Quadratic equations Questions and Answers

Review If the linear function is of the form g x mx b and the following points are on the function 4 3 and 6 2 which function correctly describes g x g x 2x 5 8 x x 1 8 x x 5 g x 2x 5 Question 2 14 4 points Review Below is a table of a partial set of values of the linear function x h x 1 1 1 2 5 6 1 If the function is of the form h x mx b what is the value of the parameter b 0 E 4 0 2 8 10

54 3 Or P 5x OY 5x Ov 2 Ov y Review What is the equation of the following parabola in vertex form T n 3 5 CURGE XA MEDIANGLE HOSINGE SZENIE C JODE PUBE Pente

A boat moves in the direction of a lighthouse whose windows are located 50 m apart above sea level From a window in the lighthouse you can see at 02 45 p m the boat at an angle of 7 8 below the horizontal plane At 3 p m is the corresponding angle 42 4 How fast is the boat traveling Answer in km h

a Given the complex numbers z 1 5 3 i and w 0 5 0 75i find the moduli and principal arguments of zu and answer in 3 decimal places b Solve the equation 25 24 4 4 0 and plot the solutions in the complex plane w giving your

Insert appropriate 13 2 1 71 3 2x6 symbol or into the box 3 2 1 2 3 1 X 22x32 2 4 6 2 4 2 2 1 314

3x 2x1 c x 6x 5x e 4x 1 b 7x 14x d x 2x 11 f NH 3x

3 a Find each of the trig ratios Leave your answers as reduced fractions P 30 11 H n 24 40 Z 25 m nz Q b Sketch AABC with ZC as the right angle If cos B 15 then find sin B and tan B Leave your answers as a fraction 17 4 a Find the missing side or angle Leave your answers exact and approximate to the nearest whole number 1 X xx sin Q 17 m cos Q 15 m tan Q sin B tan B b The angle of elevation from a ship to the top of a 35 meter lighthouse at the water s edge measure 28 To the nearest meter how far is the ship from the shore Provide a sketch in your work

Consider U x x is a negative real number Which is an empty set O x x EU and x has a negative cube root O x x EU and x has a negative square root O x x EU and x is equal to the product of a positive number and 1 O x x EU and x is equal to the sum of one negative and one positive num

Which explains how to find the radius of a circle whose equation is in the form x y z O The radius is the constant term z The radius is the constant term z divided by 2 O The radius is the square root of the constant term z The radius is the square of the constant term z

What is the center of a circle whose equation is x y2 4x 8y 11 0 O 2 4 O 4 8 O 2 4 O 4 8

Circle P has a circumference of approximately 75 inches P T What is the approximate length of the radius r Use 3 14 for T Round to the nearest inch O 12 inches 24 inches 38 inches O 46 inches

An arc on a circle measures 125 The measure of the central angle in radians is within which range 0 to radians to to radians T to 3 radians O 03 O3 to 2 radians

Circle O has a circumference of approximately 250m ft d What is the approximate length of the diameter d O 40 ft O 80 ft O125 ft 250 ft

36 C 106 In the diagram of circle C what is the measure c 17 35 70 O 71

P M 83 45 N What is MPO O 128 173 192 256

Given Circle O with diameter LN and inscribed angle LMN Prove ZLMN is a right angle K M N What is the missing reason in step 5 Statements 1 circle O has diameter LN and inscribed angle LMN 2 LKN is a semicircle 3 circle O measures 360 m LKN 180 5 m2LMN 90 6 LMN is a right angle OHL theorem 1 given Reasons 2 diameter o divides into 2 semicircles 3 measure of a circle is 360 4 definition of semicircle 5 6 definition of right angle

4 Listen Write an equation of the line Balance dollars Bank Account YA 800 600 400 3 600 200 y 0 0 2 400 4 Weeks 2

April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 16 feet high The height of the arrow is given by the function h t 1612 64t 16 where t is the time is seconds What is the maximum height of the arrow OA 64 ft OB 16 ft OC 12 ft OD 80 ft

