Complex numbers Questions and Answers

Is the triangle with the vertices A 7 3 B 0 7 and C 8 7 a right triangle Is the triangle a right triangle O Yes O No

Find the trig ratio First find the hypotenuse 0 C 15 C 8

Consider the graph of y 2x 4x 1 The x intercepts are located at No solution Enter the coordinates of ALL the x intercepts or if no x intercepts exist select that ch Question Help Video Written Example

Draw the graph of f x 4 7 6 5 4 3 2 Clear All Draw 7 6 5 4 32 H 2 23 4 5 6 7 1 2 3 4 5 6 7

Solve 2 U 15 5 2 0 Express your answer in radical form If no real solution exists enter DNE Question Help Video Written Example

Find the length of AC Use that length to find the length of CD B 10 cm 30 A C 25 D What is the length of CD Round t 2 3 cm 4 0 cm 10 7 cm 18 6 cm

Julian describes an angle in the triangle using these statements GH is the adjacent side HK is the opposite side GK is the hypotenuse G H Which angle s is Julian describing O ZG O ZH O ZK O ZH and ZK

8 TIE F 10 E Given right triangle DEF what is the value of sin E O mun m n m O O O 35

12 K Given right triangle JKL what is the value of cos L 05 13 12 13

40 50 M Given right triangle MNO which represents the value cos M ON MN MN MO ON JMO MN ON

0 30 P Given fight triangle PQR which represents the value of sin P O RP PQ PQ RQ PR

Explain how you know that the number of dots in Dot Pattern B will eventually exceed the number of dots in Dot Patterns A and C Pattern B will eventually exceed the number of dots in Patterns A and C because it is i Compare the growth rates of Dot Pattern A Dot Pattern B and Dot Pattern C In your comparison rank the growth rates from slowest to fastest Slowest Growth Rate Middle Growth Rate i Fastest Growth Rate i

Dot Pattern F Stage 0 x Clear Stage 1 Create a graph to represent the dot pattern using the table Undo Stage 2 Redo Stage 3

If cos 0 8 17 0 what is sin 0 sin 0

8 16 11 I wo 22 6 1 12 ww 14 15 17 18 19 20 21 TOTAL Section 1 Multiple Choice 15 marks Circle the correct answer for each question Question 1 1 point In the triangle displayed below what is the value of sin 5 cm 8 b sine sin 12 cm sine 13 cm 5 12 d sine 5 13 12 13 12 5 e none of the above

2 15 18 21 e none of the above Question 2 1 point In ABKR ZBRK 90 BK 4 cm and BKR 40 Standing at BKR which of the following would be used to solve for the side KR a Cosine Law b Sine c Cosine d Tangent none of the above Question 3 1 point D Naming triangles is very important when using the Sine Law and Cosine Law In A PQR which side would be labeled with p Oa PQ b QR c RP d none of the above

3 11 9 14 22 9 17 12 9 20 15 18 21 Question 8 1 point Compound interest is an example of a linear growth b quadratic growth c exponential growth d constant growth e none of the above Question 9 1 point The expression 32 x 34 simplifies to a 36 b 38 c 96 d 98 the above

8 21 The equation that represents an exponential relation is a y 2x b y x Ocy 2 d y x 2 e none of the above Question 7 1 point An equivalent form of is Oak Ob 3 c 3k el none of the aboun

The graph of y 2X has a y intercept of 0 1 True False Question 14 1 point 5x 0 5x0 True False Question 15 1 point In order to use the Sine Law to solve for an unknown side two angles and one sic must be known and the side can be located anywhere in the triangle True False Question 16 1 point In the compound interest formula If an annual rate of 4 is compounded semi annually the i value would be 0 08

Find the equation of a line tangent to the circle x y 8x 2y 4 0 at point 1 1 O 3x 2y 1 0 3x 2y 1 0 3x 2y 39 0 3x 2y 3 0

Use compass and straight edge to construct the answer Describe your constructions and then prove it Given a circle C and a point P not on C construct a line through P that is tangent to C P

