Coordinate system Questions and Answers

Graph all asymptotes of the rational function 4x 2x 1 2x 3 f x 00 4 24 M T 8 X

For Exercises 7 10 sketch and label the figure Mark the figures 7 Trapezoid ZOID with ZO ID 9 Rhombus EQUL with diagonals EU and QL intersecting at A 11 Draw a hexagon with exactly two outside diagonals 8 Kite BENF with BE EN 10 Rectangle RGHT with diagonals RH and GT intersecting at I 12 Draw a regular quadrilateral What is another name for this shape 13 Find the other two vertices of a square with one vertex 0 0 and another vertex 4 2 Can you find another answer Explain 14 What is the perimeter of one of the five congruent rectangles shown to the right The larger rectangle with perimeter 198 cm is divided into five congruent rectangles Architecture CONNECTION Quadrilaterals are used in the architecture of many cultures for both pr

Find the sample size n needed to determine a 90 confidence interval for the population proportion p given the margin of error E 6 Use 0 5 for an estimate of the sample proportion p Round to the nearest whole number as needed Enter the correct value in the box n Show Hints

1 point Laurie is constructing an angle bisector She sketched her angle then opened her compass to a radius length less than the length of the rays that make up the angle What should be her next step label the point of intersection of the two arcs mark the points of intersection draw an arc using the vertex as the center draw a ray from the point of intersection to the vertex

13 1 point Jan is constructing an inscribed circle in a triangle What is the center of this circle called centroid incenter circumcenter orthocenter

1 point 2 R The measure of arc PQR is equal to 250 degrees The measure of arc PR is equal to 110 degrees What is the measure of angle 2 125 degrees 180 degrees 70 degrees 55 degrees

2 ounces of pure gold was 2 640 Complete the double number line to show the cost for 1 3 and 4 ounces of gold 0 2 640 cost in dollars 6 600

Find the scale factor from the following similar figures 8 4 cm 28 cm Original 35 cm New 11 CH

The function G x 0 01x x 63 models the wage gap as a percent x years after 1980 in Country A The graph of function G is shown underneath the actual data a Find and interpret G 10 Identify this information as a point on the graph of the function G 10 in the year in country A Type whole numbers earnings were 8 Median Women s Earnings as a Percentage of Median Men s Earnings in Country A 87 Wage Gap percent 95 90 85 90 80 75 70 65 50 45 63 74 79 1980 1990 2000 2010 The Graph of a Function Modeling the Data

This question 1 point s possible Sketch an angle 8 in standard position such that has the least possible positive measure and the point 3 3 is on the terminal side of 0 Then find the values of the six trigonometric functio for the angle Rationalize denominators if applicable Do not use a calculator Choose the correct graph below OA B Select the correct choice below and if necessary fill in the answer box to complete your choice O C O D Submit quiz

O A 18 Sketch an angle 0 in standard position such that has the least possible positive measure and the point 6 8 is on the terminal side of 0 Then find the exact values of the six trigonometric functions for 0 p 18 18 9 X 18 A o OB 18 Ay 18 9 9 18 X 18 nus pos This question 1 point s possible Select the correct choice below and if necessary fill in the answer box to complete your choice O C possible 18 9 18 Ay 19 19 W 18 18 Submit quiz 5

The terminal side of an angle 8 in standard position passes through the point 2 1 Use the figure to find the following value cos e cos 8 Type an exact answer in simplified form Rationalize all denominators

Consider two displacement vectors defined by their magnitudes and directions as follows A has a magnitude of 37 0 m and is directed in the direction B has a magnitude of 52 0 m and is directed 33 0 clockwise from the direction Let C A B What is the direction of C Note Express your answer as an angle

Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point Let a be the independent variable and y be the dependent variable Vertex 6 21 point 7 0 X

he figure to the right shows the feasible set of a transportation problem and the straight line of all ombinations of shipments for which the transportation cost is 108 Complete parts a through c elow D feasible set a The objective function is cost 288 3x 2y Give the linear equation in slope intercept form of the line of constant cost c 3 Simplify your answer Do not factor Use integers or fractions for any numbers in the equation A C B y x 0 Q

