Heights & Distances Questions and Answers

6 M AS A M is the result of translating ASAM If the slope of SS is the the slope of MM is If the length of AA is 6 then the lengths of MM is If the length of AM is 5 then the length of A M is

Role I Service Fact service line id service id I service type id employee id I labor cost I service start date service end date I I total service price I Part Fact I service line id I part id I I part vendor I I unit cost I I part count I I part cost at service Explanations Bike Type and Bike Brand Type 1 SCD is chosen because bike types and brands are unlikely to change If they do change a new record can be inserted

Measurement Seated elbow position Calculations Percentile 9 5 inches Males Males 50th percentile 0 3 inches 7 5 inches 10th percentile Standard Deviation 9 1 inches Females 50th percentile 0 2 inches Males Minimum resting elbow height 9 5 inches 2 inches 7 5 inches Maximum resting elbow height 9 5 inches 1 inch 10 5 inches Females Export t Minimum resting elbow height 9 1 inches 2 inches 7 1 inches Maximum resting elbow height 9 1 inches 1 inch 10 1 inches Percentile range

Read Explore and complete the following adapted from Lesson 3 2 Show all your work Two geometric figures are congruent if and only if they have the same size shape and angle measures In geometry the symbol can be used two indicate the two figures are congruent A landscape architect uses a grid to design the landscape around a mall Use tracing paper to confirm that the landscape elements are congruent A Trace planter ABCD Describe a transformation you can use to move the tracing paper so that planter ABCD is mapped onto planter EFGH What does this confirm about the planters B Trace pools JKLM and NPQR Fold the paper so that pool JKLM is mapped onto pool NPQR Describe the transformation What does this confirm about the pools CDetermine whether the lawns are congruent Is there a rigid transformation that maps ALMN to ADEF What does this confirm about the lawns Reflect 1 How do the sizes of the pairs of figures help determine if they are congruent D C M M N A B H G K Q E E R L N D

Your Turn The figures shown are congruent Find a sequence of rigid motions that maps one figure to the other Give coordinate notation for the transformations you use Then check your answer 1 JKLM WXYZ Step 1 Look at the graph and or table for similarities and differences 8 M 81y Figure 1 0 W 4 X Step 4 Check your answer L K 8 Step 2 Look at coordinate notation rules that could map Figure CDE onto JKL Select two Step 3 Write the coordinate notation for the transformations you use Describe the rule in words x y A Rotation B Reflection C Translation OD The figures are not congruent 1st Transformation 2nd Transformation Did the two rigid motions map one figure onto to another Why or why not Figure 2

X Determine the value of x 5x 16 2x 3 3x 4 B

Determine the values of x and y X y 8y 6 34 6y 12 x

75 5

3 Complected and transfered at 745 000 100 745 000 100 40 Exeling work in process 183000 100 18 3000 1928000 Total units 928000 745000 452 00 790200

Select the correct choice that completes the sentence below The domain of y arcsin x equals the of y sin x function domain inverse range

Given 2 similar triangles Delta ABCand Delta KJI AB 7 9 cm AC 3 8 cm BC 4 8 cm and JK 5 7 cm Construct a diagram of the triangles and determine the lengths of the unknown sides

a moving truck uses a 13 ramp to unload When the ramp is fully extended the distance between the base of the ramp and the back of the truck is 8 What is the angle of elevation

ve the general solution for the following trigonometric equation without a calculator in grees Type DNE on the larger angle if only one equation is necessary tan 48 29 1 275 Reference Angle B B degrees round to two decimal places where kZ smaller angle where kEZ larger angle

15 Write a program that will find the third one if you are given two out of three from the vertex centroid and midpoint For example the second screen shot shows the vertex when 4 7 and 12 2 are inputted for the centroid and midpoint NORMAL FLOAT AUTO BEAL RADIAN MP MISSING VERTEX 2 CENTROID 3 MIDPOINT NORMAL FLOAT BUTO REAL RADIAN MP GCA B MCC D A 74 B 7 C 12 D 2 12 25 Done

Select all the correct figures Which numbers have line symmetry 2 3 7 8

Which letter has point symmetry A L D

se an identity to simplify the following expression tan 17 1 tan 17 Choose the correct expression equal to OA 1 2 cos 17 OC 1 2 tan 34 tan 17 1 tan 17 below B 1 TIN tan 17 OD sin 34 G

