Complex numbers Questions and Answers

2 Three indistinguishable coins are tossed and the number of times heads comes up is noted A C 0 1 2 3 HHH HHT HTH HTT THH THT TTH TTT B D 1 2 3 HHH HHT HTT TTT

E and F be as above The event E UF is A C 1 4 1 5 1 6 2 3 2 4 2 5 2 6 3 2 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 1 2 2 1 1 1 1 3 2 2 3 1 3 3 B D 1 1 1 2 1 3 1 4 2 1 2 2 2 3 3 1 3 2 3 3 3 4 3 6 4 1 4 3 6 1 4 1 5 2 5 2 6 3 4 3 5 4 3 4 2 5 5 4 4 5 6 5 1 4 1 6 1 6 2 5 4 5 5 6 3 6 5 6

a Yes No b Using eight straight cuts can the dessert be cut into 16 equal pieces Yes

Directions State the degree and the leading coefficient of each expression x 2x 1 2 15y 84y 100 3y 1 3 5s 3s 3 s7 4 2x 3x 1 HW 3

Use the graphs to help you answer the question Figure 1 Figure 2 Figure 3 Which graph shows Y 2X 3 Select one O a figure 4 O b figure 1 O c figure 2 O d figure 3 Figure 4

Which of these figures does not have two pairs of parallel sides Select one O a parallelogram b trapezoid O c rhombus d square

Which one is an equation of a line perpendicular to Y 2X 3 passing through the point 2 2 Select one a Y X 1 O b Y 2X 6 O c Y 2X 6 O d Y 1X 6

Solve 9x y 1 dx 4y x dy If y 1 0 y 1 0 0 then y 1 Which of the following is within 0 01 of the right answer A 2 9221 B 0 C 2 D none of solutions A B C

7 46 PROVE the diagonals of a rhombus bisect the angles Statements What D A C B Justification Why

are of ZROS in AROS below is 60 S R px a The curved arrow represents the rotation of OR beginning from the positive x axis Through how many degrees has OR rotated b If OR 1 what are the exact lengths of OS and SR C What are the exact coordinates of point R

Evaluate the roots without using a calculator Write undefined or imaginary for any that are not real numbers a 27 b 27 c 27

Compute the following Use undefined or imaginary for non real results 3 2 100

te a polynomial function of least degree that has rational coefficients a leading coefficient of I and the zeros 3 and 2 1

ify the identity algebraically Use the table feature of a graphing utility to check your result numerically Simplify at each step cos 6 cot 0 1 sin 0 1 csc 0 cos 6 cot 0 1 sin 0 1m cos 8 cot 8 cos 0 cos 0 sin 0 sin 0 1 sin 0 O cos 0 cot 0 sin 0 1 sin 0 cos 0 sin 0 sin 0 sin 0 1 sin 0 1 sin 8 1 sin 8 1 sin 0 1 sin 0 sin 0

Pit in the tabie using this function rule y 6x 2

Find the exact value of the expression sec sin 1

A 0 180 L tube of toothpaste sells for 4 500 If you use 10 mL every brushing what s the cost per brushing

6y 3y 8 6y 2 Simplify your answer

A person 5 6ft tall is walking away from a lamp post that is 14ft high Find a relationship between the length of the man s shadow y and the distance x between the lamp post and the man

b Use the table c Check your so 7 n 11 n 1 n 1 Need Help

The shaded region is composed of four smaller regions b b a Write an expression for the area of the shaded region as the area of a A a b 2 OA 2 a b OA 4 a b A 2 a b OA a b 2 b Write an expression for the area of the shaded region as the sum of A a ab ba b A ab ab ba ba A a b a b A a b ab ba a b A 3 a b b c Evaluate each expression for the area of the shaded region when part a expression part b expression

A What are machine translations and how do the various methodologies differ B Neural machine translation is the future Defend or challenge this statement

N 1 points References Indicate whet True or F Tru

A 1 1 3 3 4 5 SHE and AB 4 10 10 determine the first and second columns of B Let b be column 1 of B and by be column 2 of B

A bacterial colony is growing at an exponential rate It is known that after 4 hours its population is at acteria and after 9 hours it is 189 bacteria a Determine an equation in y a b form that models the population y as a function of the numb of hours x let x of ars 98 ccb 14 189 a 619 10 a 25 2 4 5 At what percent rate is the population growing per hour

The population of a town t years after it is founded is given by P t 300 t 100 500 000 What is the towns population when founded

The trajectory of a projectile launched from the origin at an initial speed of v at an angle of degrees to the horizontal is given by the parametric equations x v cos 0 t y 1 291 where g is acceleration due to gravity typically 32 feet per second per second or 9 8 meters per second per second x v sin 0 t Find parametric equations for the trajectory of a golf ball with an initial speed of 180 feet per second at an angle of 40 to the horizontal Enter either exact value coefficients in radians or correct to at least three decimal places y How many seconds will the ball be in the air before it hits the ground seconds How far will it travel horizontally in total

