Coordinate system Questions and Answers

A board is 29 inches long How long is the board in centimeters Use the following conversion 1 inch is 2 54 centim cm X

Use the diagram to answer the following question EQ b QE Z What is another name for EQ a O A OB O C OD te C NE d NQ

Find the distance between the pair of points shown below Round your answer to the nearest tenth if necessary 09 2 6 07 1 O2 9

The endpoints of GH are a 6 2 b 6 6 O A OB OC OD G 0 4 and H 6 2 Find the coordinates of the midpoint M C c 3 1 d 3 3 C C 5

uno DA C If BC bisects LABD and mLABC 51 find mLABD and mZCBD B m ABD m CBD

oundations of G figure below is a rectangular shipping box Name two different planes B D E G H A plane CDA plane CDG plane AED plane BEF one CDG plane AED CDA plane BEF

The following parametric equations trace out a loop Find the t values at which the curve intersects itself t Find the x and y values of the intersection Y 8 t y 4t 2 Graph the curve on a calculator Turn in a sketch of the curve

Draw a dilation of the figure using the given scale factor 15 k 2 C 2 y A B 16 k C AY B

Determine whether the dilation from Figure A to Figure B is a reduction or an enlargement Then find its scale factor 5 7 A A VBI y B k x y k H SIA 6 8 A 6 B y A k B 6 x k the dile

A line segment has the given endpoints Use the scale factor to write the ordered pairs after the dilation 12 A 1 1 B 3 1 and k 2 13 A 4 4 B 8 12 and k 14 A 0 0 B 3 2 and k 5

Question 14 Find the point at which the line f x x 6 intersects the line g x Question Help Video Message instructor 3x 6

Match the following equations with their direction field Clicking on each picture will give you an enlarged view While you can probably solve this problem by guessing it is useful to try to predict characteristics of the direction field and then match them to the picture Here are some handy characteristics to start with you will develop more as you practice A Set y equal to zero and look at how the derivative behaves along the z axis B Do the same for the y axis by setting equal to 0 C Consider the curve in the plane defined by setting y 0 this should correspond to the points in the picture where the slope is zero D Setting y equal to a constant other than zero gives the curve of points where the slope is that constant These are called isoclines and can be used to construct the direction field picture by hand 1 g 2 2 y 2 2y z e 2x y 3 g 2y 4 g y 2 11 11

2 Given 1 m 11n Prove mIn 1 1 m 1 In Statements Reasons 1 Given 23 43 35 69

1 Label this shape ABC Reflect it over the x axis Write the coordinates below A B C A B C 2 Label this shape DEFG Reflect it over the y axis Write the coordinates below D E F G D E F G 3 Label this shape HJK Translate x y x 3 y 4 Write the coordinates below H H J K J K

ARST is congruent to AUST by ASA What is the value of x S R 0 0 0 76 5x 1 U T x 2 6 X 76 x 20 6 X 15

2 Select the correct answer from each drop down menu Consider triangles ABC and QPR shown Triangle ABC is triangles are B not congruent congruent P R triangle QPR Since the transformations Reset Next

Federal Government How a Bill Becomes a Law How a Bill Becomes a Law Quick Check Explain what happens when a bill is vetoed 1 point O When a bill is vetoed a committee member rejects the bill O When a bill is vetoed it moves from committee review to chamber review O When a bill is vetoed the president rejects the bill O When a bill is vetoed Congress rejects the bill

1 What is the value of r 1 10 3 4 In the accompanying diagram line a intersects line b 5 10 90 14 x 5 2x 5

Match the trigonometric function with one of the graphs I VI f x tan x Select V klei NI h E AT THE 1 III

5 Using visual observation determine whether the graph is symmetric with respect to the a x axis b y axis or c the origin a is the graph symmetric with respect to the x axis Choose the correct answer below A MO C No because for 2 3 No because for on the graph OB Yes because if a b is on the graph then so is a b the point 1 3 NH the point 3 is not JU 3 is not on the graph OD Yes because if a b is on the graph then so is a b 21 8 2

Bob is flying two kites He has 98 feet of string out to one kite and 116 feet out to the other kite The angle formed by the two strings is 29 as shown in the figure below Find the distance between the kites 98 ft feet 116 ft Carry your intermediate computations to at least four decimal places Round your answer to the nearest tenth of a foot 29 X S

Write the coordinates of the vertices after a reflection over the line y 1 10 8 6 TOO U 0 v 4 2 10 8 6 4 2 2 4 618 6 W 8 10 2 4 9 6 ND T 80 U 10

Extra Practice In Exercises 1 4 classify the polygon by the number of sides Tell whether it is convex or concave 3 TODO 1 2 4 In Exercises 5 8 find the perimeter and area of the polygon with the given vertices 5 X 2 4 Y 0 2 Z 2 2 6 P 1 3 Q 1 1 R 4 2 7 J 4 1 K 4 2 L 6 2 M 6 1 8 D 5 3 E 5 6 F 2 6 G 2 3

Which of the following is true 1 2 B C 70 A m BCD mzDBC 10 B m BCD m DBC 20 C m BCD m DBC 60 D m BCD m DBC 80 130 D

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

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

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

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