Coordinate system Questions and Answers

Question Watch Video Answer Attempt 1 out of 2 Show Examples From a hot air balloon Adriel measures a 22 angle of depression to a landmark that s 743 feet away measuring horizontally What s the balloon s vertical distance above the ground Round your answer to the nearest hundredth of a foot if necessary

Question Answer Attempt 1 out of 2 Watch Video Mamadou leans a 18 foot ladder against a wall so that it forms an angle of 75 with the ground What s the horizontal distance between the base of the ladder and the bottom of the wall Round your answer to the nearest tenth of a foot if necessary foot Show Examples

4 Suppose a large population has an unknown mean and a known standard deviation 0 4 4 How many individuals should be randomly sampled from this population so that the sample mean is within 0 75 unit of with 95 confidence Answer Previous Answer 133 Q Search Return to overview H hp Jy

3 A cosine function has the given properties Amplitude 3 phase shift a Write the function in the form y Acos z d where A 0 3 points b What is the domain of the function 3 points c What is the range of the function Use interval notation 3 points d Sketch one period of the graph starting at z 0 Clearly label each intercept and other key points such as max and mins 2

and closer to the given angle than any other coterminal angle Give the quadrant of the angle if applicable A 103 Choose the correct graph below where the curve on each graph traces the angle beginning at the positive x axis and ending at the ray OA OB 100 B 48 103 F

29 Given PS QR PQ SR P S He Prove APRSARPQ R

19 Given ABDE BC EF and B E B A C D Prove AABC ADEF E F

cos alpha 8 17 and alpha is in quadrant III and sin beta 5 13 and beta is in quadrant I Find cos alpha beta

Intensity 2888 8 20 Peak 60 1 50 P 40 30 20 Procedures 1 2 10 40 45 50 hkl 110 200 55 4 Calculate lattice parameter a according to a d h k 1 5 Calculate the averaged lattice parameter a 2 60 65 Two Theta degree From the XRD pattern measure the 20 angle of the peak 1 2 and 3 Calculate and sin20 20 measured from the XRD pattern 3 Calculate lattice parameter d according to the Bragg s law 2dsin 0 2 where is wavelength 1 541 70 0 sin 75 d 80 3 a 85

Given AD AB ABL BC and AD 1 DC Prove AABC AADC Step Statement AD AB AB LBC ADL DC try Type of Statement Reason Given B A D

11 Are the two shaded triangles below similar If so then what is the scale factor If not why are they not similar 5 8 cm 4 5cm 6 7 3 48 cm 27cm 4 02 cm

8 When asked to state the nature of the roots for you are a Finding the location of the x intercepts b Finding the location of the axis of symmetry Determining the number of x intercepts d Determining the direction of opening

5 8 Find a vector a with representation given by the directed line segment AB Draw AB and the equivalent representation starting at the origin 5 A 1 1 B 3 2 6 A 4 1 B 1 2

Write a rule to describe each transformation 31 G H H y A

Question 10 of 14 10 Suppose X is a normal random variable with probability density function defined by 1 16 What is the mean of X f x Answer e 16 Previous Answer 0 Return to overview

3 On Sunday Tiana runs on a straight path to the park located at 8 12 on the grid and from there she runs on a straight path to her friend s house located at 10 6 on the grid From there she runs on a straight path back to her house Ronald runs on a straight path to the library located at 12 0 From there he runs on a straight path to the store located at 10 6 From the store he runs on a straight path directly back home Draw the routes on the coordinate plane 4 Demonstrate that the two triangles formed by their routes are congruent Include a triangle congruence statement Then determine a series of transformations that maps one triangle onto the other

HQ Four Quadrant Ordered Pairs B C 3 3 G E C Z 4 3 2 4 S Write the ordered pair for each given point 8 4 9 W 11 I 10 12 Z 2 2 2 1 1 2 4 4 5 8 Tell what point is located at each ordered pair 1 3 7 3 6 4 2 8 7 4 9 7 8 9 5 8 9 6 3 8 13 G 14 T Plot the following points on the coordinate grid 17 O 7 4 19 V 2 5 18 F 3 6 20 A 2 9 W X messa 21 Y 1 6 22 U 2 5 1 2 6 1 D 7 4 4 8 1 3 15 D 8 6 16 J 3 1 23 M 1 5 24 N 8 8

F C Q A 10 y 8 6 4 4 2 0 2 2 6 8 10 2 B E 4 D X 6 Move the points so that they all lie on the graph of f x x 4 x 3 x 5 x 1 x 2 and do not coincide

6 4 C 10 A 8 6 4 1 2 0 2 4 6 8 10 y 2 B 4 D 946 X Move the points so that they all lie on the graph of f x x 4 x 3 x 5 60 and do not coincide

K For the given equation and graph of the quadratic function do each of the following Complete parts a through e f x 2 x 8 2 a Give the domain and range The domain is 00 00 Type your answer in interval notation The range is 0 2 Type your answer in interval notation b Give the coordinates of the vertex The vertex is 0 Type an ordered pair 986 10 2 4 6 x 4