Determine the magnitude and direction of the vertical shift and the phase shift for the function below f x sin x 7 3 Select the correct answer below O O O The vertical shift is left 7n units down and the phase shift is 3 units to the 4 The vertical shift is 7 units up and the phase shift is 3 units to the left 4 7 The vertical shift is 3 units up and the phase shift is right The vertical shift is right 7 The vertical shift is 3 units down and the phase shift is left 4 7n 4 units to the units up and the phase shift is 3 units to the 4 7x O The vertical shift is 3 units down and the phase shift is right 4 units to the units to the 11

0 NUMMMM 1 2 5 2 1 0 0 Ay 1 T 10 47 5 2 y sin x X n 5 Q G 5 3 2 1 0 0 Ay I 0 1 2 3 2 Drag each graph above to match the function below y sin x n x X T 5 1 0 0 V 6 5 15 5 y cos x GLOB T 5 y cos x 5 3 2 1 0 0 2 0 6 11x 5 Q

4 y x 5 y x 5 PART A Graph the functions Q

2 5 pts Two cables are attached to a tower to stabilize it In the figure the cable on the left is 150 ft long and forms an angle of elevation of 58 The cable on the right forms an angle of elevation of 29 How long is that cable marked with an x Show your work Round to 1 decimal Use correct units 150 ft 58 Tower X 29

Roll the Die C X Let s implement your randomization plan Roll the die below and assign treatments to each of the nine cows shown in the picture below by marking or circling each cow eyes marking place a circle around the cow crosses marking place an X over the cow no marking underline the cow Below is the randomization plan you proposed on the previous screen You can go back and make changes to your plan if you need To use a 6 sided die to randomly assign each cow in a herd of 50 cows to one of three treatments artificial eyespots cross marked or unmarked you can follow these steps 1 Label the die Assign two faces e g 1 and 2 for the artificial eyespots treatment Assign two faces e g 3 and 4 for the cross marked treatment Assign two faces e g 5 and 6 for the unmarked treatment 2 Roll the die for each cow in the herd By following this labeling

A pyramid was built about 2590 BC Its original height was 518 feet 11 inches but due to loss of its topmost stones it is now shorter Find the current height of the pyramid using the information given in the figure on the right The current height of the pyramid is feet CHCEC 38 8 45 52 the final newer Thed to two decimal places as needed

7 Graph the equations below to form the figure Label the coordinates of the vertices 10 3 y 4 2 3 y 2 x 1 y 1 x 4 x 5y 10 10 4 points a How many sets of parallel sides does the figure have Show calculations to justify your answer 4 points b How many right angles does the figure have Show calculations to justify your answer 1 point c Does the figure have 4 congruent sides Show calculations to justify your answer d What is the most precise name for this figure 4 points 2 points

Q i ii A iii iv D 6cm 8cm B Q4 The diagram above shows the net of a right rectangular pyramid in which ABCD is base and 0 0 03 04 are brought together to form the vertex O When the solid is formed ABCD is the base AB 8cm AD 6cm and BO 13cm a Draw a sketch of the pyramid b Calculate the C height of the pyramid volume of the pyramid area of triangle AOB inclination of the triangle BOC to the hoge ABCD

33 Given K N JK MN KL NO K K N J LM Prove AJKLAMNO DEL F 0

24 Given ZJELM JK MN and K N K 0 Prove AJKL AMNO L N M

Use the figure to solve triangle ABC Round lengths of sides to the nearest tenth and angle measures to the nearest degree A Round to the nearest degree as needed Round to the nearest degree as needed B C O Round to the nearest degree as needed Find the measures of the unknown sides of triangle ABC O b a Round the final answer to the nearest tenth as needed Round all intermediate values to the nearest thousandth as needed 17 36 4 21 2 27 B a 13 7

9 Using Figure 9 13 below a Draw isobars at 4 mb intervals e g 1004 mb 1008 mb 1012 mb 11 b Label the low pressure center with an L c Draw the warm and cold fronts L49 38 124 31 O 41126 33 O 128 34 22 36 124 28 38 110 41103 30 L48 4 40 088 42 109 36 20 48 126 38 38 448 026 50 52 128 45 096 43 4569 R 40 66 59 d Label a maritime tropical mT and continental polar air mass CP e Outline the area where cloud cover exceeds 75 f Shade the areas receiving precipitation 61 075 57 60 040 48 63 153 61 Figure 9 13 45 114 66 24 60 ras 57 39 084 39 024 61044 57029 54 66 53 70 40 591 39 154 39 4332 41 46 124 43 54 097 43 45 099 66 111 55 71 72 69171 64 61 60 9 149 45 163 8 4 1 11

4 Find all points on the curve r 2 2 cos 0 where the tangent line is vertical List the points in polar form

Find the exact value of each expression it it is defined If an answer is undefined enter UNDEFINED a tan 0 b tan sqrt 3 c tan sqrt 3 3

