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Math 73 Test II Review 1.- Solve the following systems by elimination and substitution. (a) 2x + 3y = 8 x + 2y = 3 (b) 3x + 4y = 12 6x + 8y = 12 2.- Solve the following word problems. (a) The sum of two number is 32. One of the numbers is 4 less than 5 times the other. Find the two numbers. (b) James Bond has 20 coins totaling $1.40. If he has only dimes and nickels, how many of each coin does he have? (c) Batman has $8, 000 to invest. He puts the money in two accounts. The first one pays 5% annually and the second pays 6% annually. The total interest after one year is $450. How much money did he invested in each account? 3.- Multiply (and simplify) the following. (a) (4x 2)(x3 (b) (2x3 + 2)2 (c) (x + y 5x2 + 4x (x3 4)(x3 + 4) z)(x + y + z) 4.- Simplify the following. (a) 54x 4 x12 (3x)2 [3x(5x)0 ] 6) (b) (2x4 y 3 z 5 )5 (6x 2 y 3 z 7 )2 (c) ✓ 2x3 y 5 z 3x6 y 5 z 9 ◆3 5.- Factor the following. (a) 3ax + 21x (b) x3 5x2 a 7 4x + 20 (c) x2 + 6xy + 9y 2 (d) 3x2 + 19xy (e) 2x3 50x (f) 8m3 + 1 14y 2 (g) 27x3 64 6.- Solve the following by factoring. (a) x3 5x2 4x + 20 = 0 (b) 6x2 = 24x (c) 3x3 12x = 0 (d) (x + 3)2 = 49 7.- The path of a missile is given by h(t) = 16t2 + 64t + 80 where h represents the altitude of the missile after t seconds. How long does it take to hit the ground? 8.- Write the following in Scientific Notation. (a) 0.000000054 (b) (3, 000, 000.0)(2.5 ⇤ 10 3 ) (c) 9.0 ⇤ 1024 1, 500, 000, 000.0 9.- Solve the following system by graphing x 4y = 20 1 y = x+2 4 y x