Complex numbers Questions and Answers

Graph the solution set of the system of inequalities or indicate that the system has no solution 2x y 6 2x y 1 O A 10 B 10 C S D

Problem 4 24 points Consider the conic equation with equation 7 6ry y 1 a Identify this equation as a hyperbola or ellipse b Find the change of variables RT needed to eliminate the mixed term ry and have the conic equation in standard form A a The symmetric matrix is A equation will correspond to a hyperbola b The eigenvectors are 1 2 1 2 1 2 1 2 rotation matrix R A y2 1 1 3 s since the eigenvalues are 4 2 which have opposite sign the 3 1 for 4 and 1 for 2 After normalizing the eigenvectors we have the 1 2 1 2 1 2 1 V so the change of variables is

4 x 2 y 3 16 25 Type of Conic Orientation Vertices Foci Values for a b c 1 Label vertices v foci f and draw in asymptotes on graph

DIC You will be comparing 4 people who are throwing objects into the air Their throws are represented in different ways below You will identify the following for each Maximum height longest time in air type of object and age of sibling Person 1 Represented by the equation below y 16 x 1 x 3

OA 108 sophomores 92 juniors OB 124 sophomores 92 juniors OC 46 sophomores 62 juniors OD 62 sophomores 46 juniors algebra class If there are 108 students in this class find the number of sophomores and the number of SKLED

plete the square and write the equation in standard form Then give the center and ra 16x 64 y 8y 16 64 A x 4 y 8 64 Center 4 8 radius 64 B x 8 2 y 4 64 Center 8 4 radius 64 C x 8 2 y 4 64 Center 8 4 radius 8 D x 4 2 y 8 64 Center 4 8 radius 8

3 Evaluate Sc dz n 2 3 4 where z a is inside the simple closed curve C

Write an equation modeled by the envelopes and counters and then solve the equation Provide your answer below

The system of equations is shown on the gra 3x y 8 x 2y 4

For items 1 through 3 show that there exists a projective transformation r A B C S A2 B2 C A A B N B A2 B P B3 C C3 C R S S r P

d the average rate of change of the function from x to X 3x x from x 5 to x 6 A OB 2 OC 34 D D 1 6

have 228 feet of fencing to enclose a rectangular region Find the dimensions of the rectangle that maximize the enclosed A 114 ft by 28 5 ft B 57 ft by 57 ft C 114 ft by 114 ft D 59 ft by 55 ft

Write the partial fraction decomposition of the rational expression 7x 11x 36 x x 4 x 3 O A OB O C O D 3 X X 3 X 9 X 4 x 3 7 3 x 4 x 3 8 2 x 4 x 3 4 x 8 2 x 3

rational zero of the polynomial function and use it to find all the zeros of the 2x3 12x 10x 3 1 3 2 2 2 2 1 3 2 5 2 5 1 4 2 2 2 2 1 3 2 5 2 5

Solve the equation by the square root property x 2 6 OA 2 6i OB 2 6 OC 21i 6 OD 4 8

Solve the equation by the square root property x 9 2 O A 7 11 OB 9 21 OC 9 2 OD 9 2

2x y 6 2x y 1 O A 10 Q B 10 O C 2 D

A box of washing powder is 12 cm tall and contains 750 g of washing powder A similar box is 18 cm tall How much washing powder does it contain

There are two similar cylindrical drink cans The larger can is 15 cm high and contains 350 mL of drink If the smaller can is 9 cm high how much drink does it contain

48 The property demonstrated in the equation 10 9 1 10 9 10 1 is O distributive O commutative O associative ONeither side of the equation is equal to the other EN English United States

37 Considering the inequality 5x 4y 12 the shaded area of its graph is described by Oshaded below a solid line O shaded below a dashed line Oshaded above a dashed line Oshaded above a solid line

27 Solve the linear system of equations using the substitution method y x 5 7x 2y 15 This question is weighted four times as heavily as the other questions In or partial credit for this question use the space provided to justify your an x 7 y 12 A x 3 y 18 l x 5 y 10 Ox 4 y 1

23 Find the length of the diagonal of a rectangle whose dimensions are 17m by 13m Approximate to the nearest hundredth O22 2926 O22 29 O21 4009 21 40 EN English United States

22 Solve for x 0 23x 4 2 0 55x 7 2 O O O 356 25 O 3 56 O 35 63 X

18 How many ml of 50 percent acid should be added to pure acid to make 40 ml of 90 percent acid O2 4 ml 8 8 ml 3 2 ml 8 ml X 4

