Geometry Questions

The volume of the rectangular pyramid below is 120 units Find the value of x X 9 4

Identify a semicircle that contains C A O ABC CB 0 B

C Directions Complete the two column proof 10 15 Given A LMN where IM IN MN Prove MN IN IM MN LM IN ZM IN MN 1 2 3 Statements 1 2 3 N Reasons

y y Use linear regression to find the equation for the linear function that best fits this data Round to two decimal places Hint 876 1407 2237 3454 5545 8731

Are the triangles similar How do you know 30 4 84 6 O no O yes by SSS O yes by AA O yes by SAS 84 6

The polygons are similar but not necessarily drawn to scale Find the value of x A 5x B 4 C 04 O 20 5 01 D

iven the three statements below identify which represent exponential equations 1 The cost of living allowance for state employees increases salaries by 3 1 each year 2 The value of an investment is increasing by 300 each year 3 Tuition costs have increased by 2 8 each year for the last 3 years ooking at the following two equations that represent the balance in two different avings accounts which account is growing faster and which account will have a higher balance after 3 years A 1 000 1 05 t B 900 1 075 t Complete the table The first one has been done for you Equation Initial Value y 615 0 79 y 500 1 03 y 3 200 1 2 y 19 611 0 98 615 50 Growth or Decay Decay Growth Rate as a 21 12

Find the area of the circle Leave your answer in terms of 4 1 m 2 4 2025 m 8 405 m O 11 2 m 16 81 m

4 y you 44 y 0 1 y 0 0 y 0 2 e

Gumball A gumball has a radius that is 25 mm The radius of the gumball s spherical hollow core is 21 mm What is the volume of the gumball if you do not include its hollow core Answer stion Help Read Viden mm Use 3 14 or the key on your calculator Round your answer to the nearest tenth if necessary

Find the volume of the cone 12 cm r 8 cm V cm

Use the Law of Cosines to determine the indicated side x Assume b 14 and c 18 Round your answer to one decimal place C b c a Step 1 The Law of Cosines states that for the triangle ABC with sides a b and c b 108 a 18 x 14 B 324 196 In the given triangle you know sides b and c and angle A and need to find a So you can rewrite this formula a c b 6 cos A Step 2 Substitute known values into the alternate form of the Law of Cosines Round your answer to three decimal places a 2 b 2ab cos A 2 2 2ab 28 14 2bc cos C 1 18 cos 108 1x cos 108

What is the solution of each proportion D 5 A 120 10 10 C bo B 5 Not drawn to scale N 3 12 M 120 1 2 O ABCD KIMN 10 1 2 1 2 The polygons are not similar O ABCD NKLM 5 3 12 O ABCD KIMN 5 1 2 K 3 12 L

Which theorem or postulate proves the two triangles are similar 20 19 7615 Not drawn to scale O SA Postulate O SSS Theorem OAA Postulate 16

What is the value of x x 5 O 10 O 7 5 O 2 5 X 2 x 1

What similarity statement can you write relating the three triangles in the diagram T U V ATWV AVUW AUWT O AWUT AVUW AWVT O AUVW AUWT AWVT O AUVW AWUT AWVT

Segment BD bisects segment AC Solve for x Round to the nearest tenth if necessary Image not necessarily to scale A 20 Answer p 8 B D 17 X

Qu GivensABC A B C midpoint of the sives respectively let O the perpendicular from it onto L M B a let feet of the onto bisects 6 Compute the angle between OmJ 13 c P be the BC CA ond var be the foot of BC be the respective perpendiculars from D C A A B prove that ADJ 28 12 3 U LM

5 In the accompanying diagram of quadrilateral QRST LRST SRLQR and ST 1QT Prove QR QR QT QT is the angle bisector of R T S

Which trigonometric statement is NOT an identity Select one a cse 0 1 cot 0 b 1 cos sin 0 c 1 sin 0 cos 0 Od 1 tan 0 sec 0

Solve each equation to the nearest tenth Use the given restriction tan 1 4 for 180 270

7 10 points Given ui 5j and v 3i 4j find i the dot product u ii 2u 3v

rom what you learned about radians which circle best represents how radians are meas elect one a O b OC 66 42 44 41 41 a 44 SA a 41 44

Choose the statement that is NOT true Select one Oa As B gets larger the period gets smaller and frequency becomes greater O b The period and the frequency vary indirectly OC The red graph is y sin x The phase shift for the blue graph is 1 2 1 Od The vertical phase shift of y 3sin 5x T 6 is 5

