Complex numbers Questions and Answers

Add 4x 5x x 1 2x4 7x 6x 2x Enter your answer in standard form in the box

What is the product of 5 Enter your answer in standard form in the box Basic 7 4 8 of 5 2i and 3 4i 5 9 6 X X X

What is the radical form of the expression 2z y5 O 2x y8 8x12y15 64x32 y 40 2x 2 y 15 Interim Checkpoi

Simplify 7 50 6 24 Enter your answer in simplest radical form in the box

VUITE IN A 0 2x 3x 5 X X X x 3 i 50 4 3 i 31 4 3 i 15 2 3 6i 4

What are the roots of the equation 2x x 6 Select each correct answer 3 10 2 0 1 1 3 0

E 2x 3y6 5 3 2 5 4 3 2 1 54 3 C Interim Checkpoint Algebra 2 Checkpoint 1 Part 1 O 5 3 2 1 5 4 3 2 1

we JII Subtract 2x 2x 8x 2 x 5x 2x 7 Enter your answer in standard form in the box Basic 7 Interim Checkpoint Algebra 2 Checkpoint 1 Part 1 8 9 0

variation is 23 What is the median in the following data set 32 15 27 18 28 18 28 22 41 17 31 12 36 Round your answer to the nearest tenth 24 Simplify 5w 12 8 w 5 0 12 the constant of 25 Solve for a 10x 7 30x 21 O x 0 Ox all real numbers O has no solution 26 Convert to slope intercept form 8 321 12 x

35 What is the scale factor if a 6 inch by 6 inch photograph is enlarged to a poster that is 4 ft by 4 ft 4 ft 48 in 0 t t O Ott 08 O 1 5 36 How many ml of 60 percent acid should be added to pure acid to make 50 ml of 85 percent acid O 18 75 ml O 1 88 ml 9 38 ml 37 Rewrite the following expression as a fraction times the variable 9a

rational O irrational 39 Simplify completely 16 40 Bill is going into business selling homemade sandals The supplies for each sandal cost him 3 07 and he wants to earn at least 18 00 for each sandal to compensate for his time The best cost equation the cost of the sandal when you sell it for this situation is Use x to represent the number of sandals C 41 Change the equation x 8y 5 0 into an equivalent equation written in the slope intercept form O y x 1 Oy x 1 O y fx 1

O 9 and 1 O9 and 1 O 9 and 1 33 Write and solve the equation based on the following diagram x X X 1 34 The point 3 0 is found in quadrant O IV O I ON

25 Solve for a 10x 7 30x 21 x 0 O X O has no solution all real numbers 26 Convert to slope intercept form 8x 3y 12 y 27 Graph the equation y 0 8x 1 If you have a graphing calculator you may Find a when y 1 3

K Graph the solution set of the following system of inequalities x 1 y 1 36 x 1 y 1 16 Choose the correct graph below O A Ay OB Ay Q O C Q OD

15 Find the mean the median and the mode of the temperatures 61 89 93 102 45 89 O mean 95 8 median 97 5 mode 89 O mean 79 8 median 89 mode 1 O mean 95 8 median 89 mode O mean 79 8 median 97 5 mode 89 real numbers x irrational numbers whole numbers 16 To which number set s does the following number belong 11 Multiple answers may be correct Mark all correct answers rational numbers 89 integers 89

1 There are 48 socks in a drawer 24 pairs 2 pair s are silver 6 pairs are white and the rest are indigo If you took out a indigo sock and you didn t put it back what is the probability that you pull out another indigo sock If you enter your answer as a decimal round to the thousandths place x 2 Evaluate 5 5 9x8 5 O 84 O 77 O 80 82 3 Use Substitution to solve 1x 22 2y y x 2 3 y quation of a line passing through points 28 71

milk costs 1 50 more than a bottle of water how much does each item cost How much does a snack size bag of chips cost Type an integer or a decimal How much does a bottle of water cost Type an integer or a decimal How much does a gallon of milk cost Type an integer or a decimal

A wire with current i 5 61 A is shown in the figure Two semi infinite straight sections both tangent to the same circle with radius 9 91 cm are connected by a circular arc that has a central angle 8 and runs along the circumference of the circle The connecting arc and the two straight sections all lie in the same plane If B 0 at the center of the circle what is 0 Number Units Connecting are

LEARNING OBJECTIVE Simplify a square root or a CU Which of the following would result in an integer

