Complex numbers Questions and Answers

Determine if the given number belongs to the set Whole 1 78778777 Natural Integers Rational Irrational Real

Determine if the given number belongs to the set Natural 5 6 5 6 Natural Yes Whole Whole Integers Integers Rational Rational Irrational Irrational Real Real

Determine if the given number belongs to the set 50 25 Natural Yes No Whole Integers Rational Irrati

Determine if the given number belongs to the set 6 Natural Yes Whole Integers Rational Irrational

Replace the with the correct symbol 1 13 0 08

Determine whether the statement is true or false 3 2 1 5 Is the statement true or false O True O False

List all elements of the set Select all that apply A 5 3 53 3 C 0 E 8 737717 that are also elements of the set of integers 8 0 6 2 7377377 B 6 D 2 73773777 F No elements in the set are in the set of integers

List the numbers in the given set that are whole numbers 13 5 5 7 0 12 1 42 x 6 Select all that apply A 0 C 5 E T G 7 6 00 B 5 D 13 2 F 1 42 H There are no whole num

Use the number 33 a List all the prime numbers that must be checked for divisibility b Determine whether the number is prime or composite a Choose the correct answer below OA 2 3 5 7 8 OB 2 3 5 OC 2 3 D 2 3 5 6

List all elements of the set Select all that apply A 0 C 10 E 9 9 0 10 5 73773777 that are also elements of the set of natural numbers 3 B 5 73773777 D 8 3 F No elements in the set are in the set of natural numbers

Step by Step Solution Step 1 Find the least common denominator of the fractions Find the least common denominator LCD of the rational numbers and Then rewrite each rational number with the LCD 50 9 50 11 1 14 Write each denominator as the product of prime factors

7 Vrite the fractions and 11 7 7 as equivalent fractions with the least common denominator 13

Round the given number to the nearest hundredth 561 009

Step 1 Write each number as the product of prime factors aligning common factors vertically 14 77 Type your answer in factored form

A surveyor places poles at points A B and C in order to measure the distance across a pond The distances AC and BC are measured as shown to the right Find the distance AB across the pond The distance AB across the pond is about yd Type an integer or decimal rounded to the nearest tenth as needed 44 yd

3 4 2 4 3 4 2 4 Simplify your answer Type an exact answer using radicals as neec

Calculate acute angles only without a calculator 5 1 1 If sin Asin B the values of and B 5 1 2 If sin A 1 2 then 5 1 3 If sin A cos B the values of and B

10 1 point To attract business the manager of a sports equipment store decreased the price of a hockey stick from 500 to 440 What was the percent of decrease 20 15 12 60

9 1 point A cereal company used to fill the boxes with 16 ounces of cereal They have reduced that amount to 14 ounces The percent decrease is 87 5 True False

Your fitness tracker says you ran 2 640 yards on your most recent run How many miles is that 1 3 miles 2 miles 1 5 miles 1 mile

4 1 point Evaluate if t 2 and x 3 3 2x t 102 30 12 48 Previous

Consider the following a Evaluate 1 b Evaluate f 1 c Solve for f x 3 d Solve for f x 3 7 TI X 7 6 5 4 3 2 1 2 3 4 5 6 7 y 4 6 5 T 3 2 book 2 LE 1 3 LE In 6 7

ou are in a submarine tracking a ship that is not changing direction or speed Its first position on the radar is 9 113 After one minute the ship is at 8 5 94 What is the equation of the position of the ship in rectangular coordinates In polar coordinates what will be its position after 4 min In polar coordinates what will be its position after 7 min

Find the centroid of the area of the composite shape shown below Find BOTH x and y values but input y 1 ft 6 ft 3 ft 2 f

The function h x 4 is graphed at the right What is the range of the function h x shown Range h x 4 Range h x 4 Range h x 2 Range ALL REALS A Asymptote y 4 M M 24 4 w h x 4

shown to the right Find the distance AB across the pond to measure the distance across a pond The distances AC and BC are The distance AB across the pond is about yd Type an integer or decimal rounded to the nearest tenth as needed 43 yd 21 yd

You should be able to answer this question after studying Unit 12 a Find all roots to the following equation in Cartesian form 28 3 i b Express 2 in Cartesian form to 4 decimal places Hint The rules for logarithm on page 273 of Book A still apply to complex numbers

Given h x is a transformation of the graph f x 2 determine which of the below correctly describe h x H 3 2 1 2 Asymptote y 0 12343 h x 2 x h x 2 x h x 2 x Oh x 2x 1 Asymptote y 3 h x

Review What is the equation of the following parabola in vertex for 4 3 2 1 O 6 ev 1 y 3x y 3x Or 2 O N 23