Note In case the lines L and L do not pass through the origin we may take lines L and L which are parallel to L and L respectively and pass through the origin If instead of direction ratios for the lines L and L direction cosines namely 1 m n for L and l m n for L are given then 1 and 2 takes the following form cos 0 1 mm nn as m 1 m n and sin 0 1 m 1 m m n m n n 1 1 4 Two lines with direction ratios a b c and a b c are i perpendicular i e if 0 90 by 1 ii parallel i e if 0 0 by 2 a a by C Now we find the angle between two lines when t acute the angle between the lines then aa bb ce 0 F a Ab and F b b b B In Cartesian form if 0 is the angle between the lines 3 3 2 2 b cos8 4 not to cos 8 19 T M cos 8 9 56 3 4 12 19 3x7 21 X X y 2 2 and a by where a b c und a b c are the direction ratios of the lines 1 and 2 respectively then Example 7 Find the angle between the pair of lines given by F 3i 2 4k M 2 2k aa bb cc b b c Rationalised 2023 24 and 7 57 2j 37 2j 6k Solution Here 7 23 2k and h 3i 2 6k The angle 8 between the two lines is given by bb 2 2k 37 27 6k THREE DIMENSIONAL GEOMETRY equations are given If 0 is 1 4 4 9 4 36 3 Hence 0 cos Example 8 Find the angle between the pair of lines x 3 y 1 2 3 published 4 ched 1 2 385

Draw a line representing the rise and a line representing the run of the line State the slope of the line in simplest form de o Click twice to plot each segment Click a segment to delete it 5 7 k 3 10 6 9 00 N Un 3 a M M 02 C T 700 56 Y 8 10

Use the diagram to the right If AD 16 and AC 2y 2 find the value of y Then find AC and DC What is the value of y y Type an integer or a decimal Find AC and DC Type an integer or a decimal DC Type an integer or a decimal AC A E D B C

he following balance sheet for the Los Gatos Corporation was prepared by a recently hired accountant In reviewing the statement ou notice several errors Cash Accounts receivable Inventory Machinery net Franchise net Total assets LOS GATOS CORPORATION Balance Sheet At December 31 2024 Assets Liabilities and Shareholders Equity Accounts payable Allowance for uncollectible accounts Notes payable Bonds payable Shareholders equity Total liabilities and shareholders equity 44 000 86 000 57 000 122 000 32 000 341 000 54 000 7 000 59 000 112 000 109 000 341 000 Additional Information 1 Cash includes a 22 000 restricted amount to be used for repayment of the bonds payable in 2028 2 The cost of the machinery is 194 000 3 Accounts receivable includes a 22 000 notes receivable from a customer due in 2027 4 The notes payable balance includes accrued interest of 7 000 Principal and interest are both due on February 1 2025 5 The company began operations in 2019 Net income less dividends since inception of the company totals 37 000 6 52 000 shares of no par common stock were issued in 2019 200 000 shares are authorized equired repare a corrected classified balance sheet Use the additional information to help determine appropriate classifications and account

Triangle ABC has the following coordinates A 1 1 B 5 4 C 4 1 and Triangle ABC will be translated 3 units right and 6 units up 1 Write a coordinate rule to describe the translation 2 What will be the coordinates of the image of point A

Find the coordinates of the vertices of the figure after the given transformation Take the following coordinates and translate each point 2 units down D 4 1 A 2 5 S 1 4 N 1 2 D 4 1 A 2 5 S 1 4 N 1 2 D 4 2 A 2 6 S 1 3 N 1 1 D 4 1 A 2 3 S 1 2 N 1 0 D 3 1 A 3 5 S 1 1 N 1 2

K Question 9 2 Use the currency exchange rates in the table for the following question You arrive in Montreal with 580 How many Canadian dollars can you buy You can buy Canadian dollars with 580 Simplify your answer Round to two decimal places as needed

Perpendicular Bisectors Cool Down Walk the Line Here is a hallway with lasers Laser 1 You Laser 2 Imagine that you must cross the hallway while staying an equal distance from each laser If you get closer to one laser than the other it will blast you Use a compass and straightedge to draw a safe path through the hallway

e g e g a 1 b Function y 3x 1 y x 2 d g x x 8 2 5 y x 7 3 0 y 5 x 2 1 h x 6 x 4 1 f x 1 x 8 3 y 2 x 3 h x x 5 7 y x 7 6 ying the transformations Two examples have been completed Horizontal Translation 3 5 7 none 2 8 7 2 4 none Vertical Translation none 1 7 none 5 3 Reflection in the x axis no yes Vertical Stretch 2 none 5

Triangle DEF is rotated about point P Find the measure of ZF P D D E 42 69 E F

Soru 10 B 17 D 4 A 7 E X C ABC geninde m AED mA AD 4 br DB 17 br AE 7 br Buna g re EC x ka birimdir A 5 B 6 C 7 D 8

Which of the following is equivalent to 1tan 0 1 tan 0 2 sin 0

xly 2 2603 7 3x 2y 10 1157 0 6 2 10333 2 3 4 321 8 2y 4x 6 29 12 6 1 3200 0 32610 26 P 345 2 i Sy 6 12 M 4 1 1 9 y 3 1 1 4904 IMI 4 7 T LL 1 3