1 point Consider the points which satisfy the equation y x ax b mod p where a 5 b 6 and p 19 Enter a comma separated list of points x y consisting of all points in Z satisfying the equation Do not try to enter O the point at infinity What is the cardinality of this elliptic curve group

Problem 1 Sketch the following parts of generalized circles and determine which of them are d lines l x y y 3x 2 l2 x y 3x y 1 02 l x y x y 2x 2y 1 0 ng

e the following triangles a In the right angle triangle PQR shown below find the regular Trig Ratios for P Q 5 12 13 0 R

Plot y 5 x 7 4 by identifying the slope and one point on the line 6 2 6 4 2 y 2 4 40 H 3 0

48 How many milliliters of water must be added to 70 ml of 35 corn starch solution to produce a 30 solution Round your answer to the nearest hundredth ml

32 There are 32 green socks and 8 white socks in your drawer If you close your eyes and take one sock out of your drawer what is the probability that the sock will be green Write your answer as a fraction x 33 Find the length of the diagonal of a rectangle whose dimensions are 17m by 14m Approximate to the nearest hundredth O 22 02 O22 0227 O 22 4722 O22 47

34 Find the equation of the line with the given slope and through the given point slope 6 1 7 y 35 Evaluate 1 4 36 Solve for y 3 0 y 37 Using a calculator express the following rounded to the nearest hundredth 43

180 22 Simplify completely 1125 x

18 Use the following data set to answer the following question 28 29 30 31 33 34 54 54 56 56 57 74 76 77 78 79 Find the interquartile range of the data Interquartile range 19 If a satellite travels 49000 feet per second how many in per minute does the satellite travel Do not include commas in the answer in per minute 20 If the line passes through 3 7 and 2 2 the equation for the line is V

Use the following similar triangles AABC ADEF If BC 28 when EF 39 and DF 23 what is the length of the corresponding side to DF Solve mathematically drawings not to scale Round your answer to the nearest tenth AC B D E

A FIND THE NUMBER OF DEGREES IN THE MISSING ANGLE OF EACH TRIANGLE BELOW TYPE YOUR SOLUTION IN THE WHITE BOX B C 70 66 62 E 54 68 71 71 33 80 78 44

3 26 Solve the following algebraically your answer may be an integer a fraction or a decimal 24 2z 13 2 x 27 The ne repeating decimal 0 297297297 may be expressed in a fraction as 28 For your new landscaping job your mom will buy you a number of garden tools p They are 7 each Write the equation which best describes total cost C of the tools as a function of the number of tools purchased

A statistics professor was curious to find out if students would rather take an English class a history class or a mathematics class He surveyed 120 students in total and got the following results Men Women Total 25 75 10 30 5 15 40 120 English History Mathematics 50 20 10 Total 80 What kind of relationship does this table describe O This table is an example of the principle of independence O This table is not an example of the principle of independence O There is not enough information to answer this question 15 Solve for 10 20 5

12 Solve for a 10x 2 70x 14 a has no solution O x 0 Ox all real numbers 13 If sales tax is 8 00 what is the total cost of a 36 40 baseball glove

3 Solve the inequality 9x 10y 20 Oy 2 10c Oy 2 1 x Oy 2 10x Oy 2 1x Oy2 2 1x Oy 2 1 x 4 Solve for a x x 9 33

9 Solve the inequality set Graph the solution on a numberline x 11 22 and x 10 6 Ox 11 and x 4 O 11 and x 4 4 Ox 11 O all real numbers Ono solution 10 Solve for x 2 4 x 5 O 21 1

47 Use the following scenario and frequency table to answer the question A classroom of 15 students polled to see who had studied for a quiz that morning The results were as follows Yes No 3 5 4 13 7 18 Boys Girls Total Total 18 17 15 Which of the following describes a joint relative frequency O Of the 15 students surveyed 7 were girls O Among the 7 girls 4 studied for the quiz O Of the 15 students 5 were boys who did not study for the quiz O of the 15 students surveyed 8 people neglected to study