19 The speed of a spaceship in orbit is about 11400 miles per hour How many feet per second does the spaceship travel 130 feet per second O7773 feet per second 16720 feet per second O 1003200 feet per second C

15 Solve for a 0 30 7a12a 4 O 0 74 O 0 19 0 86 0 23 12

17 Find y when x 53 if y varies inversely as x and y 108 when x 17 30 2 O 39 9 34 64 36 51 4

16 Given the formula M u5 solve for u Ou 54 Ou 2 M 5 u M 5 5 2M O 5 2 5M U 4

13 Two ordered pair that are solutions of the equation 3y 2x 8 are This question is weighted four times as heavily as the other questions In answer or show your work 2 4 3 5 O 1 2 2 5 1 0 3 3 5

12 Given two circles whose radii are 10 and 15 the ratio of their areas is This question is weighted four times as heavily as the other questions In or partial credit for this question use the space provided to justify your ans O4 to 6 O4 to 9 2 to 3 l

9 Solve for b Abh This question is weighte or partial credit for this qu O O C A Ah 2A A

5 Given two circles O and P with radii 7 in and 12 in respectively the ratio of the areas is Oin 12 O in 4 49 144 both of these choices are equivalent

6 Use properties of exponents to simplify and then write the answer in radical form 81 4 x y O 1 81zy O 3xy6 O 3 xy C 8 81 ru6 4

1 Greg is going into business selling homemade blankets The supplies for each blanket cost him 3 00 and he wants to earn at least 17 00 for each blanket to compensate for his time If P 17n3n represents Greg s profit as a function of the number of blankets sold what is the domain of the function O all positive real numbers O all positive integers O all rational numbers

2 Solve the linear systems of equations using the elimination or addition multiplication method 11x 11y 66 14x 7y 0 O x 3 y 5 x 3 y 7 x 2 y 5 x 2 y 4

Write the sentence as an equation in two variables Then graph the equation he y value is five more than three times the x value DA y 3x 5 G OB y 3x 5 GITS O C y 3x 5 Q O D y 3x 5

notation x 110 x OA 0 10 U 11 00 0 OC 10 11 12 2 4 6 4 0 8 10 4 8 12 12 OB 00 11 U 10 00 12 OD 11 10 12 8 4 4 8 8 12 12

15 The marginal revenue per unit is MR 0 6x 12 dollars The total revenue from the sale of 80 units is a 2880 b 2100 c 1800 d 1230

a Find the binomial expansion of 1 3 x in ascending powers of x up to and including the x term simplifying each term 4 mark 2 mark 97 97 1000 e Substitute x into the binomial expansion in part a and hence obtain an approximation 3 mar 1 100 to 97 Give your answer to 5 decimal places b Show that when x 1 100 the exact value of 1 3x is

and rises 3500 vertical feet above the surrounding plain A cable car is to be installed that will travel from a point 810 ft from the base of the mountain to the top Find the shortest length of cable needed Your answer is ft 3 pts 1 Details To estimate the height of a building two students find the angle of elevation from a point at ground level down the street from the building to the top of the building is 31 From a point that is 200 feet closer to the building the angle of elevation at ground level to the top of the building is 51 If we assume that the street is level use this information to estimate the height of the building Question 21

The logistic growth function f t nearest whole number OA 382 butterflies OB 182 butterflies OC 282 butterflies OD 11 200 butterflies 800 0 15 1 15e describes the population of a species of butterflies t months after they are introduced to a non threatening habitat How many butterflies are expected in the habitat after 14 month GELER

5 Consider the sequence an defined by the recursion for n 3 4 5 an an 1 1 4 An 2 a Calculate h such that an h 1 fulfills the recursive definition 1 b What is the limit of the sequence an if it exists

tent III Simplify 261 o i 01 0 1 Inte

Simplify 3 2i 5 4i 0 2 22 8 6i 0 2 2i 0 8 2i

Multiply 7x 4 4x 3 Enter your answer in standard form in the box 7 8 B

Which expression is equal to O O 3 3 5 3 5 5 5 3 3 9 45

Factor the expression over the complex numbers x 24 Enter your answer in the box

11 Solve for x 10 5 25 45 Enter your answer as one inequality in the box 7 Interim Checkpoint Algebra 2 Chee 8 9

Factor 3ab 66 2bc ac O O O a 2b c 3b a 2b 3b c a 2b c 3b a 2b 3b c