Review The graph of the linear function x is shown below If the function is of the form h x mx b what must be true of the parameter m m 0 O m 0 Om m2 0 Question 2 14 4 points Review If the parent function is f x mx b what is the value of the parameter b fo the line passing through the points 4 0 and 0 2 2 h x 4 2

Starting from the group N 1 12 construct a chain of distinct normal subgroups of at least 5 elements that is find 5 groups N N N3 N4 N5 in such a way that each is a normal subgroup of the next

graph to determine the domain and range of the function E A domain xx 1 x 1 range yly 0 B domain all real numbers range all real numbers OC domain xx 1 x 1 range all roal numbers OD domain all real numbers range yly 1 y 1

The circle shown above has center point 0 Chord AC is perpendicular to radius OD and intersects OD at point B Line segment OB has a length 8 and line segment BD has length 9 What is the length of chord AC A 2 145 B 30 C 24 2 D 34

ALGEBRA 2 DIAGNOSTIC TEST REFRESHER NAME 2 SOLVE and Graph using key features 0 5x2 12

X y input 5 2 1 0 6 4 X 5 5 5 5 y 1 2 3 4 2 8 10 12 14 output 2 8 7 6 6 11 14 13 14 3 12 114 4 11 4 6 8 6 8 11 14 9 4 2 8 0 1 input 3 6 9 12 6 5 2 3 X 9 11 15 20 9 8 8 6 output 2 4 6 y 4 3 1 0

Set A Set B E U IV On the Venn diagram which region s represent the intersection of Set A and Set B ANB OII OI and III OI II and III O I II III and IV

The Venn diagram shows the number of patients seen at a pediatrician s office in one week for colds C ear infections E and allergies A U 5 2 10 15 A 3 E 9 How many patients total were seen for only a cold onl an ear infection and only allergies O 16 O 28 O44 O 49

An arc on a circle measures 85 The measure of the central angle in radians is within which range O 0 to radians Oto radians O to 37 radians 2 O 37 to 7 radians

D C B A The smallest of the three circles with center D has a radius of 8 inches and CB BA 4 inches What is the sum of the areas of all three circles 80 min 96 in 208 in 464 in

T 14 ft n circle V r 14ft What is the area of circle V 14m O 28tf O 49m O 196

The measure of central angle RST is a radians What is the area of the shaded sector 4 units 8 units 16m units 20 units

72 x P 360 x In the diagram of circle P mzXYZ is 72 What is th value of x 108 O 144 16 O216 O252

TRIANGLES Apply your knowledge of angles in similar triangles to answer each question below 1 Three students sketched the triangles shown Which students sketched similar triangles Explain Beau 180 116 3 Use the triangles below to answer a b B E 14 cm A 63 48 10 cm C 20 D 2 Spencer constructed triangle XYZ where ZX 76 and 2Y 49 Morgan constructed triangle JKL where J 49 and ZK 65 Are the two triangles yes Tho corresponding angles similar Explain your reasoning 89 48 15 cm b If possible find the value of x X 21 116 61 F a Is triangle ABC similar to DEF Explain yes two corresponding angles BEAU 55 55 61 KAI D 64 4 Use the triangles to answer a b 12 in A 5 Richard believes the two triangles shown are similar while Penelope believes there is not enough information to tell Who do you agree with Explain your choice C 55 NYLANA 4 in 55 51 61 b If possible find the value of x B 8 in a Is triangle ABC similar to CDE Explain yes 70 61 51

CY 48 B What is the measure of angle CAB in circle O 24 48 72 96

Slope 3 passing through 6 7 OA y 3x 11 OB y 3x 11 OC y 7 3x 6 OD y 7 x 6

K use the train also have the option of purchasing a frequent rider pass for 18 75 each month With the pass a ticket costs only 1 75 per ride How many train ride month make the frequent rider pass a better deal than standard train tickets OA 24 or more rides OB 27 or more rides OC 25 or more rides OD 26 or more rides

Q8 If z a ib Z c id then Z Z Z Z l a ac bd bc ad ac b d ac b d b ac bd bc ad ad a c ac bd bc ad a c b d d ac bd bc ad a c b d

K Find the y intercept of the polynomial f f x x 2x 8 OA 0 OB 1 O C 8 O D 8

The logistic growth function f t nearest whole number OA 175 butterflies OB 375 butterflies OC 275 butterflies OD 4 800 butterflies 320 1 7e 0 25t 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 1 GELEB

than juniors in an 8 AM algebra class If there are 68 students in this class find the number of sophomores and the number of junior OA 39 sophomores 29 juniors OB 29 sophomores 39 juniors OC 78 sophomores 58 juniors O D 68 sophomores 58 juniors EXCE