Homework 1 4 To verify the linear inverse by composition State if the given functions are inverses 1 f x x 4 g x x 4 f gex x 4 4 X 4 4 X g f x x 4 4 X 4 4 X Yes they are inverses 3 f n 3n 9 4 h n 2n 2 F ha I 0 2 3 A 2 5 g n 4 3n 2 2n 4 3 f n 9 4 60 6 9 1 65 2429 4 64 H FONDI 1 4 7 8 x x 3 3 f x x 2 2 g n 5n 20 8 f n 20 8n 5 f g x 5 2013 20 4 g x x 1 4x 8 3 f x 6 f x 2x 1 g x x 2 1 1 Period 4 8 g x x f x x 8

Exercise 1 Some exercises on the Week 10 exercise sheet will give you all the tools you need for this roblem You should work through those exercises but you can use them without including proofs of them Let b 2 2 and b 4 4 1 Is Bo b b2 a basis of Z 2 Let B spanz Bo Prove that B is a free abelian group of rank 2 3 Find a basis B b b of B a basis y c c of Z and positive integers d d2 such that b d c and b d c 4 Express Z2 B as a direct product of cyclic groups

The 1st 5th and 13th terms of an arithmetic sequence with common difference d d 0 are the first three terms of a geometric sequence with common ratio r r 1 Given that the 1st term of both sequences is 12 find the value of d and the value of r

5t 21 2 A drug is injected into a patient and the concentration of the drug is monitored The drug s concentration C t in milligrams after t hours is modeled by C t means in practical terms OA y 1 25 After 1 25 hours the concentration of the drug is at its greatest OB y 2 50 2 50 is the final amount in milligrams of the drug that will be left in the patient s bloodstream OC y 2 50 After 2 50 hours the concentration of the drug is at its greatest OD y 0 0 is the final amount in milligrams of the drug that will be left in the patient s bloodstream What is the horizontal asymptote for this function De

K Graph the solution set of the system of inequalities or indicate that the system has no solution 2x y 2 2x y 1 A 10 10 Q OB Q C O C 44 O D

olve the logarithmic equation Be sure to reject any value that is not in the domain of the original loga pg 3x 4 A 1 262 B 64 C 81 D 12 www

4 Let C be the curve y x 3x 4x 1 joining points 1 1 and 2 3 Find the v Sc 12z 4iz dz

Find a unit vector in the direction of V 10i 4j O 10 i 116 j 116 None of these 10 u 7 i j 84 84 0 10i 4j O 10 i 4 j 6 O 106 i 110 U

Let f be a function satisfying f 0 0 f 0 8 f 0 5 and f x 12 for 0 x 1 a The second Taylor polynomial p x of f about x 0 has the form p x ao a a x with ao a1 a2 b We approximate the function f by the second Taylor polynomial p of f about x 0 in the interval 0 1 Usin Taylor s theorem with the Lagrange remainder find the biggest a and the smallest b such that a and write the values of a and b in the boxes below b 1 1 ABY a f b

K x 6 x OA 2 3 12 OC 0 2 U 3 00 10 OB 00 3 U 2 00 OD 3 2 12 12 8 0

system of linear equations in three variables and then use matrices to solve the system ble below shows the number of birds for three selected years after an endangered species protection program was started mber of years after 1980 1 2 3 y Number of birds 42 61 86 ne quadratic function y ax bx c to model the data Solve the system of linear equations involving a b and c using matrices Find the equation that model y 5x 10x 32 y 3x 10x 29 C y 6x 30x 25 D y 4x 20x 24

Three shrimp boats supply the shrimp wholesalers on Hilton Head with fresh catch The Annabelle takes 50 catch to Hudson s 20 to Captain J s and 30 to Mainstreet The Curly Q takes 40 of its catch to Hudson o Captain J s and 20 to Mainstreet The SloJoe takes 30 of its catch to Hudson s 40 to Captain J s at o Mainstreet One week Hudson s received 236 5 pounds of shrimp Captain J s received 205 4 pounds and Mainstreet received 157 1 pounds How many pounds of shrimp did each boat catch OA Annabelle 202 lbs Curly Q 226 lbs SloJoe 171 lbs OB Annabelle 226 lbs Curly Q 202 lbs SloJoe 171 lbs OC Annabelle 171 lbs Curly Q 226 lbs SloJoe 202 lbs D Annabelle 202 lbs Curly Q 171 lbs SloJoe 226 lbs