The angle 0 is an acute angle and sin i 180 Use the Pythagorean identity sin 20 cos 0 1 to find cos 0 8 www cos 0 Simplify your answer Type an exact answer using radicals as needed Rationalize all denominators

Starting with the graph of a basic function graph the following function using the Lechniques of shifting compressing stretching and or reflecting Find the domain and range of the function g x x 4 2 Use the graphing tool to graph the equation Click to enlarge graph GELEED 10 B 2 40 6 2 24

For a 2D problem given any combination of forces the direction of ALL moments created by those forces will ALWAYS be in what direction Explain why F d Mo O Sense of rotation Moment axis Mo O Sense of rotation

nas abo 15 drops One drop of

State two other ways to name Zx T y X U

e table below gives the shape and color of toy blocks in a certain set ese are the only toy blocks in the set Shape Star Square Circle Triangle Clover Color Purple Green Red Blue Red conditional statement is given below Give the converse contrapositive and inverse of the statement Also use the table abc ecide if each statement is true or false Assume that any toy block mentioned comes from the set Given statement If a toy block is a triangle then the toy block is blue Converse Contrapositive Inverse If Choose one then Choose one If Choose one then Choose one If Choose one then Choose one O True True True True False False False False X

The midpoint of ST is M 3 0 One endpoint is S 6 5 Find the coordinates of the other endpoint T T M 3 0

7 Jaime randomly surveyed some students at his school to see what they thought of a possible increase to the length of the school day The results of his survey are shown in the table below Lengthening School Day Survey In Favor Grade 9 10 11 12 12 15 8 5 Opposed 6 3 12 16 Undecided 9 11 10 9 Part A A newspaper reporter will randomly select a Grade 11 student from this survey to interview What is the probability that the student selected is opposed to lengthening the school day Part B The newspaper reporter would also like to interview a student in favor of lengthening the school day If a student in favor is randomly selected what is the probability that this student is also from Grade 11

8 a 9 10 Are the following points collinear QNM circle one Yes No b Are the following points coplanar Q NP circle one Yes No Name line a in two other ways Name one pair of opposite rays N M a

For Exercises 13 15 find the measure of the angle formed by the hands at each time 13 3 00 14 4 00 19 15 3 30 10 9 8 12

P is the weighted average of A and B on the number line Find the coordinate of P under the given conditions 5 4 3 2 1 0 1 2 4 1 A has a weight of 6 and B has a weight of 3 2 The weight of A is one third the weight of B 3 The weight of B is 0 and the weight of A is greater than 0

7 2 3 7 7 9 5 9 7 7 11 10 7 8 1

Suppose f z y tan z y and u is the unit vector in the direction of 3 2 Then a f z y b f 0 5 9 sec x 2vtanx y 2vtanx y c fu 0 5 9 Du f 0 5 9 0 0311 A

or the following exercise evaluate the expression writing the result as a simplified complex number 5 4i 5 3i 3 2i

Find the slope of a line parallel to each given line 7x 2y 4 x y 2 3x 5y 0 x y 4

6 1 point B C F E S D A If chord AB is congruent to chord CD then what must be true about EF and EG They are different lengths They have no relationship They are parallel They are the same length

7 5 9 13 2 8 1 16 15 18 Write the slope intercept form of the equation of each line I 10 9

46 Which coordinate point is in the solution set for the system of inequalities shown in the accompanying graph 1 3 1 2 2 2 3 1 1 4 0 1 2 1 3 2 1 y 2 X

Find the midpoint of each line segment 1 5 2 3 154 43 AY M x x yfy 2 2 M 1 S 2 M 62 2 1 20 M 3 1 2 3 4 2 2 4 AY AY Y

On a reality show contestants had to spin two wheels of fate Spinning the first wheel determined the remote location where contestants would reside for the duration of the season Spinning the second wheel determined which bonus survival tool they would be allowed to bring along with a few other necessary items A tent Matches A rope Desert Rainforest 3 7 9 4 4 3 What is the probability that a randomly selected participant spun the second wheel and landed on matches or a tent Simplify any fractions

61 66 Right triangle relationships Draw a right triangle to simplify the given expressions Assume x Q 62 cos sin x 3 61 cos sin x 63 sin cos x 2 64 sin cos e for 0 0 2 65 sin 2 cos x Hint Use sin 20 2 sin 0 cos 0 cos 0 sin 0 66 cos 2 sin x Hint Use cos 20

3 6 A linear function contains the points 2 5 and 15 20 Does the point 43 53 also lie on the line Explain 2