Coordinate system Questions and Answers

S AS A M is the result of reflecting ASAM over BC If the slope of AA is then the slope of BC is If the slope of AA is then the slope of MM is If AA intersects BC at Point X what is the measure of ZBXA

1 Use the figure to find the value of x y and a 12

Consider ATUV in the figure below The perpendicular bisectors of its sides are AD BD and CD They meet at a single point D In other words D is the circumcenter of A TUV Suppose CD 30 UV 142 and UD 78 Find BV VD and TC Note that the figure is not drawn to scale T D A B V BV 0 0 VD TC X

SIDE SIDE SIDE In 1 2 find the indicated lengths d x x y y Mark congruent sides If all three sides are congruent write a triangle congruency statement by SSS 1 2 JH LK G 6 H HG KM Congruence Statement 6 8 GJ ML PN XY M NM YZ Congruence Statement MP ZX

Barnes Company reports the following for its product for its first year of operations 36 per unit 26 per unit 12 per unit 54 000 per year 2 per unit 21 000 per year Direct materials Direct labor Variable overhead Fixed overhead Variable selling and administrative expenses Fixed selling and administrative expenses The company sells its product for 160 per unit Compute contribution margin using variable costin company a produces and sells 2 000 units and b produces 2 700 units and sells 2 000 units Contribution margin using variable costing Variable expenses Contribution margin a 2 000 Units Produced and b 2 700 Units Produced 2 000 Units Sold and 2 000 Units Sold

is divided into smaller chunks that can fit into memory In this phase we read the input data sequentially and write the chunks to temporary files 1 7 Merging Phase The sorted temporary files are merged together in a way that minimizes the number of passes In this phase data is read from the temporary files and written into a final output file To calculate the cost of performing this modified external merge sort you can break down the costs into these phases Intermediate Sorting Phase Each of the temporary files created in the initial splitting phase is sorted in memory For each file you read its content into memory sort it and write the sorted data back to a new temporary file Sequential Reads You mentioned that 8 sequential reads are free and that the cost of 8 sequential reads is 1 You ll want to count how many sets of 8 sequential reads are needed in each phase initial splitting intermediate sorting and merging For any leftover reads you can apply the cost of single reads Sequential Writes Sequential writes are never free You mentioned that the cost of N writes is always 2N So count the total number of writes in each phase and calculate the cost accordingly Here s a simplified example to illustrate how to calculate the cost Suppose you have an external merge sort with Input size 80 pages Memory can hold 10 pages Number of temporary files created in the initial splitting phase 8 Number of temporary files created in the merging phase 2 1 Initial Splitting Phase D Sequential Reads 10 reads per file x 8 files 80 reads D Sequential Writes 10 writes per file x 8 files 80 writes 2 Intermediate Sorting Phase Assuming each sorted file fits in memory Sequential Reads 1 read per file x 8 files 8 reads Sequential Writes 2 writes per file x 8 files 16 writes 4 Merging Phase

The mov How would the following triangle be classified 4 O isosceles right O scalene acute O scalene right isosceles acute

Prove that for every x cos 3 x cos x 2 sin 2x sin 3x sin x

Learning Goal from Lesson 3 1 When given a geometric figure and a specific transformation I can draw the transformed figure by using graph paper tracing paper or geometry software Given two figures I can specify a sequence of transformations that will carry one figure onto another 4 ty 5 Reflect AABC over the y axis translate by 2 1 and rotate the result 180 about the origin Plot AA B C on the grid below 2 points 2 4 2 0 A 2 B Transformation rule Preimage ABC How I Did Circle one Image A B C I got it I m still learning it Image A B C Image A B C

da 2 3 8 7 6 5 4 3 2 2 3 4 O 5 3 q The graph of a function y f x is shown Make a sketch of the antiderivative F given that F is continuous and F 0 1 OS 6 7 6