1 8 Write a polar equation of a conic with the focus at the origin and the given data 1 Ellipse eccentricity 12 directrix x 4 2 Parabola directrix x 3 3 Hyperbola eccentricity 1 5 directrix y 2

6 A reservoir R supplies two towns Alton and Barnsville with water The pipelines from R to each town are being replaced to cope with increased demand The towns are connected by a straight road through them and the reservoir is 7 km from this road 4 km R 7 km 11 km B a Find the distances AR and BR to the nearest metre b Find the total cost of the new pipelines given that each 100 m will cost 2550

18 Solve the following inequality for y y 6x 3 Identify the statements which represent the inequality There may be more than one correct answer select all that apply The correct inequality begins with y The graph has a solid line The graph has a dotted line The correct inequality begins with y None of these statements are true

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Find the exact value of the expression given below 7 12 COS 2 1 3 4 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denomin COS 7 12

par and of a in the xy plane are given below Identity the particle s path by finding a Cartesian equation for it Graph the Cartesian equation Indicate the portion of the graph traced by the particle and the direction of motion x 5 sint y 4 cost 0 t The Cartesian equation for the particle is O A Graph the Cartesian equation Draw an arrow at the end of the particle s path showing the direction of motion as t increases Indicate the portion of the graph traced by the particle using a solid curve and the portion not traced by the particle by a dashed curve Choose the correct graph below Ay x y 25 16 O B 1 C Ay O D X

If these patterns are continued how many dots will be in the 100th figure of each sequence 3 Explain Jussends To S06990 08

1 The angle of elevation from the top of a 95 foot tall building to a hot air balloon in the sky s 76 If the horizontal distance between the building and the hot air balloon is 354 feet find the height of the hot air balloon

10 Jada is standing 10 feet from the base of tree and spots a nest sitting on a branch The angle of elevation from the ground where she is standing to the nest is 55 Find the height of the nest

1 Cross two ducks with a match Answer L 180 110 2 Cross a stick of dynamite with a lemon pie Answer T 113 68 63 34 34 54 38 54 67 99 57 90 36 59 67 Find the angle measures indicated Look for each answer in the code Each time the answer appears write the letter of the exercise above it 40 37 57 99 67 104 76 59 113 42 53 67 99 18 A mzPQR E mzPQT m28 57 F mZMNL K m2M 83 B 67 R N C S 37 29 K G m J 115 B MIDDLE SCHOOL MATH WITH PIZZAZZI BOOK D Creative Publications 56 A N mZDAB OmZDAC 41 D QmZEFD B MZE D 35 D E F U S mZWOX X 72 104 59 79 mZXZY U m2Y 180 79 42 B A W 27 X 138 180 Systolet Z M MZAOB R mZBOC O 0 54 D TOPIC 3 k Review Related Ang

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The equation gives parame equations and parameter intervals for the motion of a particle in the xy plane Identify the particle s path by finding a Cartesian equation for it Graph the Cartesian equation Indicate the portion of the graph traced by the particle and the direction of motion x 4t 3 y 16t t y x 3 Graph the Cartesian equation below Indicate the direction of motion as t increases Choose the correct graph below OA OB O C 10 40 10 TIH I Ay Indicate the portion of the graph traced by the particle Select the correct choice below and if necessary fill in the answer box to complete your choice OA The portion of the graph where t is less than B None of the graph C The entire graph OD The portion of the graph where t is greater than

or geometry software I can describe transformations as tions visually eg by using manipulatives functions with inputs and outputs Lesson Reflection Circle one Starting Getting there Got it Lesson 1 3 Checkpointsu bas svarbai galiolges Once you have completed the above problems and checked your solutions complete the Lesson Checkpoint below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 Draw the image of the figure under the given transformation Then describe the transformation as a rigid motion or not a rigid motion Justify your answer y 0 5x y 4 2 Match each transformation with the correct description A x y 3x y B x y x 3 y C x y x 3y D x y x y 3 E x y 3x 3y S S dilation with scale factor 3 translation 3 units up translation 3 units right horizontal stretch by a factor of 3 vertical stretch by a factor of 3

Home W Assignment 12 Midsegment Numeric Midsegment Algebraic es of Isosceles Triangles de Relationship ngle Inequality Triangles of a Given Type Triangle Lines Centroid enter Incenter Orthocenter and Exterior Triangle Angles Triangle LMN is formed by connecting the midpoints of the side of triangle IJK The lengths the sides of triangle LMN are shown What is the length of IJ Figures not necessarily drawn scale Answer Attempt 1 out of 5 N 2 L 2 2 K M J G

