Quadratic equations Questions and Answers

ladder that is 20 ft long is leaning against the side of a building If the angle formed between the ladder and the ground is 75 how far is the bottom of the ladder from the base of the building

shadow that is 60 feet long when the angle levation of the sun is 65 How tall is the tower 2 Matt is standing on top of a cliff 305 feet above a lake The measurement of the angle of depression to a boat on the lake is 42 How far is the boat from the base of the cliff

5 A ladder that is 30 ft long needs to reach 27 ft up a building 6 You are standing 50 meters from a hot air balloon that is What should the angle off of the vertical be preparing to take off The angle of elevation to the top of the balloon is 28 Find the height of the balloon

a Indicate the defining property for two integers to be congruent mod m b Use this definition to show that if a b mod m and c d mod m then ac bd mod m c Is the converse of b true I e if ac bd mod m is then true that a b mod m and c d mod m If so prove it If not find a counter example For the toolbar press ALT F10 PC or ALT EN F10 Mac

A 67 B 204 x C 71 A middle school counselor randomly sampled students about their favorite subjects According to the table what is the total number of students participating in the randor sample C Grade 6 Grade 7 Grade 8 Totals 71 68 65 204 408 Math Science 29 Language Arts 18 Totals 67 20 26 19 27 72 25 20 20 65

Standard Form Graph Domam 00 00 Range Quadratic Equations y intercept Y NAST zeros 9 and 3 vertex AXIS OP symmetry X KENNE M

Compute the conditional probabilities from the two way frequency table Drag the item from the item bank to its corresponding match Favorite Summer Activity for 50 Children Reading Sports Swimming TOTAL P Favorite activity is reading if a girl P Girl if favorite activity is sports P Girl if favorite activity is reading P Boy if favorite activity is swimming Boys Girls 2 4 TOTAL 6 20 7 27 8 9 17 30 20 50

EXPLORATION Solving a Quadratic Equation by Graphing Go to BigIdeasMath com for an interactive tool to investigate this exploration Work with a partner 101 a Sketch the graph of y x 2x b What is the definition of an x intercept of a graph How many x intercepts does this graph have What are they 6 4 2 8 6 4 2 2 2 4 c What is the definition of a solution of an equation in x How many solutions 2x 0 have What are they does the equation x T 6 X

4x A standard deck of playing cards contains 52 cards equally divided among four suits hearts diamonds clubs and spades Each suit has the cards 2 through 10 as well a jack a queen a king and an ace If the 3 of spades card is drawn from a standard deck and is not replaced what is the probability that the next card drawn is a spade OR a king X 4x x x A B C D 5 51 4 17 1 17 16 51

e table shows the blood type of male and female patients at a hospital What is the relative frequency of a patient who is male and has blood type AB 4x A B 0 139 0 118 Blood Type Male Female A 105 93 B 99 84 O 160 140 AB 15 18 C 0 021

4x A bag of marbles contains 5 red 3 blue 2 green and 2 yellow marbles What is the probability that you choose a blue marble and then another blue marble assuming you replace the first marble A 3 4 B C 12 1 16

4x Michael has a drawer with 8 pairs of black socks and 12 pairs of white socks Without looking he takes a white pair of socks out of the drawer What is the probability that the next pair he takes out is black 4x A x B 4x C 4x D 11 19 500 00 20 19 8 11

x Mrs Brown gives two tests to her class 30 of the class passed both tests and 45 of the class passed the first test What percent passed the second test given that they passed the first test x A 67 B 33

1 red shirt 2 black slacks 1 white pair of pants 1 white shirt 1 pair of jeans 1 pair of sandals 2 pairs of running shoes Alex is on vacation and has the clothes listed above with her She is trying to pick out an outfit What is the probability she chooses a blue shirt and running shoes 4x A B 0 33 C 0 04 C 0 16 0 03

4x Tate has bag of golf balls 3 red 5 blue 2 yellow and 2 green What is the probability that he pulls out a red one replaces it and then pulls out another red one 4x x 1x A B O 4x D 5 12 1 22 16 1

If ZECD 45 and BED 110 is AABE ACDE If so by what criterion A B C yes by AA criterion yes by SSA criterion A no not possible to tell 65 E 65

4x Julie has two formal events to go to She has six formal dresses two blue ones one black one red and two white Given she will not wear the same dress to both events she calculates the probability of her wearing blue to both events as 22 66 p blue and blue Is she correct x x A no the two events are independent B no the probability of the second dress being blue changes after she chooses the first dress 4x C yes the two events are independent D yes the probability of the second dress being blue is not dependent on the first dress

d the value of sin W rounded to the nearest hundredth if necessary 8 Y 4 X

4x Pentagon JKLMN is similar to pentagon STUVW If NJ 4 WS 3 and JK 5 find ST A 5 8 x B C 9 2 4x D 2 4 E LU N 3 75 L M S W U V

1 point Click on the graph to view a larger graph For the given angle in the triangle given in the graph X 3 sin x COS X tanr cotr secx CSC X 2

x A B D The two triangles shown are congruent by the SAS Theorem Which statements when combined describe a sequence of rigid motions which maps AABC to AEDF A reflection across CB mapping AC to EF and ZA to ZE T A A translation mapping CB to FD and ZB to ZD A translation between the two figures maps ZC to ZF A rotation mapping CB to FD and ZB to ZD C A reflection between the two figures maps C to ZF B F E D

x Triangles UWW and KLM are similar Triangle UWW is the smaller triangle Arrange the side lengths correctly on the diagram U K V L W M

What theorem can be used to prove that the two triangles are similar x A SSA Similarity Theorem B C SSS Similarity Theorem AA Similarity Theorem G 3 1 5 6 3 B 30