ASSESSMENT Credit Checkpoint Complete the following Show all your work Learning Goal from Lesson 2 1 2 3 I can develop definitions of translations reflections and rotations in terms of angles perpendicular lines parallel lines and line segments A x y x 5 y 2 B x y x 2 y 5 C x y x 5 y 2 D x y x 2 y 5 1 Which of the following rules correctly represents the translation from ABC to MNP 1 point A R 2 N T 9 2 the 1 og 2 Reflect the shape below across the line x 2 Label the new coordinates 1 point 9 When no direction is specified you can assume the rotation is counterclockwise Transformation Rule x y B How I Did Circle one C I got it 2 4 2 ON 2 N 4 P I m still learning it M Image

P I can show that triangles are congruent if and only corresponding sides and angles are congruent Lesson 3 3 Checkpoint below Once you have completed the above problems and checked your solutions complete the Lesson Checkpoint Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 AABC ATUV Find the following side length and angle measure a Find the mzU b Find the length of BC M Z 3y 2 6x 2 cm 2 Given that AYMZ and AQMP are identical and YZ 13 QM 15 and PM below to determine the remaining measurements Q B Side QP YM ZM 6x 1 cm 5x 7 cm Chry T Measure Kasay 4y 4y 18 15 complete the table MUC

Draw and 1 Rotate AABC 270 about the origin and then reflect over the x axis B T C Preimage ABC A 1 2 B 3 4 C 2 5 6 2 A 0 TY 6 Transformation rule y B 2 8 6 4 2 image of AABC after the given sequence of transformations 2 Translate AABC by 4 4 and rotate 90 about the origin 4 6 A 8 6 2 0 Transformation rule Image A B C Preimage ABC A 1 1 B 3 3 C 2 4 2 4 6 8 Image A B C X Image A B C Image A B C

Rules for Rotation on a Coordinate Plane 90 rotation counterclockwise 180 rotation 270 rotation counterclockwise 360 rotation long Example Draw and label the final image of AABC after the given sequence of transformations Reflect AABC over the y axis and then translate by 2 3 Above are examples of rigid transformations you have learned in this credit Now you will apply sequences of transformations as in multiple transformations on one figure to map it elsewhere on the coordinate plane Coordinate Notation Step 1 Identify the type of transformations and its order x y y x x y x y x y y x x y x y 1st Reflection across the y axis 2nd A translation by 2 3 Step 2 Write the transformation rule Preimage ABC A 1 1 B 3 3 x y x y x 2y 3 Step 3 Draw and label the 1st transformation Label the image A B C Use a table to organize your work C 2 4 Preimage ABC A 1 1 B 3 3 C 2 4 Image A B C x y x y A 1 1 B 3 3 C 2 4 Step 4 Draw and label the 2ndst transformation Label the image A B C read as A double prime B double prime C double prime Image A B C x y x y x 2 y 3 Image A B C x y x y A 1 1 B 3 3 C 2 4 Image A B C x y x y x 2 y 3 A 3 2 B 5 0 Your Turn Draw and labs 1 Rotat C 4 1 r

Your Turn Draw the image of the triangle after the given rotation You will need a protractor 1 Counterclockwise rotation 40 about point P 2 Clockwise rotation of 125 around point Q S P L

A B C B Line I has a slope of 2 the segments must have an opposite reciprocal slope of Line I has a slope of the segments must have an opposite reciprocal of

2 S 3 4 T 3 1 U 2 1 V 2 4 Reflection across the x axis ty 4 2 2 0 2 3 D 1 1 E 3 2 F 4 1 G 1 3 Reflection across y x 2 2 4 4 2 0 2 2 4 X Transformati Preimage Coordinates Transformation Rule x y Preimage Coordinates x y Image Image

