Geometry Questions

If we want the median of these five numbers to be 45 what number belongs in the blank If nothing will work just type NOT POSSIBLE 25 90 10 60

Find the value of x and all missing angles Then classify the triangle by the angles 2x 3x 55 5 P 3x 3x 20 9x 5 S R 6 55 60

1 Points DETAILS LARPRECALCRMRP7 5 2 072 Powers of trigonometric functions are rewritten to be useful in calculus Verify the identity Simplify your answers completely sec x tan x tan x tan x sec x tan x tan x sec x Need Help Read It Submit Answer 10 1 Points S DETAILS tan6 x sec x tan x h ft Gnomon The lengths of a shadow cast by a vertical gnomon a device used to tell time of height h when the angle of the sun above the horizon is 8 see h sin 90 0 sin 0 5 Watch It a Verify that the expression for s is equivalent to h cot 0 Use the Cofunction Identity Simplify your answer completely h sin 90 0 sin 0 h cot 0 0 1 tan x sec x LARPRECALCRMRP7 5 2 079 sin 0 b Use a graphing utility to complete the table Let h 4 feet Round your answers to two decimal places 15 30 45 60 75 90

Rewrite the expression as a single logarithm and simplify the result Hint Begin by using the properties of logarithms 7 In cott 7 In 1 tan t

Fill in the blank to correctly complete the If a function f has an inverse then the graph off may be obtained by reflecting the graph of f across the line with the equation Type an equation

A telephone line hangs between two poles 14 m apart in the shape of the catenary y 22 cosh 7 5 0 0 0 7 x 2 17 where x and y are measured in meters 22 a Find the slope of this curve where it meets the right hand pole Round your answer to four decimal places b Find the angle 8 in degrees between the line and the pole Round your answer to two decimal places 8

angle me Jane and Opal s straw designs knowing that the lines created by the straws in their designs were parallel 70 Jane s straw design 135 140 xo to 70 Opal s straw design Find all of the labeled angle measurements knowing that the lines created by the straws are parallel Explain the reasoning for your results

Each one was making a line design using either 3 or 4 straws They had just come from math class where they had been studying special angles Paul pulled his pencil out of his book bag and labeled some of the angles and lines He then challenged himself and the others to find all the labeled angle measurements in Paul and Justin s straw designs and to determine whether the lines that appear to be parallel really are parallel Paul s straw design 2C B 40 20 2x 10 5x 20 Justin s straw design began playing with drink straws 3x 30 Find all of the labeled angle measurements Determine whether the lines that appear to be parallel really are parallel Explain the reasoning for your results

Find the number of integer values of BC x 8 A D

Use a graphing utility to determine which of the six trigonometric functions is equal to the expression Verify your answer algebraically 1 1 sin 0 cos 8 cos 0 1 sin 0

Factor the expression and use the fundamental identities to simplify Use a graphing utility to check your result graphically sec r tan x sec r STEP 1 Multiply constants sec x tan x sec x 16 STEP 2 Factor sec x tan x 6 sec x 16 sec x tan x sec x 16 tan x 1 STEP 3 Apply the appropriate fundamental trigonometric identity and simplify 7 sec x tan x sec x 16

Use the values to evaluate if possible all six trigonometric functions If an answer is undefined enter UNDEFINED tan 0 is undefined sin 0 0 cos 0 sin 0 csc 0 sec 8 cot 0

Complete the equation for the line perpendicular to g x 6x 5 and passing through the point 9 2 help equations Y

a Find the domain of f The domain of f is 0 00 Type your answer in interval notation b Choose the correct graph of f A Ay B O C Q O D

Describe a pattern in the sequence of numbers Predict the next number 5 2 6 18 54 6 0 1 4 9 7 256 64 16 4 8 3 0 3 0 3 0 9 7 0 7 5 8 0 8 5 10 13 7 1 5

Sketch the next figure in the pattern 3 ADO 4

1 Explain what a conjecture is 2 How can you prove that a conjecture is false Sec 10 F

A parcel delivery service has contracted you to design a closed box with a square base that has a volume of 11 000 cubic inches Complete parts a d a Express the surface area of the box as a function of x X

2 2x 3 For the function F x X domain and range and c use the final graph to list any vertical horizontal or oblique asymptotes a graph the rational function using transformations b use the final graph to find 17 2 a Which of the following transformations is required to graph the given function 1 OA Shift the graph of y 3 units to the left and shift it 2 units up 2 x O B Vertically stretch the graph of y by a factor of 3 reflect it about the x axis and shift it 2 units down X OC Vertically stretch the graph of y by a factor of 3 reflect it about the y axis and shift it 2 units up X Vertically stretch the graph of y hy a factor of 3 reflect it about the x avis and shift it 2 units un

Use the graph shown to find the following a The domain and range of the function b The intercepts if any c Horizontal asymptotes if any d Vertical asymptotes if any e Oblique asymptotes if any MIDD 9 6 3 Q Find the vertical asymptotes if there are any Select the correct choice below and fill in any answer boxes within your choice O A x Type an integer or a simplified fraction Use a comma to separate answers as needed OB There are no vertical asymptotes Find the oblique asymptotes if there are any Select the correct choice below and fill in any answer boxes withi

