This is my final assignment for my class and I need to show my work along with putting my answers on the answer sheet attached
Untitled4.tst Final Exam Intermediate Algebra Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the expression for the given values. 1) x - 7 x + 9 (a) x = -2 (b) x = 2 (c) x = 0 A) (a) - 9 7 (b) - 11 5 (c) - 7 9 B) (a) - 7 9 (b) - 11 5 (c) - 7 9 C) (a) - 9 7 (b) - 5 11 (c) - 7 9 D) (a) - 7 9 (b) - 5 11 (c) - 7 9 1) Simplify the square root. 2) (3x + 5)2 A) |3x + 5| B) 9x2 + 30x + 25 C) -3x - 5 D) 3x + 5 2) Use the right triangle shown and find the missing length. If necessary, round to three decimal places. 3) c = 12, b = 8 A) 14.422 B) 4.472 C) 2 D) 8.944 3) Indicate whether the graph represents a one-to-one function. 4) x y x y A) Yes B) No 4) Find the distance d(P1, P2) between the points P1and P2. 5) P1 = (6, -7); P2 = (2, -5) A) 6 B) 2 5 C) 12 D) 12 3 5) 1 Write the standard form of the equation of the circle whose radius is r and whose center is (h, k). 6) r = 14; (h, k) = (0, 0) A) x2 - y2 = 14 B) x2 + y2 = 28 C) x2 + y2 = 14 D) x2 + y2 = 196 6) Find the inverse of the function. 7) {(-3, 4), (-1, 5), (0, 2), (2, 3), (5, 7)} A) {(3, 4), (1, 5), (0, 2), (-2, 3), (-5, 7)} B) {(-3, -4), (-1, -5), (0, -2), (2, -3), (5, -7)} C) {(3, -4), (1, -5), (0, -2), (-2, -3), (-5, -7)} D) {(4, -3), (5, -1), (2, 0), (3, 2), (7, 5)} 7) Solve the equation. 8) 22x + 1= 32 A) {16} B) {4} C) {2} D) {-2} 8) Approximate the value using a calculator. Express answer rounded to three decimal places. 9) 5 7 A) 70.681 B) 39,062.500 C) 13.229 D) 129.642 9) Change the exponential expression to an equivalent expression involving a logarithm. 10) 63 = 216 A) log3 216 = 6 B) log6 216 = 3 C) log6 3 = 216 D) log216 6 = 3 10) Find the domain of the logarithmic function. 11) f(x) = log8(x 2 - 12x + 36) A) (6, ) B) (- , 6) (6, ) C) (-6, ) D) (- , 0) (0, ) 11) Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 12) log 108 9 + log 108 12 A) 12 B) 9 C) 1 D) 108 12) Write the expression as a logarithm of a single expression. Assume that variables represent positive numbers. 13) 3 loga (2x + 1) - 2 loga (2x - 1) + 2 A) loga (2x + 3) B) loga a2(2x + 1)3 (2x - 1)2 C) loga (2x + 1) + 2 D) loga 2(x + 1) 13) Solve the problem. 14) Newton s Law of Cooling states that the temperature of a heated object decreases exponentially over time toward the temperature of the surrounding medium. Suppose that a coffee is served at a temperature of 130°F and placed in a room whose temperature is 70°F. The temperature (in °F) of the coffee at time t (in minutes) can be modeled by (t) = 70 + 60e-0.08t. When will the temperature be 105°F? A) 6.7 minutes B) 3.4 minutes C) 2.7 minutes D) 1.1 minutes 14) 2 15) Find out how long it takes a $3300 investment to double if it is invested at 9% compounded quarterly. Round to the nearest tenth of a year. Use the formula A = P 1 + r n nt . A) 8 years B) 7.8 years C) 7.6 years D) 8.2 years 15) Use the square root property to solve the equation. 16) x - 3 2 2 = 25 4 A) {1, -4} B) {2, -8} C) {8, -2} D) {4, -1} 16) Solve the problem. 