Your Turn 1 Match the quote to the correct coordinate notation One is done for you Rules for Reflection on a Coordinate Plane D Reflection across the x axis x y x y Reflection across the y axis x y x y Reflection across line y x x y y x Quote A To reflect the figure all x values will take the opposite sign all y values will remain the same B To reflect the figure all x values will be the opposite sign of the y values all y values will be the opposite sign of the x values C To reflect the figure all x values will be the y values all y values will be the x values

Draw the preimage and image of each triangle under a translation along 4 1 1 Triangle with coordinates A 2 4 B 1 2 C 4 2 y 4 2 0 2 Transformation Rule x y Preimage Coordinates x y Image

15 13 51 Find the value of x 6x 3 4x2 2x 1 110 6x 12 16 18 6x 5 3x 2 x 6 6x 3 85 f 61 30 2x 1

The blue figure is a dilation image of the black figure The labeled point is the center of dilation Tell whether the dilation is an enlargement or a reduction Then find the scale factor of the dilation Is the dilation an enlargement or a reduction Enlargement Reduction Find the scale factor n n Simplify your answer E 0

1 R 20 7 J sin S cos S tan S find sin R cos R tanR Write each answer as a fraction and as a decimal rounded to three decimal plac 3 T 2 15 25 S sin S cos S tan S 24 26 T 10 8 16 S sin S cos S tan S 30 34 R

asurement For the below problem you will need to reference the Kodak Anthropometry pdf file provided on Canvas Neatly show all work for partial credit 1 A desk is 30 inches tall The desk chair has a seat height of 20 inches For keyboard work it is recommended that resting elbow height be between 1 inch above and 2 inches below the J key on the keyboard Using the Kodak data what percentile range of males and what percentile range of females will fit this workstation Assume that the J key is 0 5 inches above the desk and that a footrest is provided for workers with shorter legs ANDING Forward functional reach a Includes body depth at shoulder Tibial height Knuckle height Elbow height Shoulder height Eye height Stature b Acromial process to functional pinch c Abdominal extension to functional pinch Abdominal extension depth Waist height Functional overhead reach Males Females 1 50th 50th 1 percentile S D percentile S D 32 5 31 2 26 9 24 4 9 1 41 9 41 3 17 9 29 7 43 5 45 1 56 6 57 6 64 7 68 7 699 82 5 1 9 2 2 1 7 3 5 29 2 28 1 24 6 23 8 0 8 8 2 2 1 40 0 2 1 38 8 1 1 16 5 1 6 28 0 1 8 40 4 2 5 42 2 2 4 1 9 3 1 56 3 2 4 59 6 2 6 63 8 2 6 64 8 3 3 78 4 Population Percentiles 50 50 Males Females 5th 50th 95th 1 5 27 2 30 7 1 7 25 7 29 5 1 3 22 6 25 6 2 6 19 1 24 1 29 3 0 8 7 1 8 7 2 0 37 4 40 9 35 8 39 9 2 2 0 9 15 3 17 2 2 4 2 8 3 4 35 0 34 1 29 3 1 6 25 9 28 8 31 9 45 8 48 6 1 4 38 0 42 0 2 7 38 5 43 6 2 7 48 4 54 4 2 6 49 8 55 3 2 2 56 8 62 1 60 8 66 2 61 1 67 1 74 0 80 5 10 2 44 7 44 5 19 4 59 7 61 6 67 8 72 0 74 3 86 9

Determine the values of x and y 3y 2 40 4y 1

cot 8 tan 8 X O tan 8 Ocot 8 5 0 1 point Which of the following is equal to sin 337 8 cos 8 sin 7 8 cos 8

Write as an algebraic expression in x free of trigonometric or inverse trigonometric functions sin cos x 1 x 1 Note that sqrt x is the syntax for and x 2 is the syntax for 1 x 2 O sqrt 1 x 2 O 1 x 2 O sqrt 1 x 2 O None of the above

Which of the following best describes the translation rule and the scale factor of the dilation for transforming the circle C to C C G 10 987654 7 3 10 9 8 7 6 5 4 3 2 1 321 734487999 2 3 5 7 8 10 Y x 1 2 4 5 6 7 8 9 10 C

