2D Geometry Questions and Answers

13 Prove these quadrilateral are parallelograms using the following formulas 2 x x x 325 40 6 5 A 6 2 y y 2 5 8 8 I

What is the volume of a hemisphere with a radius of 4 8ft rounded to the nearest tenth of a cubic foot Answer ft 3

The angles shown are compleme angles Determine the measures 42 What are the measures of 41

Suppose an arc of length s lies on the unit circle x y2 1 starting at point 1 C and terminating at the point x y Use a calculator to find the approximate coordinates x y Round coordinates to four decimal places when appropriate X COS B y sina 1 0 00 1 0 1 Are of lengths The unit circle x2 y2 1 1 0

1 Given that y y x is a function of x Find dy dx using implicit differentiation if y 2xy x 2 Find the tangent line to the graph y y x at the point 1 3 2 Given that x x t and y y t are two functions in the variable t and that

5 A box is shown below where x is in meter 2x 2x A Find total surface area S and the volume V in terms of x then express S in terms of V B Find dS in terms of dV and approximate the change in the surface S when

8 Is the following function continuous at x 1 Give the reason for your answer clearly If it s not continuous at x 1 is the discontinuity removable 9 Find the following anti derivatives A x x dx c f 1 dx dx x 4 ln x S E x 2x 3 x 1 1 x 3 x 1 x 1 5 x Show all steps B Stan x sec x dx D fxe dx

Find the supplementary The supplementary and Simplify your answer

Find the value of x and the value of both angles 13 5x 2 x 8

5 In the circle C above mzBCA x 12 and mAB 3x 24 What is the mZAFB X 12 3x 24 a 15 b 30 C 48 d 60 B 08 cup 12 H28 403 681 PP pp up A

e diagram belo Which of the following best describes line AB a Arc b Chord C Radius d Tangent Line Which of the following best describes line FD a Secant Line b Chord C Radius d Tangent Line Which of the following best describes EC a Arc b Chord C Radius d Tangent Line hich of the following best describes line BE a Secant Line b Chord B A D C F

Use the diagram below to answer 7 and 8 In circle B below the radius is 6 inches and the mzABD What is the area of sector CBD 7 a b C a d b C d 117 6 25T 6 117 2 8 What is the arc length of AD 25T 2 117 6 25T 6 117 2 25 2 Central angle 180 55 125 55 Area 125 TI X 360 2 of sector

In the circle below m2F 6x 40 and mzG 2y What is the mHEF 6 points 6x 20 8x 34 6x 40 180 20 94 180 94 94 20 20 20 M HEF 1 H being 8x134

4 Claire is considering investing in a new business In the first year there is a probability of 0 2 that the new business will lose 10 000 a probability of 0 4 that the new business will break even 0 loss or gain a probability of 0 3 that the new business will make 5 000 in profits and a probability of 0 1 that the new business will make 8 000 in profits a Claire should invest in the company if she makes a profit Should she invest Explain using expected values b If Claire s initial investment is 1 200 and the expected value for the new business stays constant how many years will it take for her to earn back her initial investment

5 Tanya is considering playing a game at the fair There are three different ones to choose from and it costs 2 to play a game The probabilities associated with the games are given in the table Game 1 Game 2 Game 3 Lose 2 0 55 0 15 0 20 Win 1 0 20 0 35 0 60 Win 4 0 25 0 50 0 20 a What is the expected value for playing each game b If Tanva decides she will play the game which game should she choose Explain

2 A game at the fair involves a wheel with seven sectors Two of the sectors are red two of the sectors are purple two of the sectors are yellow and one sector is blue Landing on the blue sector will give 3 points landing on a yellow sector will give 1 point landing on a purple sector will give 0 points and landing on a red sector will give 1 point a Let X the points you have after one spin Fill out the missing values in the table X P X b If you take one spin what is your expected value c What changes could you make to values assigned to outcomes to make the name fair

1 Miguel is playing a game in which a box contains four chips with numbers written on them Two of the chips have the number 1 one chip has the number 3 and the other chip has the number 5 Miguel must choose two chips and if both chips have the same number he wins 2 If the two chips he chooses have different numbers he loses 1 1 a Let X the amount of money Miguel will receive or owe Fill out the missing values in the table Hint The total possible outcomes are six because there are four chips and you are choosing two of them C X P x 2 7 1 b What is Miguel s expected value from playing the game Based on the expected value in the previous step how much money should Miguel expect to win or lose each time he plays d What value should be assigned to choosing two chips with the number 1 to make the game fair Explain your answer using a complete sentence and

holastic Student 1 i SRI College Career use the Fossil Life An In NG METHODS Tell whether you would us metric ratios to solve the triangle with the 5 a 12 b 21

ESTIONS Item 1 Item 2 Item 3 Item 4 8 CCSS G MG 3 Find the Area of regular polygon 6 ft

IS 5 Find the area of the figure sho 4 cm 3 cm 18 cm 12 cm 3 cm

ss PowerSchool YouTube Figures Regular Polygons Find the area of the figures shown below and drop th DRAG DROP THE ANSWER 55 cm 36 m 38 cm DeltaMath E Edulas 9 58 cm 39 m O 5 cm