17) An express train travels 237 miles between two cities. During the first 96 miles of a trip, the train traveled through mountainous terrain. The train traveled 15 miles per hour slower through mountainous terrain than through level terrain. If the total time to travel between the cities was 6 hours, find the speed of the train on level terrain. A) 62 mph B) 17 mph C) 32 mph D) 47 mph 17) Determine the discriminant of the quadratic equation. Use the value of the discriminant to determine whether the quadratic equation has two rational solutions, two irrational solutions, one repeated real solution, or two complex solutions that are not real. 18) x2 + 6x + 9 = 0 A) Two complex solutions that are not real B) One repeated real solution C) Two irrational solutions D) Two rational solutions 18) Solve the equation. 19) x4 - 18x2 + 32 = 0 A) {-4, 4, - 2, 2} B) {4, 2} C) {16, 2} D) {-4, 4, -i 2, i 2} 19) 20) x-2 - 4x-1 + 3 = 0 A) {-1, -3} B) - 1 3 , -1 C) {1, 3} D) 1 3 , 1 20) Express the function in the form f(x) = a(x - h)2 + k and indicate the vertex. 21) f(x) = -x2 + x + 5 A) f(x) = -(x - 1)2 + 5 vertex: (1, 5) B) f(x) = -(x + 1)2 + 3 vertex: (-1, 3) C) f(x) = -(x - 1 2 ) 2 + 21 4 vertex: 1 2 , 21 4 D) f(x) = -(x + 1 2 ) 2 + 17 4 vertex: - 1 2 , 17 4 21) 3 Determine the quadratic function whose graph is given. 22) x-10 -5 5 10 y 10 5 -5 -10(-4, -9) x-10 -5 5 10 y 10 5 -5 -10(-4, -9) A) f(x) = x2 - 8x + 7 B) f(x) = -x2 + 8x + 7 C) f(x) = x2 + 8x + 7 D) f(x) = x2 + 8x - 7 22) Solve the problem. 23) A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 304 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? A) 23,104 ft2 B) 5776 ft2 C) 11,552 ft2 D) 17,328 ft2 23) 24) A person standing close to the edge on top of a 48-foot building throws a baseball vertically upward. The quadratic function s(t) = -16t2 + 64t + 48models the ball s height above the ground, s(t), in feet, t seconds after it was thrown. After how many seconds does the ball reach its maximum height? Round to the nearest tenth of a second if necessary. A) 4.6 seconds B) 1.5 seconds C) 112 seconds D) 2 seconds 24) Find the domain of the given function. 25) f(x) = x(x + 4) A) (- , 0] [4, ) B) [-4, 4] C) (- , -4) (0, ) D) (- , -4] [0, ) 25) 4 Solve the inequality. Graph the solution set and write the solution set in set -builder notation. 26) x2 + 5x -6 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 A) {x x -2} -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 B) {x x -3 or x -2} -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 C) {x -3 x -2} -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 D) {x x -3} -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 26) Solve the rational inequality. 27) 12x 6 - x 4x A) (- , 0] [3, 6) B) [0, 3] [6, ) C) (- , 3] [6, ) D) [6, ) 27) 28) x + 72 x < 17 a) (0, 8) (9, ) b) (- , 0) (8, 9) c) (- , 0) (9, ) d) (0, 8) (8, 9) 28) tell if the square root is rational, irrational, or not a real number. if the square root is rational, find the exact value; if the square root is irrational, write the approximative value rounded to 2 decimal places. 29) 8 a) irrational, 2.83 b) irrational, -2.83 c) not a real number d) rational, 2 2 29) rewrite the expression with a positive rational exponent. simplify, if possible. 30) 5 y a) y 1/2 5 b) y1/5 c) y 5 d) y5/2 30) solve with calculator. 