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M115 (Beginning Algebra, Fall 2015) Final Exam You must show work. Insufficient/inadequate work receives no credit. Solve the equation. 9 1 1 7 1) x + x = 2x + + x 8 8 4 8 Name: 2) 0.7(5x + 15) = 2.3 - (x + 3) 1) 2) Solve the problem. 3) Midtown Antiques collects 4.5% sales tax on all sales. If total sales including tax are $ 1615.24, find the portion that is the tax. Round to the nearest cent if necessary. Solve the inequality using interval notation. 4) -5(4y + 3) < -25y + 25 3) 4) Solve using the addition and multiplication principles. 2 5) (2x - 1) < 2 3 5) Write an equation in slope-intercept form of the line satisfying the given conditions. 6) Through (-2, -5), parallel to 2x + 3y = -22 7) Through (-9, -6), perpendicular to -6x + 7y = 96 6) 7) 1 Find the equation for the graph. 8) 8) Graph the equation. 9) 3x - y = 3 9) Find an equation of the line containing the given pair of points. Write your final answer as a linear function in slope-intercept form. 10) (6, -6) and (-1, 2) 10) Simplify. Do not use negative exponents in your answer. -4 x 6 y4 11) wz 5 11) Divide. 12) ( 4 m 2 + 11 m - 45 ) ÷ (m + 5 ) 12) 2 13) -4x3 - 16x2 - 7x + 20 -2x - 5 13) Find the x-intercepts for the graph of the equation. 14) y = x2 - x - 42 14) List all numbers for which the rational expression undefined. x2 - 4 15) x2 + 3x - 54 Simplify, if possible. t3 + 64 16) t3 - 4t2 + 16t 16) Multiply and, if possible, simplify. 3x + 9 4x2 + 8x + 4 · 17) x+1 x2 - 9 Solve. 15) 17) 18) One maid can clean the house three times faster than another. Working together they can clean the entire house in 3 hours. How long would it take the faster maid cleaning alone? 3 18) Solve the problem. 19) Fred bicycles 6 km/h slower than Samantha. In the time it takes Fred to bicycle 24 km, Samantha travels 36 km. How fast does Fred bicycle? Solve. If no solution exists, state this. -40 = -3 20) x + x 21) 19) 20) y y y + = 2 2 2 y - 7y + 10 y - 4 y - 3y - 10 21) Solve using the substitution method. 22) 5x - 2y = -1 x + 4y = 35 22) Solve using the elimination method. 23) 8x - 7y = 7 -4x - 3y = 3 23) 4 Solve the problem. 24) The total sales made by a salesperson was $24,000 after 3 months and $72,000 after 23 months. Predict the total sales after 32 months. 1. Find the equation of the line in slope intercept form: S = mt + b 2. Predict the total sales after 42 months. 5 24)