A cell phone tower is anchored by two cables on each side for support The cables stretch from the top of the tower to the ground with each being equidistant from the base of the tower The angle of depression from the top of the tower to the point in which the cable reaches the ground is 23 If the tower is 140 feet tall find the ground distance between the cables

5 After performing the translation described below what will be the coordinate of point M translation x y x 7 y 1 11 M 9 5 8 8 5 M 6 After performing the translation described below what will be the coordinate of point R D Whe For 7 10 Name the type of transformation shown by the given rules The names you can choose from are Reflection Translation Rotation Dilation 7 x y x y 8 6 2 12 4 translation x y x 5 y 1 A R Match each transformation with the correct description A x y x y B x y x y C x y x y 43 10 x y x 9 y 2 7 reflection across the y axis rotation of 180 about the origin reflection across the x axis Optional Complete problems 1 2 4 8 15 from your textbook on separate lined paper

15 Rotate the figure 90 clockwise about the origin 19 Rule x y 6 mwoll ayana Tung bongo astsupa DE CE bias te

5 O H E 3 4 5 6 Stateless Nation Kurds An ancient group with a distinctive language and culture and concentrate in Turkey Iran and Iraq Smaller numbers live in Syria Armenia and Azerbaijan Ethnic Enclave completely surrounded by another state but not controlling it Bretons and Basques in France In France the concept of being French permeates virtually everyone who lives there Nevertheless two minorities on the mainland are distinctly non French the Basques of the southwest and the Bretons of The peninsula known as Brittany Perfect Nation State Icelanders Although they are of Northern European origin the people who live on the island of Iceland have evolved as a nation of their own Virtually the entire population of Iceland is today comprised of Icelanders and few Icelanders live anywhere else in the world Another example is Japan Occupied by a distinct nation or people Bi National State Flemings and Walloons in Belgium Although the

Find the values of m and n me G 15

Directions Give each trig ratio as a fraction in simplest form 1 D Rimeti 29 F 20 E This is a 2 page document work 20 TPI Sin D Cos D Tan D Sin E Cos E Tan E

14 The bottom of a ladder must be placed 3 feet from a wall The ladder is 12 feet long How far above the ground does the ladder touch the wall CH

he smallest positive number for which f x 2x 1 f cos f z 0

Find sin 2x cos 2x and tan 2x from the given information sin x 8 17 x in Quadrant III sin 2x cos 2x tan 2x

1 Explain what a conjecture is 2 How can you prove that a conjecture is false Sec 10 F

A man starts walking north at 3 ft s from a point P Five minutes later a woman starts walking south at 4 ft s from a point 500 ft due east of P At what rate are the people moving apart 15 min after the woman starts walking Round your answer to two decimal places ft s

Simplify the trigonometric expression cos x sin x cos x

Lesson 21 Practice Problems 1 The triangles here are each obtained by applying rigid motion 5 10 N 11 3 12 8 4 2 The quadrilateral is a parallelogram Find the measure of angles 1 2 and 3 13 9 5 14 10 80 6 15 a Which triangles are translations of triangle 17 Explain how you know 11 b Which triangles are not translations of triangle 1 Explain how you know 7

3 How many lines of symmetry exist in each of the flowers below Draw them please

17 reflection across the y axis M W N X 18 reflection across the y axis P g

Write short answers Consider the inverse tangent function defined by y tan xory arctan x Complete parts a d a What is its domain Type your answer in interval notation Simplify your answer Type an exact answer using x as needed Use integers or fractions for any numbers in the expression b What is its range 00 00 Type your answer in interval notation Simplify your answer Type on exact answer using as needed Use integers or fractions for any numbers in the expression c Is this function increasing or decreasing O decreasing O increasing d is there any real number x for which arctan x is not defined If so what is it or what are they O Yes o bo Use a comma to separate answers as needed

Ruben knows triangle ABC and triangle DEC are similar B 43 C E uestion What is the measure of angle DCE What is the measure of angle DCE Skip Question Scratch Paper Optional To Use Functions 7 4 Previous Questi 1 8 AC 5 6 2 3

How does the figure help verify the triangle inequality theorem to 15 A OA by showing that a triangle cannot be formed when the sum of the lengths of two sides equals the length of the third OB by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third OC by showing that only one triangle can be formed when the sum of the lengths of two sides is less than the length of the t OD by showing that only one triangle can be formed when the sum of the lengths of two sides equals the length of the third

What single transformation maps AABC onto AA B C A C B B C A 2 0 3 O A rotation 90 clockwise about the origin OB OC O D 0 rotation 90 counterclockwise about the origin reflection across the x axis reflection across the line y x X