By which rule are these triangles congruent A SSS 4x 4x B CO C SAS D ASA M N P

Given the picture what is the length of AC A 4 5 B C 7 5 D A y B 3 6 x 4 D 6 E

The quadrilateral shown is a parallelogram If m ZADC 125 and m 1 30 what is m 2 x x A B 35 A 25 2 B

The quadrilateral shown is a rhombus What is m 24 A 28 B 32 C 58 3 32 2 8 7 6 4

A The quadrilateral shown is a rhombus If AB 17 and AE 8 what is the measure of BE B C 15 29 D 11 A E C B

20 If y x 6x at which of the following points is there a change in concavity a 0 0 b 1 5 c 2 8 d 1 5

1 Determine the unknowns in each triangle using the proper trigonometry formula SINE LAW OR COSINE LAW 8 marks d B e 8 10 cm 17 cm A 85 18 cm C 15 cm

2 A 16 ft long ladder is leaning against a wall The base of the ladder is 7 ft from the base of the wall Draw a diagram and determine the angle of elevation that the ladder makes with the ground 5 marks

a 1 Determine the unknowns in each triangle using the proper trigonome formula SOH CAH TOA 9 marks b 30 c B B 770 C 15 cm A 22 cm C 24 cm A

The circle below has center M Suppose that m ZKML 72 Find the following E L M a m KL b m ZKJL 0 0 0

A 3 B 360 180 2 P S 2x 120 0 120 120 2x 120 X LEFT 2 y 2cos 3x 180 2 AY D 1 Down

2 Solve Graph the following equations 4x a 110 10 55 b log 4 log c 9 5

Questions are 1 The lectures show three different methods on solving quadratic equations Explain each method in a great detail 2 One of the method to solve quadratic equation is completing the square Write your explanation step by step on completing the square Do not just copy from the online resource 3 How appropriate is to check your solutions What happens if there is no solution In what scenario there is no solution in quadratic equation

18 C D Find g x where g x is the reflection across the y axis of f x 3z A B 8 x 3 x 8 x 33 8 x 3x 3 8 x 3 x

Solve 6 2x 2 7 143 If there is a rational solution enter as an integer or reduced fraction If there are multiple solutions separate them using commas For no solutions click No solution O No solution

Solve 3w 4 81 If there is a solution enter as an integer or reduced fraction If there are multiple solutions separate them using commas For no solutions click No solution No solution

Find any real solutions to the equation x 7 0 Enter any real solution as an integer or reduced fraction If there is more than one real solution separate with commas If there are no real solutions click the No Solution button One or more solutions No real solution

Solve c 5 16 Enter any solution as an integer or reduced fraction If there is more than one solution separate with commas If there are no solutions click the No Solution button No solution

2 What is the frequency of a sine curve that has a period of 3 Graph y 4 sin 2x over the interval 0 x 2 Label the axes and identify the following Amplitude Frequency

The function f x 10 has been reflected across the x axis shifted 4 units to the right shifted 2 units down and vertically stretched by a factor of 3 to create the transformed function g x Which graph best represents g x A 6 D 2 t

37 ERROR ANALYSIS You invest 500 in the stock of a Acompany The value of the stock decreases 2 each year Describe and correct the error in writing a model for the value of the stock after years y Decay Initial amount factor y 500 0 02 41 r 1 26 compounded monthly In Exercises 39 42 use the given information to find the balance in the account earning compound interest after 6 years when the principal is 3500 39 r 2 16 compounded quarterly 5 MTR 43 STRUCTURE In the compound interest formula for interest compounded yearly A P 1 r what does P represent What does 1 r represent Does P depend on 1 r Does 1 r depend on P Explain 5 COMPARING FUNCTIONS Compare the graph of f x 2 1 5 to the graph of g Which graph has a greater y intercept Which graph is increasing at a faster rate Explain your reasoning 4 2 Ay 2 g 38 ERROR ANALYSIS You deposit 250 in an account that pays 1 25 annual interest Describe and correct the error in finding the balance after 3 years when the interest is compounded quarterly X 4 X 14 3 A 250 1 1 25 1 5 6533 29 40 r 2 29 compounded monthly 42 r 1 83 compounded daily MTR 5 44 STRUCTURE The equation y 1000 1 12 represents the balance y in dollars in an account after t years a What is the annual interest rate Explain b Rewrite the function in the form y 1000b 2r c Explain how you can use your equation in part b to find the monthly interest rate 46 HOW DO YOU SEE IT Chapter 6 Exponential and Logarithmic Functions The graph shows an exponential function of the form f x abx a Determine whether frepresents exponential growth or exponential decay 1 4 0 1 1 4 2 6 b What are the domain and range of the function Explain

Find the equation NE 2 A y 2 sin x B y 2 sin x C y 2 sin x D y 2 sin x

Find the equation 1 ww A y 1 sin x B y 2 sin x C y 2 sin x D y 1 sin x

Find the equation A y 1 cos x B y 1 sin x C y 1 cos x D y 1 sin x

In Exercises 15 19 write a quadratic function in standard form whose graph satisfies the given conditions 15 vertex 5 4 16 x intercepts 2 and 7 17 passes through 3 0 1 0 and 1 8 18 axis of symmetry x 3 19 passes through 4 0 and 4 0

4 Kent can paint a certain room in 6 hours but Kendra needs 4 hours to paint the same room How long does it take them to paint the room if they work together

In Exercises 11 14 use zeros to graph the function 11 y x 1 x 3 13 g x g x x 10x 21 12 f x 2 x 2 x 6 14 y x x 6