 1/x-2 = 1 - 6/x2 - 6x + 8
Simplify the radical expressions.
21) √(8x3y4z4)
22) (4√5 - 3)(-3√5 - 1)
Solve the equation and show the check of the potential answer(s). If any answers are extraneous solutions, state this on your answer sheet.
23) -2 = -r + √(32 - 7r)
Show all work as you solve the following problems and write complete answers, including appropriate units.
24) Kayla left school and traveled toward the ocean at an average speed of 24 km/h. Danielle left three hours later and traveled in the same direction but with an average speed of 60 km/h. How long did Kayla travel before Danielle caught up?
25) Shana put $25,000 in an education account on the day her daughter was born. If the account earned 7.15% interest compounded quarterly, what was the total in the account when her daughter turned 18? Round the final answer to the nearest cent.