Geometry Questions

In the following figure the smaller triangle is the image of the larger triangle under a dilation centered at point O Find the scale factor and the length of x and y as pictured scale factor Tyne an integer or a simplified fraction Z 18 The numbers and letters represent the leng the sides of the triangles

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

May 05 7 42 21 AM A parabola can be drawn given a focus of 10 6 and a directrix of x 2 Write the equation of the parabola in any form

Find the angle of taper on the steel bar shown if it is equal to twice m The angle of taper of the steel bar is Round to the nearest minute as needed www 25 0 mm m 22 5 mm

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

10 One card is randomly drawn from a deck of 52 cards What is the probability of getting a Jack or a King 3 pts

6 Heather flips a coin 8 times and gets heads 5 times What is the experimental probability of getting heads 1 pt

Determine if the following scenarios are mutually exclusive or overlapping Explain your reasoning 2 pts each 7 You are taking a multiple choice test Event A is you choose the correct answer Event B is you choose D as the answer 8 You survey students in your school about what grade they are Event A is the person is a senior Event B is the person is a junior

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

4 Explain the difference between experimental and theoretical probability Give an example of each 4 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

Transform Quadrilateral DEFG by rotating the image 90 Counter Clockwise around the origin 0 0 to create the image of Quadrilateral D EF G A minimum of 4 points at the new vertices must be graphed you may connect the dots but it is not required because the drawing tool is not as accurate as we d like it to be x Clear Undo Redo 5 4 3 2 1 YA 6 54 32 2 1 1 2 3 D G E 2 3 4 5 6 7 F Ax X

73 3 points Given cos 2a and 2a is in quadrant I find exact values of the six trigonometric functions Note You are not allowed to use decimals in your answer sin a cos a tan a csc a sec a cot a

Find the identical expression for the following 4 Cos 0 1 1 cos 0 cos 0 Hint consider the numerator as a difference of squares sin 8 tan 8 cos 8 2 sin e 2 cos 0

O is the center of the regular dodecagon below Find its perimeter Round to the nearest tenth if necessary 20 0

Question 4 of 10 The circle below is centered at the point 3 1 and has a radius of length 2 What is its equation 5 10 5 OD x 1 2 y 3 2 10 OA x 3 2 y 1 22 OB x 3 2 y 1 4 OC x 1 2 y 3 4 SUBMIT

Write an equation for the translation of y 26 x 0 and y 4 27 x 2 and y 3 TEM 29 Construction The weight Pin pounds that a beam can safely carry is inversely that has the given asymptotes See 28 x 4 and y 8 See

Answer each question below Estimate any irrational answers to one decimal place 3 Find the magnitude and direction angle of p 12i 23j 60 4 Find the unit vector that s in the same direction as q 12i 5j 60

Ci 10 5 0 5 T I 5 27 S 10 T X 15 Graph f x logx by finding 4 points and the asymptote AFTER you have plotted your points and asymptote press Check my graph CHECK MYOINTS If your points were not accurate make corrections to your written work

Write a quadratic function in STANDARD FORM whose graph satisfies the given conditions 7 a Passes through the points 4 0 3 0 2 18 b Passes through the points 1 0 5 0 3 16

g x x x 6

3

Several different kinds of cheese are for sale The cheese comes in wedges shaped like sectors of the wedges are the same height 6 7B Mai bought a wedge with a central angle of 45 degrees and a radius 10 inches What is the area of the top surface of this wedge

Let sinA 12 13 with A in QIV and cosB 3 5 with B in QI Answer exactly

The circle with center B is a dilation of the circle with center A using scale factor 2 Select all true statements a a The circumference of the circle centered at B is greater than the circumference of the circle centered A by a factor of 2 b The ratio is greater than the ratio by a factor of 2 c The value of is greater than the value of a by a factor of 2 d The angle marked a measures radians 6 12 87 e The angle marked measures radians

25 Part 1 of 5 The center of the ellipse is 1 Part 2 of 5 16 The vertices are 2 1 and 8 1 Part 2 5 Part 3 of 5 The endpoints of the minor axis are 00 and 00 olo 8

Solve the following system of equations by graphing y 2x 6 y x 1

1 7A The image shows a circle centered at point O Angle AOB measures 50 degrees What is the measure of angle ACB Explain how you know a 25 degrees b 40 degrees c 50 degrees d 100 degrees B 50

F 1 3 m Find the surface area of each figure 12 in 5m Q 12 in 18 cm 5 cm 12 in ANS ANS 10 m ANS

4 7B A circle has a radius of 20 centimeters and a central angle that measures 216 degrees Find the length of the arc defined by this central angle

3 7A The image shows a quadrilateral inscribed in a circle Select ALL true statements a The arc from B to D passing through C measures 70 degrees b The arc from A to C passing through D measures 200 degrees c Angle BCD measures 140 degrees d The sum of the measures of the arcs from A to C one passing through B and the other passing through D is 360 degrees e Angle CDA measures 80 degrees f Angle CDA measures 100 degrees A D 70 100 B C

2 7A Line BC is tangent to the circle centered at A Find the measure of angle BCA Explain or show your reasoning B 57

Find the area of the shaded sector Round your answer to the nearest tenth 10cm 90 10cm 8

Minor arc KL measures 135 K L Which is the radian measure of central angle KOL O O 3 radians O 3 4 radians O radians 7 8 13 T 5 radians

5 T Consider circle T with radius 24 in and 8 6 4 24 in T T1 radians What is the length of minor arc SV O 20 in O287 in 40 in O 637 in

Arc CD is of the circumference of a circle What is the radian measure of the central angle O O O 2 radians 3 3 T 4 47 3 radians radians O 3T radians TE

Circle O has a circumference of approximately 44 in P What is the approximate length of the diameter d O 7 in O O O 14 in 22 in 44 in

Circle P has a circumference of approximately 75 inches T What is the approximate length of the radius Use 3 14 for T Round to the nearest inch O O 12 inches 24 inches 38 inches 46 inches

n circle O the length of radius OL is 6 cm and the length of arc LM is 6 3 cm The measure of angle MON is 75 6 cm 75 6 3 cm N M Rounded to the nearest tenth of a centimeter what is the length of arc LMN O 7 9 cm O 10 2 cm 12 6 cm O 14 2 cm

Circle O has a circumference of approximately 2507 ft Jud O What is the approximate length of the diameter d 40 ft 80 ft O 125 ft 250 ft

Two circles are shown in the diagram C d 1 C2 d 2r Since all circles are similar a proportion can be set up using the circumference and diameter of each circle Sub the values d 1 C and d 2r into the proportion C C d d Which shows how to correctly solve for C the circumference of any circle with radius r

An arc on a circle measures 295 The measure of the central angle in radians is within which range O 0 to radians Oto radians O to 3 T 2 3 T 2 radians to 2 radians