Find a rational zero of the polynomial function and use it to find all the zeros of the f x x 3x 4x 10x 4 OA 1 2 2 2 2 2 OB 1 2 2 2 2 2 OC 1 3 2 3 2 3 OD 1 2 2 3 2 3

A drug is injected into a patient and the concentration of the drug is monitored The drug s concentration C t 7t What is the horizontal asymptote for this function Desc 31 4 milligrams after t hours is modeled by C t his means in practical terms OA y 2 33 After 2 33 hours the concentration of the drug is at its greatest OB y 1 00 After 1 00 hours the concentration of the drug is at its greatest Oc y 2 33 2 33 is the final amount in milligrams of the drug that will be left in the patient s bloodstream OD y 0 0 is the final amount in milligrams of the drug that will be left in the patient s bloodstream

Find the zeros of the function f x 2x 3 x 1 1 OA 3 1 OB 3 1 OC 3 OD none

A stick 1 meter long casts a shadow 1 3 meters long A building casts a shadow 18 meters long How tall is the building to 2 decimal places

45 If triangle ABC is similar to triangle XYZ and side AB 16 when side XY 18 what is the length of side BC when side YZ 27 O24 O 10 3 O 22 O 15 2

29 Identify the solution of the inequality 2x 3 6 7 Ox 5 Ox 8 or x 5 Ox 8 O 8 x 5 2

31 Simplify 10 a 9 7a 25 266 b 12 4 O62a 236 15 54a 756 15 7a 756 6 E

25 Solve the linear system of equations using the elimination or addition multiplication method 6x 2y 6 5x 5y 5 O 3 y 12 O 4 y 3 Ox 3 y 6 Ox 2 y 3

21 Simplify completely 11 2 5 32 2 8 35 2 O 35 2 58 2 X O 58 2

20 Solve the linear system of equations using the graphing method y 7x 12 y 3x 8 x 1 y 5 x 3 y 17 x 2 y 2 x 5 y 22 4

e figure shows the graphs of the cost and revenue functions for a company that manufactures and sell hat is the profit when 974 binoculars are produced 3500 2500 1500 500 R x 3x Break even Point 750 2250 A 2 396 B 5 396 C 3 448 D 448 C x 1500 x 200 400 500 000 Binoculars Produced and Sold GELE

Find the vertical asymptotes if any of the graph of the rational function x 4 x 16 h x OA x 4 x 4 OB X 4 OC x 4

With the data provided in the following table it is requested a Calculate the marginal product b Calculate the average product c In a graph plane total product marginal product and average product d Interpret each of the terms graphed e Based on the results explain the theory and function of production Marginal Product Work units 0 1 2 3 4 5 Total product 0 2 000 3 000 3 500 3 800 3 900 Average Product

A survey was conducted to determine who was the best bad guy in the Star Wars franchise Darth Vader Emperor Palpatine of General Grievous The rankings are shown in the preference table below Use pairwise comparison to determine who was the best bad guy among the three candidates Rankings 1st 2nd 3rd Total Votes O General Grievous Emperor Palpatine Darth Vader Vader Palpatine Grievous 206 Palpatine Grievous Vader 415 Grievous Vader Palpatine 124

There are 14 more sophomores than juniors in an 8 AM algebra class If there are 92 students in this class find the number of sophomores and the number OA 53 sophomores 39 juniors OB 39 sophomores 53 juniors OC 92 sophomores 78 juniors OD 106 sophomores 78 juniors SEXCES

Vrite the given sentences as a system of inequalities in two variables Then gr ne system The sum of the x variable and the y variable is no more than 5 The y variable ess than the difference between the square of the x variable and 2 Complete the system of inequalities in two variables first sentence 18 second sentence Type inequalities Simplify your answer

For this problem consider a triangle with side lengths A B C with opposite angles a B Y respectively Suppose that A 2 B 5 C 39 Calculate y in degrees Enter only a numerical value Do not type degrees 30

Use a system of linear equations to find the quadratic function f x ax bx c that satisfies the given conditions Solve the system using matrice 2 2 f 1 2 2 14 F x

Use the dot product to find the magnitude of u u 9 12

Multiply 8 14 21 Enter your answer in simplest radical form in the box