Write the equation of the line with a slope of 2 and a y intercept of 0

In what problem you would use the multiplication principle Select ALL that applies A student can choose a computer project from one of three lists The three lists contain 23 15 and 19 possible projects respectively No project is on more than one list How many possible projects are there to choose from Suppose that either a member of the mathematics faculty or a student who is a mathematics major is chosen as a representative to a university committee How many different choices are therefore this representative if there are 37 members of the mathematics faculty and 83 mathematics majors and no one is both a faculty member and a student In any group of 27 English words there must be at least two that begin with the same letter because there are 26 letters in the English alphabet Among any group of 367 people there must be at least two with the same birthday because there are only 366 possible birthdays The chairs of an auditorium are to be labeled with an uppercase English letter followed by a positive integer not exceeding 100 What is the largest number of chairs that can be labeled differently How many different bit strings of length seven are there

In what problem you would use the addition principle Select ALL that applies Among any group of 367 people there must be at least two with the same birthday because there are only 366 possible birthdays How many different bit strings of length seven are there Suppose that either a member of the mathematics faculty or a student who is a mathematics major is chosen as a representative to a university committee How many different choices are therefore this representative if there are 37 members of the mathematics faculty and 83 mathematics majors and no one is both a faculty member and a student A student can choose a computer project from one of three lists The three lists contain 23 15 and 19 possible projects respectively No project more than one list How many possible projects are there to choose from The chairs of an auditorium are to be labeled with an uppercase English letter followed by a positive integer not exceeding 100 What is the large number of chairs that can be labeled differently In any group of 27 English words there must be at least two that begin with the same letter because there are 26 letters in the English alpha

A student can choose a computer project from one of three lists The three lists contain 23 15 and 19 possible projects respectively No project is on more than one list How many possible projects are there to choose from O 57 38 23 O 19

Andrew can paint the neighbor s house 6 times as fast as Bailey The year Andrew and Bailey worked together it took them 5 days How long would it take each to paint the house days It would take Andrew It would take Bailey days Simplify your answers Type an integer a fraction or a mixed number

Write the number in standard form 12 288 3 12 288 3 Type your answer in the form a thi Tyne an exact answer using radicals as ne

Check AB That Apply 7 0 the fusion rate wel increase with a higher concentration of the substance the amusion rate will decrease with a higher concentration of the substance the diffusion rate will increase with a lower concentration of the substance the amusion rate will decrease with a lower concentration of the substance the offusion rate for the substance is the same for all concentrations

20 yd 240 Arc Length and Sector Area Find the APPROXIMATE area of each sector Round your answers to the nearest tenth

Find the EXACT area of each sector 13 7 cm 270

d the EXAC 2 length of each arc 90 18 in

Arc Length and Sector Area Find the APPROXIMATE length of each arc Round your answers to the nearest tenth 8 1209 6 yd

Arc Length and Sector Area Find the EXACT length of each arc 3 135 16 cm

Find the EXACT length of each arc 1 759 9 cm

5 Find FD 8 8 D U 19 9 2x 9 E F Line Segments abou Circles Find the measure o the line segment indicated

Find the measure of the line segment indicated 5 Find FH 6 Find BK N 10 8 M

Find the measure of the line segment indicated 5 Find FH 10 15 G 14 A A 4x 7 331

Determine the measures of KLM KLN and NML P 117 N K 152 TIT M L

rmine the equation of the line given in the graph below 4 18 5 10 SE 1 5 18 y 1 5 18 x

22 Find mMG 6x 4 5x 14 M F 3x 26 E

18 Find m2KSL K 3 28 x 29x 1 S L

Solve the following equation for t 1 14 S gt all denominators

2 i 2 i 2 i 2 1 0 Type integer or fractions Type your answer in the form a

Solve the equation by using the square root property x 4 The solution set is Simplify your answer Type an exact answer using radicals and i as needed Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed

Subtract and simplify 6 8i 3 i 6 8i 3 i Simplify your answer Type your answer in the form a

Find the product and write the result in standard form i 8 3i 8 3i i 8 3i 8 3i Type an integer or a simplified fraction Tyne your answer in the form a

39 Identify which of the following equations represents an exponential function Select ALL options a 0 b 1 c 2 d 3 40 Based on the shape of the graph determine if the function is linear exponential or quadratic Do this for each graph provided A B Members y 1800 1200 600 Website B 0 0 10 20 30 Day C A 2 g 2 X D e e 4 2 N IN 24 2

Add or subtract as indicated 10 5x 7x 8 3x4 5x 6x 11 4n n 2n n 3n n 4 1

4 Find the coordinate vector of p 4 3x x relative to the basis S p1 P2 P3 for P2 where p 1 p2 x p3 x

3 Find the coordinate vector of w 0 1 relative to the basis S 1 2 where v 1 1 and v 1 1