10 5 10 5 10 5 5 1 038210 1 040808 1 043413 1 046025 1 048643 1 051267 1 053899 1 056536 1 059180 1 061831 1 064429 1 067153 1 069824 1 072501 1 075185 1 077876 1 000573 1 083278 1 005 909 1 088706 1 091431 1 094162 1 096900 1 099645 1 302397 1 105156 1 107921 1 110654 1 113473 1 116260 1 119053 1 121853 1 124660 1 127475 1 13029 1 038151 1 040742 1 043338 1 045940 1 048548 1 051162 1 053782 1 056 408 1 059040 1 061678 1 064322 1 066972 1 072290 1 074958 1 077633 1 000313 1 083000 1 085692 1 088391 1 091096 1 093807 1 096524 1 099248 1 101977 1 104713 1 107455 1 110203 1 112958 1 115719 1 118486 1 121259 1 124039 1 125825 1129617 1 038031 1 040604 1 043182 1 045745 1 048353 1 050945 1 053543 1 054145 1246056 1 058752 1258577 1 061364 1 271224 1 062980 1 283998 1 066602 1 296900 1 069228 1 309932 1 323094 1 336389 1 071859 1 074495 1 077136 1 079782 1 082432 1 085088 1 087748 1 090413 1 093083 1 095758 1 098438 1 101123 1 103813 1 106508 1 109207 1 111912 1 114621 1 117336 1 120055 1 161825 1 173501 1 385293 1 197204 1209235 1 221386 1 233659 1 122779 1 125509 1128241 1 349817 1 363380 1 377079 1 390916 1 404852 1 419008 1 433266 1 447667 1 462212 1 476904 1 491743 1 506731 1 521870 1 537160 1 352604 1 568203 1 542959 1 599673 1 615947 LETT 1 361563 1 173199 1 184949 1 196814 1 208796 1 220895 1 233113 1245451 1257909 1270489 1283199 1 296429 1308974 1 322054 1 335262 1 348599 1362067 1375666 1 389398 1 403265 1 417267 1 431405 1 445682 1 460098 1474655 1 489354 1 504196 1 519184 1 534317 1 549598 1 565028 1 580608 1 596341 1612226 LEM 1 161023 L172579 1 3800 1 196015 1207857 1231994 1264211 1256541 1 258906 1 281546 1 294222 1 307017 1319929 1 346114 1 359389 1 372706 1 396306 1399952 1413723 1427621 1 441648 1455803 1 470009 1 484506 1 499055 1 513738 1528556 1543509 1 558600 1 573829 1 58919 1 604706

Steve bought 58 shares of stock chat paid annual dividends of 0 23 per share What was the total annual dividend 3 points

Carmen invested 2 000 in a mutual fund that is front loaded with a loading rate of 4 75 What was the loading charge of this fund 3 points

a b b2 2020 School of Mathematics and Statistics UNSW Sydne a Show q A is a minimum when A Ao

113 303 H P119 48 45 Show Transcribed Text 111 524 G B LL F 134 09 47 69 32 06 104 037 C 25 This question may be completed using a Close program on a graphing calculator where necessary Using the figure below calculate the i Road secants C F and B G where the road width AH is 20 117m road lengths G F and G H for a 20 117m road width Check your solutions ii If the road width DE changes to 25m as indicated and the area of CDEF is 2600m2 calculate the bearing and

The points of intersection of the graphs of xy 7 and x y 50 are joined to form a rectangle Find the area of the rectangle The area of the rectangle is sq units

a b you are startin C Problem 2 These problems are secretly the same as the previous set The difference is instead of starting from x from a point that looks more like cx b a The goal is to become comfortable reducing expressions of this type to expressions of the previous type a 3 3 sec x 3 3 b 3 cot x 3 c 2 2 cos x 14 14 d 2 2 2 csc x 4 4 X x X 2pi 2pi 2pi 2pi 2pi 2pi n n n n n n

the length and width of a rectangle whose perimeter is 40 feet and whose area is 84 square fee length is feet Type the larger number

3 Express Z 1 Z 1 i 3 and Z3 3 i in polar form and use your results to find Find the roots of the polynomials below a P z z a for a 0 b P z z3 z z 1

A line with slope 1 passes through point P on the negative x axis and intersects the parabola y points and R as shown If PQ QR what is the y intercept of the line passing through P and R What is the slope of this line O 8 6 3 3 O 3 2 2 O 8 2 3 O 8 6 2 3 O4 3 2 y R Mt P

40 Simplify 365 4a 4a4 110 10 4 4a 5 O 36a 156 6 O 28a 156 6 O 4a 156 16

Determine which statement below is true about the relation y 18 16 10 8 7 The relation is not a function since there is only one value in the range The relation is not a function since there is only one value in the domain The relation is a function since each value in the domain is paired with only one value in the

Determine whether the relation is a function Domain Range 6 1290000 KAT 71 Select one a Yes O b No c Not enough information Check Determine whether the relation is a function 0 0 2 4 2 4 3 9 3 9 Select one a Yes b No c Not enough information