Question 1 Use matrix inversion X 4 to solve the given systems of linear equ Find the determinant A Find Adj A Find A 1 Solve X 4 8 Find values of x y and z z 4y 2 4 x 2y 3 z y E

Suppose that the average monthly low temperatures for a small town are shown in the table Month 1 2 3 4 5 6 7 8 9 10 11 12 Temperature F 24 29 37 47 58 66 70 64 57 46 38 29 Model this data by hand using f x A sin wx p B Show how you found each value

Find the missing side or angle using the Law of Cosines and or Heron s Formula 7 C 68 01 37 83 0 B 42 15

Let A be a real n x n orthogonal matrix That is AAT ATA In Show that the only possible real eigenvalues are 1

if tan s release A in Quadrant 1 find www

Use a right triangle to writ cos sin 1 8 x

Solve the following inequality Enter your answer using inequality notation and graph the solution 1 3 3 6 3 8 7 6 5 4 3 2 1 0 1 2 3 5 4 5 6 7 8 9 10 11 12 13 14

logarithm problem for the positive log x 1 32 5

Let P 3 4 and Q 2 6 be two points in the coordinate plane a Plot P and Q in the coordinate plane No Solution Hela 10 b Find the distance between P and Q c Find the midpoint of the segment PQ A 50 9 6 2 6 S 2 2 d Find the slope of the line that contains P and Q 10 e Find the perpendicular bisector of the line that contains P and Q WebAssign Graphing Tool Fill f Find an equation for the circle for which the segment PQ is a diameter Graph Layers After you add an object to the graph your can use Graph Layers to view and edit im properties

What are the solutions for sin x A x 30 and 210 and 240 B x 90 and 270 and 30 0 in the interval 0 x 360 C x 60 and 240 and 300 and 120 D x 45 and 225 and 120

Wright equation y 3 x after translation 2 units UP and lunit down

Rachel is purchasing a new camera that costs 2900 Rachel uses a credit card that has an APR of 16 11 How much will she pay in total to pay off the purchase if she makes monthly payments of 70 Round the number of monthly payments up to the nearest whole number Round your final answer to the nearest whole number if necessary

Sean also read d books that were written in the twentieth century by European authors other than those in the table The number of books referred to by the table that were written by British authors in the twentieth century is approximately 39 of d Of the following which is closest to the value of d A 6 B 15 C 38 D 46

x meters x meters A 0 5 B 1 C 5 D 23 I x meters x meters Note Figure not drawn to scale The figure represents a rectangular pool with a width of 20 meters and a length of 25 meters that is surrounded by a concrete border with a uniform width of x meters If the combined area of the pool and the concrete border is 546 square meters what is the value of x

22 What is the best interpretation of 0 28 in this context A The maximum mass of the seeds was 0 28 mg B The maximum shoot length of the seedlings was 0 28 cm C For every two seedlings with 1 cm difference in the shoot lengths the estimated difference in the masses of the seeds is 0 28 mg D For every two seeds with 1 mg difference in the masses the estimated difference in the shoot lengths of the seedlings is 0 28 cm

26 If x 0 and p of x is 13 which expression represents x in terms of p A 13p B C D 13p 100 100p 13 100 13 D

0 If x 9 5 25 what is the value of x 9 A 30 B 21 C 20 D 11

19 Which equation has no solution A x x 1 B x 2x 2 C x 1 x 1 D x 1 2x 2 hos

6 On January 15 1913 Samuel purchased s pounds of sugar and p pounds of potatoes for a total of 0 16 The total weight of the purchase was 4 pounds Based on the prices in the table which system of equations represents this situation A 0 06s 0 02p 0 16 s p 4 B 6s 2p 0 16 s p 4 C 0 06s 0 02p 4 s p 0 16 D 6s 2p 4 s p 0 16

Which of the following expressions is equivalent to A B C D 16 2 b 4 16 3 9 ab 6 12 6 ab 6 3 9

15 2x 2y 2 One of the two linear equations in a system is given The system has exactly one solution Which equation could be the second equation in this system A 8x 8y 3 B 3x 3y 8 C 10x 8y 5 D x y 1

h t 4 9t 10t The function h models the height h t in meters of a football t seconds after it is kicked What is the interpretation of h 2 0 40 in this context A The football has a maximum height of 0 40 meter B The football has a maximum height of 2 meters C The football has a height of 0 40 meter 2 seconds after it is kicked D The football has a height of 2 meters 0 40 second after it is kicked

1 What do you predict for the end behavior Sketch 2 What are the x intercepts Does the function cross at each Explain