9 Solve for x x 9 Y W 2x 3 1 R Q X Cross off the value of the first digit of your answer

6 If m MON 48 then find the m MZX O Z M X N Cross off the second digit of your answer

3 Assume lines that look parallel are parallel Find E 5 D E 7 F 8 Cross off the value of your answer

6 m21 8 mZ1 10 m 1 135 Reason Reason ff 60 Reason by stating the reason drawings are not to scale 7 m21 9 m 1 11 m 1 Reason 75 Reason 44 Reason 53

T R U 42 171 2 1360 12 711 S mRS

items Task 2 List all rows and columns for the complete INVOICES table Task 3 List the first name last name and credit limit of customers with credit limits of 1 000 or more Task 4 List the invoice number for each order placed by customer number 125 on 2021 11 15 Task 5 List the customer ID the first name and the last name of each customer represented by sales rep 10 or sales rep 15 Task 6 List the item ID and description of each item that is not in category HOR Task 7 List the item ID description and number of units on hand for each item that has between 10 and 30 units on hand including both 10 and 30 Task 8 List the item ID description and on hand value units on hand unit price of each item in category CAT On hand value is technically units on hand cost but there is no COST column in the ITEM table Assign the name ON HAND VALUE to the computed column Database Model Kim Tay The management of Kim Tay Pet Supplies a supplier of pet supplies food and accessories located in Cody Wyoming has determined that the company s recent growth no longer makes it feasible to maintain customer invoice and inventory data using its manual systems In addition KimTay Pet Supplies wants to build an Internet presence With the data stored in a database

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14 ints eBook Hint Print References Information for two companies follows Skittles Company 6 151 450 4 951 450 3 897 950 Sales Contribution margin Fixed costs 1 Compute the degree of operating leverage DOL for each company 2 Which company is expected to produce a greater percent increase in income from a 30 increase in sales Complete this question by entering your answers in the tabs below Required 1 Required 2 Starburst Company 3 739 000 1 414 000 909 000 Compute the degree of operating leverage DOL for each company Degree of Operating Leverage Skittles s DOL Numerator 1 Denominator Ratio Degree of Operating Leverage

Read the question and enter your response in the box provided Use the tools and your keyboard to construct m JK 57 and mJL 20 Find m LJK 22

Using the figure below ZFBD is 50 which is true regarding ZEBF A B C D C A E 150 B ZEBF 1400 ZEBF 90 ZEBF 500 ZEBF 400 D

Question 8 Perpendicular lines are two distinct coplanar lines that intersect to form what type of angle O A acute angle OB C D corresponding angle obtuse angle right angle

If B is between A and C then AB BC AC Angle Addition Postulate OB Addition Property of Equality Definition of Midpoint A C D Segment Addition Postulate

Two rays sharing a common endpoint is the definition of which term O A angle B C D chord line segment secant

What does the symbol AB represent segment AB Bline AB C Ray AB

13 Rewrite the following standard form linear equation into slope intercept form 4x 3y 18 Hint s 1 1 HIDE HINT

Find the midpoint of the segment with the following endpoints 8 0 and 2 4

AQSU and ARST are shown below Q R S Which statement is true AQSU is similar to ARST AQSU is not similar to ARST T U There is not enough information to determine whether the triangles are similar

Use the product to sum formulas to write the product as a sum or difference Do not simplify your answer TT sin 8 cos 5T 6

Question 9 Let right triangle ACB have C 90 and let sides a b and c be opposite angles A B and C respectively If a 15 and b 8 find c Answer exactly C

In Exercises 47 54 use the figures to find the exact value of each trigonometric function 3 5 8 0 C 7

Write a coordinate rule for the composition the blue preimage to the green image P L 2 6 Ay M S R 2 4 K 6 x