EXPLAIN 1 Introducing Proofs Read Explain 1 and complete Your Turn 1 3 adapted from Lesson 1 4 A conjecture is a statement that is believed to be true You can use inductive or deductive reasoning to show or prove that a conjecture is true Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true Deductive reasoning is the process of using logic to draw conclusions A conditional statement is a statement that can be written in the form If p then q where p is the hypothesis and q is the conclusion For example in the conditional statement If 3x 5 13 then x 6 the hypothesis is 3x5 13 and the conclusion is x 6 Most of the Properties of Equality can be written as conditional statements You can use these properties to solve an equation like 3x 5 13 to prove that x 6 Properties of Equality Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Reflexive Property of Equality Symmetric Property of Equality Transitive Property of Equality Substitution Property of Equality Example Use deductive reasoning to solve the equation Use properties of Equality to justify each step 1 14 3x 4 18 3x If ab then a c b c If ab then a c b c If ab then ac bc If a b and c 0 then ama If a b then b a If a band b c then a c If ab then b can be substituted for a in any expression 6 x x 6 Addition Property of Equality Division Property of Equality Symmetric Property of Equality Your Turn 1 Identify the Property of Equality that is used in each statement If x 2 then 2x 4 5 3a therefore 3a 5 If T 4 then 5T 7 equals 27 If 9 4x and 4x m then 9 m

1 Assuming counterclockwise rotations where would the following land Aelavkea 1 216 degree rotation of D about F 0 432 degree rotation of EA about F 144 degree rotation of ZDFC about F Be E

Label each triangle below as ABC Then transform each according to the rule Finally classify the transformation or devise a rule for it x y x y 13 9 Transformation of O 14 x y x 7 y 5 Transformation 6

27 Find the measure of the angles 20x 5 24x 1

Does the design below have rotational symmetry If so by how many degrees Bat How m

Ann planted daisies in her garden After a month she measured the height of each daisy Daisy heights 0 2 6 center 3 X X x X 4 5 Number of inches 6 spread 7 7 center X x ta Complete the sentences The median of the data is 7 inches It describes the spread of the distribution X 10 7 spread

If these two shapes are similar what is the measure of the missing length q K 75 m 9 15 m 9 meters 9m

Answer all of the following questions All questions must be solved using Excel formulas or functions Use the functions in Excel to solve for the missing item in each row Rate NPER pmt PV FV 5 8 100 1 000 Q1 9 10 0 Q2 4 8 Q4 Q5 20 Q3 50 000 0 1 000 0 2 000 8 12 000 0 5 000 7 000

Put the events in order of increasing probability P 0 P 1 You roll a 6 sided die and it does not land on 1 You pull a green ball from a jar of all pink balls On a spinner with just 3 and 5 you spin an odd number You roll a 6 sided die and it lands on 5 or 6 You flip a dime and it lands on tails

2 of 3 S kipped eBook Print eferences 2 Complete the below table to calculate income statement data in common size percents Note Round your percentage answers to 2 decimal places KORBIN COMPANY Common Size Comparative Income Statements For Years Ended December 31 2021 2020 and 2019 2021 2020 Sales Cost of goods sold Gross profit Selling expenses Administrative expenses Total expenses Income before taxes Income tax expense Net income 2019

38 Given BC AD BC AD Prove AB CD Statements 1 BC AD 2 4BCA DAC 4 AC AC 5 A Reasons 2 3 given D

d K ces 1 Compute debt and equity ratio for the current year and one year ago Current Year 1 Year Ago Current Year 1 Year Ago Numerator Numerator Debt Ratio 1 1 1 1 Equity Ratio 1 1 1 1 Denominator Denominator 11 11 Equity Ratio Equity ratio Debt Ratio Debt ratio

Solve the given equation Enter your answers as a comma separated list Let k be any integer 2 2 0 sin 8 rad List six specific solutions 0 rad

1 Points DETAILS LARPRECALCRMRP7 5 2 072 Powers of trigonometric functions are rewritten to be useful in calculus Verify the identity Simplify your answers completely sec x tan x tan x tan x sec x tan x tan x sec x Need Help Read It Submit Answer 10 1 Points S DETAILS tan6 x sec x tan x h ft Gnomon The lengths of a shadow cast by a vertical gnomon a device used to tell time of height h when the angle of the sun above the horizon is 8 see h sin 90 0 sin 0 5 Watch It a Verify that the expression for s is equivalent to h cot 0 Use the Cofunction Identity Simplify your answer completely h sin 90 0 sin 0 h cot 0 0 1 tan x sec x LARPRECALCRMRP7 5 2 079 sin 0 b Use a graphing utility to complete the table Let h 4 feet Round your answers to two decimal places 15 30 45 60 75 90

Rewrite the expression as a single logarithm and simplify the result Hint Begin by using the properties of logarithms 7 In cott 7 In 1 tan t

Describe a pattern in the sequence of numbers Predict the next number 5 2 6 18 54 6 0 1 4 9 7 256 64 16 4 8 3 0 3 0 3 0 9 7 0 7 5 8 0 8 5 10 13 7 1 5