3-4 Systems of Equations in Three Variables. Solve each system of equations. SOLUTION:
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1 Solve each system of equations. 3. Multiply the second equation by 2 and add with the third equation. Multiply the first equation by 2 and add with the second equation. Solve the fifth and fourth equations. Substitute 3 for y in the fourth equation and solve for x. Substitute 4 for x and 3 for y in the second equation, and solve for z. esolutions Manual - Powered by Cognero Page 1
2 Therefore, the solution is ( 4, 3, 6). 5. Multiply the first equation by 2, multiply the second equation by 3 and add. Multiply the second equation by 2 and add with the third equation. Multiply the first equation by 4, multiply the third equation by 3, and add. Since the equations 4, 5 and 6 are same, the system of equations has an infinite number of solutions. esolutions Manual - Powered by Cognero Page 2
3 7. DOWNLOADING Heather downloaded some television shows. A sitcom uses 0.3 gigabyte of memory; a drama, 0.6 gigabyte; and a talk show, 0.6 gigabyte. She downloaded 7 programs totaling 3.6 gigabytes. There were twice as many episodes of the drama as the sitcom. a. Write a system of equations for the number of episodes of each type of show. b. How many episodes of each show did she download? a. Let s, t and d be the number of sitcoms, talk shows and dramas respectively. The system of equations is: b. Solve. Substitute 2s for d in the first and third equation. Solve the fourth and fifth equations. Substitute 2 for s in the second equation and solve for d. Substitute 2 for s and 4 for d in the first equation and solve for t. Therefore, she downloaded 2 episodes of sitcom, 4 episodes of drama and 1 episode of talk show. Solve each system of equations. esolutions Manual - Powered by Cognero Page 3
4 9. Multiply the third equation by 4 and add the first equation with that. Multiply the third equation by 3 and add the second equation with that. Solve the fourth and fifth equations. Substitute 2 for b in the fifth equation and solve for c. Substitute 2 for b and 4 for c in the third equation and, solve for a. Therefore, the solution is ( 3, 2, 4). esolutions Manual - Powered by Cognero Page 4
5 11. Multiply the first equation by 4 and add with the second equation. Multiply the third equation by 2, and add with the second equation. Solve the fourth and fifth equations. Substitute 2 for r in the fifth equation and solve for s. Substitute 2 and 1 for r and s in the first equation and solve for t. Therefore, the solution is ( 2, 1, 4). esolutions Manual - Powered by Cognero Page 5
6 13. Add the first and the third equations. Multiply the first equation by 3 and add with the second equation. Multiply the third equation by 3 and add with the second equation. Since the equations 4, 5 and 6 are same, the system has an infinite number of solutions. 21. AMUSEMENT PARKS Nick goes to the amusement park to ride roller coasters, bumper cars, and water slides. The wait for the roller coasters is 1 hour, the wait for the bumper cars is 20 minutes long, and the wait for the water slides is only 15 minutes long. Nick rode 10 total rides during his visit. Because he enjoys roller coasters the most, the number of times he rode the roller coasters was the sum of the times he rode the other two rides. If Nick waited in line for a total of 6 hours and 20 minutes, how many of each ride did he go on? Let x, y and z be the number of raids in roller coaster, bumper car and water slide respectively. Nick rode 10 rides during his visit. The number of times that Nick rode the roller coaster is the sum of the times he rode the other two rides. So: He waited in line for a total of 6 hours 20 minutes. esolutions Manual - Powered by Cognero Page 6
7 Substitute x for y + z in the first equation and solve for x. Substitute 5 for x in the second and the third equation and simplify. Multiply the fifth equation by 3 and add with the fourth equation. Substitute 1 for y in the fifth equation and solve for z. Nick rode the roller coaster, bumper cars and water slides 5, 1 and 4 times respectively. esolutions Manual - Powered by Cognero Page 7
8 24. CCSS REASONING Write a system of equations to represent the three rows of figures below. Use the system to find the number of red triangles that will balance one green circle. t + c = s, p + t = c, 2s = 3p where t represents triangle, c represents circle, s represents square, and p represents pentagon; 5 red triangles esolutions Manual - Powered by Cognero Page 8
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0-2 Operations with Complex Numbers
Simplify. 1. i 10 1 2. i 2 + i 8 0 3. i 3 + i 20 1 i esolutions Manual - Powered by Cognero Page 1 4. i 100 1 5. i 77 i 6. i 4 + i 12 2 7. i 5 + i 9 2i esolutions Manual - Powered by Cognero Page 2 8.
1-1 Functions < x 64 SOLUTION: 9. { 0.25, 0, 0.25, 0.50, } SOLUTION: 12. all multiples of 8 SOLUTION: SOLUTION:
Write each set of numbers in set-builder and interval notation, if possible. 3. x 4 The set includes all real numbers less than or equal to 4. In set-builder notation this set can be described as {x x
Mid-Chapter Quiz: Lessons 10-1 through Refer to. 1. Name the circle. SOLUTION: The center of the circle is A. Therefore, the circle is ANSWER:
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SOLUTION: The domain of a square root function only includes values for which the radicand is nonnegative.
19. Graph each function. State the domain and range. 21. The domain of a square root function only includes values for which the radicand is nonnegative. esolutions Manual - Powered by Cognero Page 1 23.
i. Indicate on the figure the point P at which the maximum speed of the car is attained. ii. Calculate the value vmax of this maximum speed.
1. A 0.20 kg object moves along a straight line. The net force acting on the object varies with the object's displacement as shown in the graph above. The object starts from rest at displacement x = 0
6-3 Square Root Functions and Inequalities. Identify the domain and range of each function. ANSWER: ANSWER:
Identify the domain and range of each function. 7. 1. 3. Graph each function. State the domain and range. 5. Graph each inequality. 9. esolutions Manual - Powered by Cognero Page 1 11. Graph each function.
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Choose a word or term from the list above that best completes each statement or phrase. 1. A function of the form f (x) = b x where b > 1 is a(n) function. exponential growth 2. In x = b y, the variable
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