Use an addition or subtraction formula to find the ex sin 67T 44 COS 3T 11 COS 67T 44 sin 3 T 11

ividing sin 0 cos20 1 by yields 1 cot csc

Find all the values of arcsin 3 Select one or more 0 0 a 3 b 5 C KM 0 e f d 7 g 3 5n 6 6 2x 3 4 3 11x 6

The angle 810 rotate clockwise counter clockwise full time s around the origin and is radians

Simplify the following Hint Use the unit circle sin 5m 3 Select one O a 1 2 Ob undefined OC 3 2 d 3 2

Which trig functions are equal to Select one or more 3A a tan 32 b sin st C cos d cos e sin 11 it 16

2 1 9 8 7 6 5 4 3 2 10 1 2 3 U 5 6 1 2 3 4 5 6 7 8 9 R S What are the coordinates of Point S after a dilation with the center at the origin and a scale factor of 2 1 8 4 O 2 1 O 16 8 4 2

Consider the following figure b mz1 P c m 2 N Given Q Find the following in degrees a m MRP M O T V In OQ PR contains Q MR is a tangent mMP 116 mMN 60 and mMT 46 R

Use the graph of the function f x to answer the questions below 6 4 2 6 4 2 2 4 12 4 6 a On what interval s is f x increasing If necessary you should use the union symbol U to indicate that f x is increasing on multiple intervals b What is the local minimum of f x Enter your answer as an ordered pair c What is the local maximum of f x Enter your answer as an ordered pair

r t 5 4 sint cost 4 3 2 1 A Clear All Draw 5 4 3 2 1 M Z 2 3 4 5 1 2 3 4 5

An experiment consists of rolling two fair number cubes The diagram shows the sample space of all equally likely outcomes Find the probability of rolling two 2 s Express your answer as a fraction in simplest form DDD DE DA 03 06 01 0 03 0 BADHO BR BA BO AN B 88 O None of the other answers are correct

Find the Domain and the value field 7 y f x 4 3 2 3 2 3 X

the figure In the given figure lines a and b are parallel Which angles can be proven to be congruent to angle 1 1 4 3 6 a

Directions Using a five sided spinner conduct an experiment to compare experimental probability with theoretical probability Using a five sided spinner you construct or a digital five sided spinner complete the following steps write the probabilities as a fraction 1 What is the theoretical probability of spinning yellow

Watch on youtube Suppose a Ferris Wheel has a diameter of 30 meters the center is 19 meters off the ground and it makes 2 revolutions per min Draw this Ferris Wheel labeling the radius height and center Supposing the minimum height of the Ferris Wheel occurs when t 0 write the sinusoidal function for the height as a function of time Lastly graph the function on a coordinate plane do not submit a digital calculator graph label the key points Part 2 Design your own Ferris Wheel determining diameter center and speed Write the function for the height of the Ferris Wheel as a function of time Is your Ferris Wheel realistic Does it travel too fast or too slow

From the image below c sinB b SinC B A Select one O True O False Answer h a b C For triangle DEF given sides d 38 e 42 and f 47 Find measure of angle F Your answer be numerical only and round to the nearest tenth

Directions Using the digits 1 to 9 fill in the boxes to produce a log that meets the indicated requirements Each digit can only be used once log Produces an integer log Produces an irrational number

Jed is working on stained glass project and needs to draw a triangle with side of 7 11 and 15 inches out of lead cane to enclosed the glass is the largest angle he needs to create using leading cane

Directions Using the digits 0 to 9 fill in the boxes so that the chart is accurate Use each digit only once per blue box and once per red box Logs are base 10 Note The green parenthesis indicates how to enter it into a calculator Increasing Size Increasing Size 969 log log loglog 1 C log 0

For f x 4x 1 and g x x 5 find f g x OA x 4x 4 OB x 4x 6 OC 4x 4 OD 4x 19

If f x 3x 1 and g x x 2 find f g x OA 3x x 1 OB 4x 1 OC 3x x 1 OD 3x 2

For f x 3x 1 and g x x 6 find f g x OA x 3x 5 OB 3x 17 212 ne

If f x 5x and g x x 1 find f g x OA 5x 5x OB 5x 1 O C 6x O D 5x 1

A student gets paid to sell food and drinks at the school play during intermission He earns an hourly rate of 12 plus an extra 0 50 for each bakery item he sells and 0 25 for each drink he sells If h hours b bakery items and d drinks what function can he use to calculate his earnings OA T h b d 12 2 4 b d OB T 12h 2 4 O C T 2b 4d 12 24 OD T 12h b d

For f x 3x 1 and g x 6 find OA OB O C O D 3x 1 3x 1 3x 1 3x 1 32 6 3

Is the graph increasing decreasing or constant where 8 x 10 10 10 8 6 49 A Increasing B Decreasing C Constant