Complex numbers Questions and Answers

2 5 31 12 21 20

2 54 2 24

Advanced Polynomial Multiplication Find each product 1 5x 2 3 A 25x 20x 4 C 25x 4 3 2n 5 2n 5 A 9n 64 C 4n 20n 25 5 0 6n 2 2 0 6n 2 2 A 0 25n 47 61 B 0 36n 2 64n 4 84 C 0 36n 4 84 D 0 25n 6 9n 47 61 B 25x 2 4 D 5x 4 B 36n 4 D 4n 25 2 2 7n 1 7n 1 6 A 64 96n 36n B 49n 14n 1 C 64 36n D 49n 1 44 3 6a 1 8 A 3 6a 3 24 B 12 96a 3 24 C 12 96a 12 96a 3 24 D 12 96a 3 24 6 0 8n 0 3 A 0 64n 0 09 B 0 64n 0 48n 0 09 C 20 25n 70 2n 60 84 D 0 64n 0 09

B P C B 11 6 8 Prove that ZPAB ZPCB and then use similar triangles to conclude AC PC

Find the remainder of 6102 divided by 101 Reduce 8 00 mod 29 Find the remainder of 11666 divided by 13

15 n 4 9 17 3x 9 15x 19 16n 14n 21 4 7 1 3m 16 4n n 18 9k 8k 20 15n 19n 22 5n 3 6 7n

4 Are 5 and 10 like terms Why or why not

23 2n 9 10n 25 9a 10 6a 1 27 10 1 9x 6 x 10 29 3 10b 10 5 b 2 24 10 5 9n 9 26 9 6m 3 6 1 4m 28 5 2n 4 2 n 3 30 7 n 3 8 1 8n

For each of the following series tell whether or not you can apply the 3 condition test i e the alternating series test Enter D if the series diverges by this test C if the series converges by this test and N if you cannot apply this test even if you know how the series behaves by some other test 1 n 1 n 7 1 cos n n 2 18W18W18W18W18W 3 4 5 6 1 n5 1 n 2n n 1 1 n 1 n 1 1 n 0 1 en

Write the system of equations as a matrix equation AX B with A as the coefficient matrix of the system x 5y 29 6x 5y 1

a Give the order of the given matrix b If A a identify a31 and a13 if possible O A a31 OB Identify a 13 a The order of the given matrix in the form m xn is b Identify a31 Select the correct choice below and if necessary fill in the answer box to complete your choice Element does not exist a31 3 2 1 1 OA a13 O B Element a13 does not exist 9 6 Select the correct choice below and if necessary fill in the answer box to complete your choice

3 Use the parent function f x bx and transformation techniques to graph h x e x 1 2 Also indicate which transformation s is are applied Determine the domain range and horizontal asymptote of h Select all transformations that apply A Vertically stretch the graph of f by a factor of 2 B Horizontally stretch the graph of f by a factor of 2 C Shift the graph of f 2 units down D Horizontally compress the graph of f by a factor of 1 E Reflect the graph of f about the x axis F Reflect the graph of f about the y axis G Shift the graph of f 2 units up H Shift the graph of f 1 unit to the left 1 Vertically compress the graph of f by a factor of 1 J Shift the graph of f 1 unit to the right

A polynomial has the following real zeros 2 crossing 3 touching and 7 crossing What is the smallest degree that the function can have 3 02 05

2x x 3x 3x x is equivalent to A 5x 3 5x 2x C 6x 3x D 4x 3x 3x E 7

a 3x 4 5x

c 4x 10x 8y 6y

10 Combine like terms below 3x4x2 2x 4x2 2x 5x 8

1 Approximate the following value using a calculator Round the solution to four decimal places if necessary 2 Note No work needed this question ensures a student is using a calculator properly

4 It is known for a quadratic function f that f 11 f 7 55 Find the axis of symmetry of f x

10 15 n m On m 1 10 n m 3 10 Given the following graph what is the relationship between the degree of the numerator n and the degree of the denominator m 15 Activate Wine Go to Settings to

In Problems 11 and 12 evaluate each expression using the graphs of y f x and y g x shown in the figure 11 y g x a gof 1 b gof 0 c fog 1 d fog 4 1 3 1 1 2 YA 6 4 2 2 1 4 2 2 2 5 4 3 1 1 1 4 2 2 6 5 7 5 4 2 7 3 6 2 8 4 5 1 1 6 y f x 8 X

Match each function with its graph Ay 1 0 14 TO X T Q y cos 2x AY 2 1 0 1 2 TO 2T Drag each graph above to match the function below y sinx y cos x y 2 sin x 1 0 1 2 4 X y sin 2x y 2 cos x Ay 2 1 0 1 2 T 2 Q Ay 1 0 1 R x Q 2x 1 0 14

Find a calculator approximation of the following Be sure your calculator is in radian mode csc 6 7464 This question 4 point s pc csc 6 7464 Round to four decimal places

The function graphed is of the form y a sin bx or y a cos bx where b 0 Determine the equation of the graph y Type an expression using x as the variable 4 NON 2 0 2 4 6 R XA 3x 2 o 5

3 Selected values of a quadratic function g are given in the table Write the function g in the most appropriate form using the given information 2 8 0 5 6 1 0 2 15