31) the formula d = 0.07x3/2 models the duration of a storm, d, in hours, in terms of the diameter of the storm, x, in miles. use a calculator to determine the duration of a storm with a diameter of 11 miles. round to the nearest hundredth. a) 0.68 hours b) 36.48 hours c) 2.55 hours d) 0.23 hours 31) 5 simplify the radical expression. assume that all variables represent positive real numbers. 32) x9 a) x3 x b) x4 c) x5 d) x4 x 32) 33) 4 49 7 a) 7 b) 49 c) 1 d) 1 2 33) use the product rule to multiply. assume all variables represent positive real numbers. 34) 175x 7x a) 7 5x b) 35x c) 35 d) 5 7x 34) use the product rule to simplify the expression. assume that the variables can be any real number. 35) 4 48x6y10 a) 16 x y2 4 3x2y2 b) 2 x y2 4 3x2y2 c) 2 xy 4 3x2y2 d) 2xy2 4 3x2y2 35) multiply, and then simplify if possible. assume all variables represent positive real numbers. 36) 2( 2 17="" a)="" (0,="" 8)="" (9,="" )="" b)="" (-="" ,="" 0)="" (8,="" 9)="" c)="" (-="" ,="" 0)="" (9,="" )="" d)="" (0,="" 8)="" (8,="" 9)="" 28)="" tell="" if="" the="" square="" root="" is="" rational,="" irrational,="" or="" not="" a="" real="" number.="" if="" the="" square="" root="" is="" rational,="" find="" the="" exact="" value;="" if="" the="" square="" root="" is="" irrational,="" write="" the="" approximative="" value="" rounded="" to="" 2="" decimal="" places.="" 29)="" 8="" a)="" irrational,="" 2.83="" b)="" irrational,="" -2.83="" c)="" not="" a="" real="" number="" d)="" rational,="" 2="" 2="" 29)="" rewrite="" the="" expression="" with="" a="" positive="" rational="" exponent.="" simplify,="" if="" possible.="" 30)="" 5="" y="" a)="" y="" 1/2="" 5="" b)="" y1/5="" c)="" y="" 5="" d)="" y5/2="" 30)="" solve="" with="" calculator.="" 31)="" the="" formula="" d="0.07x3/2" models="" the="" duration="" of="" a="" storm,="" d,="" in="" hours,="" in="" terms="" of="" the="" diameter="" of="" the="" storm,="" x,="" in="" miles.="" use="" a="" calculator="" to="" determine="" the="" duration="" of="" a="" storm="" with="" a="" diameter="" of="" 11="" miles.="" round="" to="" the="" nearest="" hundredth.="" a)="" 0.68="" hours="" b)="" 36.48="" hours="" c)="" 2.55="" hours="" d)="" 0.23="" hours="" 31)="" 5="" simplify="" the="" radical="" expression.="" assume="" that="" all="" variables="" represent="" positive="" real="" numbers.="" 32)="" x9="" a)="" x3="" x="" b)="" x4="" c)="" x5="" d)="" x4="" x="" 32)="" 33)="" 4="" 49="" 7="" a)="" 7="" b)="" 49="" c)="" 1="" d)="" 1="" 2="" 33)="" use="" the="" product="" rule="" to="" multiply.="" assume="" all="" variables="" represent="" positive="" real="" numbers.="" 34)="" 175x="" 7x="" a)="" 7="" 5x="" b)="" 35x="" c)="" 35="" d)="" 5="" 7x="" 34)="" use="" the="" product="" rule="" to="" simplify="" the="" expression.="" assume="" that="" the="" variables="" can="" be="" any="" real="" number.="" 35)="" 4="" 48x6y10="" a)="" 16="" x="" y2="" 4="" 3x2y2="" b)="" 2="" x="" y2="" 4="" 3x2y2="" c)="" 2="" xy="" 4="" 3x2y2="" d)="" 2xy2="" 4="" 3x2y2="" 35)="" multiply,="" and="" then="" simplify="" if="" possible.="" assume="" all="" variables="" represent="" positive="" real="" numbers.="" 36)="" 2(="">