Composite Figures Regular Polygons IS 4 Find the area of 3

Assignment Area Practice Problems QUESTIONS Item 1 OItem 2 OItem 3 Item 4 Item 5 4 Find the area of the parallelogram shown below H 6 m G 11 m

roblems 7 The area of circle is g Find the radius of cin

ignment Area Practice Problems STIONS Item 1 tem 2 tem 3 em 4 em S m 6 8 Find the difference in area of Use 3 14 for pi A Select the proper units n m CI m

e Problems 11 If EF 28 ft find the sector area of the s 82

QUESTIONS 0 hem 1 hema Item 2 0 Item d frem 5 4 Item Jtem 7 Item H Hem 9 5 Ashley drew the triangle LM N on the

rea Practice Problems 2 Find the area of the trapezoid shown below 11 4 11 11 19 12 08

Complete the table Then graph the function h x 5 3 h x X Graph the function 50 45 40 35 30 25 20 15 10 5 0 1 2

3 Name the isometry that maps PQRS to each figure D A B P B R

Practice 2 Une Segment AC AB BC BC is a Find the length and slope of each line segment Then classify the triangle Length Slope Is AABC a right triangle triangle T 2 234 3 567800 6 6 7 8 1 2 3 4 5 6 7 A 9 10 8 9 10

Practice 1 Find the length and slope of each line segment Then classify the triangle 10 8 6 4 2 Line Segment AB BC CA ADEF is a 8 6 2 B Length 8 10 triangle Slope

3 True or False Explain your answer COS os 1 12 0 cos 0

Bolve the following problems and round to the nearest tenth when necessary 4 If the radius of the cone is 5 inches and the height of the cone is 18 inches what is the slant height of the cone 10 18 2 C 124 1527 20 6 An Eqyptian pyramid has a square base that measures 80 meters on each side If the height of the pyramid is 30 meters what is the slant height of the pyramid 40 4363 5 The square base of the pyramid has an area of 144 square feet If the slant height of the pyramid is 10 feet what is the height of the pyramid V 144 OF etic 7 Kathleen s ice cream cone has a diamete of 9 cm and a slant height of 7 5 cm What the height of the ice cream cone 7 5cm NV

Designs The following designs can be constructed using only compass and straightedge How many of these designs can you construct Hint It may be easier to construct versions larger than those shown TIONS 2 A C E 4 B D F

Given that cos a 13 cot a 5 6 3 with a 2 3 and cos b with 8 14 cos a b 3T 2 b 27 find the following 15 sin b

The line given by y x 1 is dilated by a scale factor centered at the origin The image of the line after dilation is given by y x 5 What is the scale factor of the dilation

Solve the equation Enter your answers as a comma separated list Use n as an arbitrary integer Enter your response in radians tan x 3 0 X

3 i e the triangle Round decimal answers 3 63 A 29 C

7 A radio tower is supported by two wires that are 130 yards long and attached to the ground 50 yards from the base of the tower How far from the ground are the wires attached to the tower Hint Pythagorean Theorem 8 Find the sum of the measures of the angles of a six sided polygon Then find the measure of an of an angle of a regular six sided polygon

AS MATH 2 i e the triangle Round decimal answers 23 25 A 14 B

1 Determine a plane motion which will take AABC to AA B C B A B

5 0 OR ANALYSIS Describe the error in finding m C A 55 5 B 6 sin C sin 55 6 5 6 sin 55 5 sin C m C79 4 he Law of Cosines should have been used he lengths of the sides in the denominators should be switc ross multiplication should have been used to obtain the solu he inverse sine function should have been used to obtain th

Consult the figure To find the length of the span of a proposed ski lift from A to B a surveyor measures the angle DAB to be 25 and then walks off a distance of L 1900 feet to C and measures the angle ACB to be 15 What is the distance from A to B eccos The distance from A to B is approximately feet Do not round until the final answer Then round to two decimal places as needed GEZER B D 25 A

10 The area of a circle is 244 cm Determine the length of the diameter to the nearest whole number

12 In the diagram below of circle 0 mABC 260 What is mLABC Label it on the diagram below A C 0 B

13 In the circle C below mzBCA x 12 and mAB 3x 24 What is the m AFB a 15 b 30 c 48 B A antwollol odsto C E F

11 5 20 4x 5 85 40 Solve for x

From Lesson 9 06 Probability Two Way Tables The two way table shows the medal count for the top performing countries in the 2012 Summer Olympics Silver Bronze 29 29 27 23 26 32 17 19 99 103 United States China Russia Great Britain Total Gold 46 38 24 29 137 Which statement is true The probability that a randomly selected silver medal was awarded to Great Britain is 17 99 Total 104 88 82 65 339 The probability that a randomly selected gold medal was awarded to China is 88 137 TH The probability that a randomly selected medal won by Russia was a bronze medal is ability that or furthe United St cib dalis 104

A fast food restaurant kept information about the drinks that were ordered along with the different sized kids meals as shown in the table Milk Regular Kids Meal Large Kids Meal Total 55 71 Juice Box 22 60 Soda 63 86 Total 156 280 Which statements are true Select three options Milk was requested for 16 of the large sized meal orders Sixty three of the orders of soda came with a regular sized meal Soda was requested for 280 of the kids meal orders