2D Geometry Questions and Answers

B D 98 The measure of arc AB is The measure of angle AOB is The measure of angle BDA is

9 Which diagram s show XY tangent to circle Z Check all that apply Z 11 7 X 7 8 15 6 A 10 A 7 X B

Use the circle below U X Y 85 Z 108 V W r 12 YK 24 meters 7 Find the length of YU Round to the nearest hundredth a 18 05 b 15 08 c 2 48 d 4 82

Which statements are true regarding the diagram for circle P and the angles created Check all that apply OZDEC is a circumscribed angle O ZBCA is an inscribed angle O ZCBA is a central angle O ZAPB is a central angle OPB PA EC CB E D B P A

Use the circle below S 71 R 46 X T 8 Find mZSTR a 23 b 152 c 142 d 92

Use the circle below for questions 8 10 E D A 52 B C 4 Find mED a 52 b 38 5 Find mAC a 38 b 52 6 Find mBCD a 38 b 52 c 142 c 90 c 148 d 308 d 308 d 308

Use the diagram below for questions 1 3 U P V IT S R 1 Which of the following is a radius B US C RT A PV D PQ 2 Which of the following is a tangent B US C RT A PV D PO 3 Which of the following is a central angle A ZPVU B ZUST C ZOUS D ZUSR

A tank in the shape of a hemisphere has a diameter of 18 feet If the liquid that fills the tank has a density of 84 8 pounds per cubic foot what is the total weight of the liquid in the tank to the nearest full pound

22 Describe the transformations a y 2x 5

8 5 pts Openstax 6 5 253 A cone shaped tank of depth H has a cross sectional area that increases with its depth A Show that the work to empty it is half the work for a cylinder with the same height and base r h H

In order to maintain a healthy weight an average adult dog that weighs 17 kilograms must consume 13 grams of dog food per kilogram of its body weight each day A specialty pet store sells dog food by the cup where 6 cups of dog food weighs 558 grams About how many cups of dog food should the dog consume each day in order to maintain a healthy weight A 0 40 B 2 17 C 2 38 D 0 42

One rectangle is framed within another Find the area of the shaded region if the frame is 1 unit wide

An artist designed a badge for a school club Figure ABCD on the coordinate grid below shows the shape of the badge D C 4 3 2 111 M Y The badge is enlarged and plotted on the coordinate grid as figure JKLM with point J located at 4 7 and point M located at 2 3 Which of these could be the coordinates for point L 1 point

12 Give a proof You will use all of the blanks Given OLENS and ONGTH Prove ZE is supplementary to T Statements 2 3 5 6 Reasons 1 2 3 5 6

The area of circle Z is 64 ft N T r Area 7 What is the value of r O r 4 ft O r 8 ft O r 16 ft O r 32 ft

W 8 X O 7 10 N Line segment WX is the radius of circle X and line segment ZY is the radius of circle Y Points W X C Y and Z are all on line segment WZ What is the area of circle C which passes though points W and Z O 81 units O 164 units O 324 units O 1296 units

The diagram shows one way to develop the formula for the area of a circle Pieces of a circle with radius rare rearranged to create a shape that resembles a parallelogram Since the circumference of the circle can be represented by 27 and the area of a parallelogram is determined using A bh which represents the approximate area of the parallelogram like figure O A 27 r O A 2 r 2 A 2 r 1 A 3 2 r

8 feet 3 feet C Garden A circular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet What is the approximate area of the path alone Use 3 14 for T O 172 70 ft O 178 98 ft O 200 96 ft O 379 94 ft

Fiona draws a circle with a diameter of 14 meters What is the area of Fiona s circle O 7 m O 14 m O 28 m 49 m

20 9 What is the area of the shaded sector of the circle O9 units O 27 units 81 units O 162 units

Arc LM on circle O has a measure of 40 M Which statements are true Check all that apply The central angle measure created by the shaded region is 40 The central angle measure created by the shaded region is 20 The ratio of the measure of ZLOM to the measure of the whole circle is 9 Circle O can be divided into a total of 9 sectors equal in area to sector LOM Circle O can be divided into a total of 10 sectors equal in area to sector LOM

C A 217 11 T Use the diagram to answer the questions What is the area of the circle in terms of pi units What is the measure of the central angle of the shaded sector What is the area of the shaded sector rounded to the nearest whole number units

N X 20 3 Y If the radius is doubled what is the effect on the area of sector XYZ O The sector area will be times greater O The sector area will be 2 times greater O The sector area will be 2 times greater 3 The sector area will be 4 times greater

The canopy of a parachute is a semicircle with a radius of 13 feet A company that is making parachutes for a Fourth of July celebration wants each parachute to be made from equal parts of red white and blue fabric Approximately how much fabric of each color will be needed to make a single parachute canopy 88 5 ft O 88 5 ft2 O265 5 ft OCE E 42