1 y sin x 6 1 What is the period of the function y sinx Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression 1 What is the amplitude of the function y sinx Type an integer or a simplified fraction Which of the following is the correct graph of the function y sinx O A 121 2 2 V 12x OB Ay 2 2 X CO tx O C 12T 2 A 12n Ly OD A 2 i

Graph the following function over the interval 2 2n Give the amplitude y 4sin x Which of the following is the correct graph of the function y 4sin x A 21 OB What is the amplitude of the function y 4sin x Type an integer or a simplified fraction 27 8 y 12T O C 2 Ay 2x

Find the measure in radians of the central angle The area of a sector is 12 sq units Q Picture is not drawn to scale The measure is radian s Type an integer or decimal rounded to the nearest tenth as needed

K Find the exact function value CSC CSC T T BOXED Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Find the exact value of tan Choose the correct answer below O A 1 OB 0 OC 3 OD Undefined OE 3 3 3 20 O F

Convert the radian measure to degrees 16 15 This que 16T 15 Type an integer or 0

Use the following information to determine cos 2x Answer cos x and sin x is positive 4

11b Evaluate your expression for x 2 and y 4

6 Write an expression and combine like terms in the expression 4 times y de creased by triple y increased by double y

4s 37 19x 3r is equivalen to F 148 11 G 108 21 H 25 22 J 14 11 K 40 24

Which of the following expressions is equivalent to the one shown below 5m 120 14r 9r A 14m 2 R 14m 27 C 14m 3 D 14M 28 E 45w 168

5 Find the sum of 3x 2 and 2x 4

1 Combine like terms in the expression 3x 4 2x 6

3 Evaluate 3 2x y if x 3 and y 3 3 x 7 3

How much interest will you have to pay for a credit card balance of 986 that is 1 month overdue if a 16 annual rate is charged You will have to pay V CAN V MER Wh ALAND TE PANTA M A in interest Round to two decimal places

Write an equation of the line that passes through 7 1 and is parallel to the line y x 9 An equation of the parallel line is

2022 Kuta Software LLC All rights reserved Multiply Polynomials Find each product 1 2n 2 n 3 A 2n 6 B 2n 4n 6 C 14n 24 D 14n 62n 24 3 7x 8 2x 3 A 6x 31x 30 B 14x 24 C 14x 5x 24 D 14x 37x 24 5 8x 4 6x x 4 A 21x 38x 41x 6 B 7x 14x 4x 3 C 20x 34x 26x 4 D 48x 32x 28x 16 7 7 2k 8 6k 5k 8 A 12k 38k 24k 64 B 12k 34k 30k 8 C 10k 44k 12k16 D 25k 48 34k 9 7b b 4 3b 4b 1 A 21b4 25b b 17b 4 B 2164 4b 4 C 16b4 20b 34b 8b 5 D 12b4 32b 7b 36b 15 2 4 8 2 2n 5 8n 2 A 16n 36n 10 B 28n 45n 18 C 28n 3n 18 D 28n 18 10 4 n 4 2n 7 A 2n B 2n 28 C 2n 15n 28 D 2n 15n 28 66 8k 7 4k 2k 2 n 28 A 42k 78k 60k 24 B 16k 34k k 35 C k 11k 23k 3 D 32k 12k 30k 14 8 8b 3 8b 5b 8 A 6b 5b 24b 7 B 216 34b 2b 8 C 86 336 3b 4 D 64b 64b 49b 24 10 7b 6b 7 6b 8b 5 A 16b4 54b 92b 54b 40 B 16b 18b 40 C 4264 92b 125b 86b 35 D 16b4 42b 56b 6b 40

1 Multiply Polynomials Find each product 1 2n 2 n 3 A 2n 6 B 2n 4n 6 C 14n 24 D 14n 62n 24 B 3 7x 8 2x 3 A 6x 31x 30 B 14x 24 C 14x 5x 24 D 14x 37x 24 5 5 8x 4 6x x 4 A 21x 38x 41x 6 B 7x 14x 4x 3 C 20x 34x 26x 4

Multiply Polynomial Find each product 1 2n 2 n 3 A 2n 6 B 2n 4n 6 C 14n 24 D 14n62n 24

For the quadratic function f x 2x 8 a Find the y intercept and x intercepts b Find the coordinates of the vertex 9

Given f x x 1 a Show analytically that f is one to one b Find fl c Describe the domain of f d Graphically what is the relation between f and f

1 Find the difference quotient Accumo huo ulator is allowed f x h f x h for the following function below

Find the A P R annual percentage rate necessary for 9000 to grow to 24 000 in 9 years given the indicated method of compounding Express each answer in decimal form rounded to four decimal places a Compounded every 3 months A P R T 11 0479 Not quite b Compounded continuously A P R T 10 8981 Not quite Preview T 11 0479 Preview r 10 8981

What is the value of 5 more than the quotient of x and 2 given that x is equal to 8 16 5

5 Camille manages the soccer team She needs to order 3 practice jerseys and 1 game jersey for each player If there are x players on the team write an expression for the number of jerseys she needs to purchase a 3x 1 b x 3 1 c 1x 3