M N 6 L The measure of central angle MNL is radians and the measure of the entire circle is 2 radians The ratio of the measure of the central angle to the entire circle measure is The area of the entire circle is The area of the sector is units VTT units

Which statements are true Check all that apply The ratio of the measure of the central angle to the measure of the entire circle is 5 2 The ratio of the measure of the central angle to the measure of the entire circle is 5 2 The area of the sector is 250 units The area of the sector is 100 units The area of the sector is more than half of the circle s area mZRQP 5 radians radius 10 units R

The graph of f x is shown below 8 6 4 1 2 If g x 10x 2 which statement is true OA The x intercept of g x is less than the x intercept of f x B y A 8 6 4 The x intercept of g x is greater than the x intercept of f x 2 2 4 6 8 2 6 8 X

Jason observed a large art sculpture in a local park and wanted to know its height but the sculpture was much taller than he could measure Jason measured the length of the shadow of the sculpture s highest point to be 15 feet long If the top of a slide in the same park measured at the same time of day has a height of 75 inches and a shadow length of 45 inches how tall is the art sculpture at its highest point OA 30 feet B 45 feet C 20 feet D 25 feet

9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 What is the rule for the transformation from the smaller polygon to the larger polygon O A x y x y 3x 3y OB x y 2x 2y O C x y x y OD x y x y X

Solve for x in the following equation OA 7 O B 72 O C 14 C 14 2x 3

0 S F 25 U AHGE 60 G 35 84 H T

Find the missing length indicated 1 5 6

Use the power reducing formulas to rewrite cos 5x in terms of the first power of cosine Simplify your answer as much as possible To indicate your answer first choose one of the four forms below Then fill in the blanks with the appropriate numbers o o o cos 5x cos x cos cos 5x cos x cos cos sx cos x cos 5x cos x OJO 8 X S

ot the complex numbers 3 1 and 1 2 in the complex plane Re X

Select the graph for each system of inequalities below 16 70 4x 4y28 2x ys l A D C B E

Find the trigonometric ratio by referring to the figure cot a cot a 30 24 B

Question 18 5 two and 2 with multiplicity one There is an ellipse with equation given below x 4 y 16 1 I what are the coordinate of the two foci O none of these answers Question 19 O 0 3 46 and 0 3 46 O 3 46 0 and 0 3 46 O 3 46 0 and 3 46 0

3 46 0 and 0 3 46 O 3 46 0 and 3 46 0 Question 19 Write equation of a line that goes through points 2 3 and 1 5 none of these answers O y 2x 7 Oy 2x 5 O y 2x 5 Question 20 finding the end behavior

The design for a painting of a farm scene is 12 x 9 The artist wants to transfer this design to the side of a building What is the largest possible complete design that can be painted on a 24 x 16 wall

The figure describes a dilation with center O and image in bold Find the scale factor and the lengths designated by x and y S K E 6 20 16

A rectangular box with no top and two intersecting partitions is to be constructed from 363 square inches of cardboard see the figure Find the dimensions that maximize the volume The dimensions of the base of the box are Llso a to no inches Patoka BRAVERSE POREMNGEVEERIFE SEINAPANE TELAT

14 Anna and Sanjay are playing a board game with the spinner shown below Each section of the spinner has a number 1 2 3 4 and a color R red Y yellow G green B blue 3 B 4R work Ans 1 G work Ans work 3 Y 4 Y 2G 2R 4B 1B 1R 3 G 3 Y 2Y 1R 2B 4 G a What is the probability that the spinner will land on a green section 1 pt b The spinner is spun and the color is recorded The spinner is then spun a second time and the number is recorded Are these events independent or dependent Explain your answer 2 pts c The spinner is spun and the color is recorded The spinner is then spun a second time and the number is recorded What is the probability that the spinner will land on a yellow section first and the number 2 second 3 pts

11 The numbers 1 15 are written on cards the cards are shuffled and one is selected at random Event A is drawing an even number Event B is drawing a multiple of 3 a Find the probability that the number drawn is an even multiple of 3 1 pt work Ans b Find the probability that the number drawn is an even number or a multiple of 3 1 pt work Ans c Find the probability that the number drawn is an odd number 1 pt

13 Travis s collection of DVDs contains 14 comedies 12 dramas and 10 action movies Hel wants to select two movies at random without replacement work Ans work Ans a Find the probability of selecting two comedies 3 pts b Find the probability of selecting two dramas 3 pts

b cos2x 3cosx 4 Find all solu cos 2 x sin 2 x 300

9 One card is randomly drawn from a deck of 52 card What is the probability of getting a Jack or a Spade pts

5 What is the theoretical probability of getting heads 1 pt

2 A six sided die is rolled What is the probability that a number greater than 4 is rolled 1 pt

and each measure 4 LO 5 B 10 X D

Find each measure GK FL X x 2 K x 4 x 8 G H