For the function H x x 2 a graph the rational function using transformations b use the final graph to find the domain and range and c use the final graph to list any vertica horizontal or oblique asymptotes a Choose the correct graph below O A O B G C O B The domain of the given function is xlx is a real number x Type an integer or a simplified fraction O C M O D b What is the domain of the given function Select the correct choice below and if necessary fill in the answer box to complete your choice O A The domain of the given function is xlx is a real number x Type an integer or a simplified fraction Q

4 For the function H x a graph the rational function using transformations b use the final graph to find the X 2 domain and range and c use the final graph to list any vertical horizontal or oblique asymptotes a Choose the correct graph below O A B Q O C Q D

Use the graph shown to find the following a The domain and range of the function b The intercepts if any c Horizontal asymptotes if any d Vertical asymptotes if any e Oblique asymptotes if any C 9 6 Find the y intercepts if there are any Select the correct choice below and fill in any answer boxes within your choice O A y Type an integer or a simplified fraction Use a comma to separate answers as needed

Charles RYE Bushels Dina On the following graph use the blue line circle symbol to plot Charles s production possibilities curve PPF and use the purple line diamond symbol to plot Dina s PPF 200 180 160 140 120 100 80 60 40 20 0 4 Corn Bushels per acre 40 28 0 100 Rye Bushels per acre 8 7 200 300 400 500 600 CORN Bushels 700 800 900 1000 Charles s PPF Dina s PPF

Graph the function by setting the x intercept and the asymptotes Provide your answer below 10 2 0 5 10 3 0 f x P 4 10

N 7 Figure 1 Map of 300 mb winds at 12Z 10 MAR 2011 1 Look at the accompanying Figure 1 With a pencil shade a small oval around each station where wind speeds are 60 knots or greater such as San Francisco Then shade the area between adjacent shaded stations where the wind speeds are also presumed to be 60 knots of more Next draw lines along the northern and the southern boundaries to highlight the shaded area limits of the 60 knot or greater region Finally draw a heavy smooth curved arrow through the core of the shaded highest wind speeds Add an arrow head to show wind direction 2 The large arrow you drew on your map approximates the location of the existing polar front jet stream across the United States Now imagine that you are in a gondola attached to a helium filled balloon that is located over central Washington State Assuming your balloon stays at the 300 millibar level and travels with the air flow draw your path as you travel across the country Through what state or states are you likely to leave the United States

15 Solve a system of equations to find the values of x and y Show all work y 30 4x 3x 2y 9 0 waled sugit ani or

16 Given c d and 3 24 Prove 42 24 Statement Reason

D C b G A F Refer to the figure index the following vectors and planes Vector AB AE and BD Plane AFEC FBCD and BFGE E B

Complete the two column proof 17 Given l 2 and 21 23 Prove j k Statement 12 2 1 Es bns b305 3 11m91512 Reason

Based on the diagram determine if the statement is True or False 1 2 3 4 5 6 7 28 218 are alternate interior angles 214 223 are same side exterior angles 414 220 42 26 24 210 23 216 are supplementary 222 224 Call 12 4 3 S6 8 13 14 1615 9 10 11 12 17 18 20 19 21 22 24 23

Based on the diagram determine whether each 48 46 1 132 46 132 8 9 10 1 11 12 cll f cll d clle dlle all b

2 If mLABD 39 and m2DBC 22 what is mLABC Draw two angle pairs that will justify your answer

R B 90 c 106 02 D Transversal CD cuts parallel lines PQ and RS at points X and Y as shown in the diagram If m2CXP 106 02 what is m SYD OA 73 98 OD 180 S

Question 10 Write a logarithmic equation corresponding to the graph shown The dashed line indicates the asymptote of the function Use y log x as the parent function 7 6 V 4 3 2 1 7 6 5 4 3 2 1 1 2 3 4 5 6 7 X 12 3 4 5 6 7

15 m 2 x 94 2 H H

120 11

Name A lighthouse that is 50 meters above sea level marks the entrance to a bay The lighthouse is used to orient ships as well as to provide a lookout point for the local coast guard 50 m a A pair of ocean kayakers estimate their distance to the entrance of the bay using the lighthouse They measure the angle of elevation from their position to the top of the lighthouse to be about 16 Draw a diagram showing the kayaks in relation to the lighthouse illustrating the angle of elevation b Knowing the height of the lighthouse and the angle of elevation from the kayakers to the top of the lighthouse calculate the kayakers distance to the entrance of the bay c A member of the coast guard is on lookout at the top of the lighthouse She spots a distress signal from a boat She measures t angle of depression to the boat to be 8 Draw a diagram showing the boat in relation to the lighthouse illustrating the angle c depression d Knowing the height of the lighthouse and the angle of depression from the top of the lighthouse to the boat in distress calc the distance from the lighthouse to the boat

WS Mix with Algebra Systems of Equations and Quadratics 1 Triangle MNP and OMNare equilateral triangles What method can be used to verify the triangles are congruent Find the value of x and y 3X 12 X 4 M 3x 12 3 In triangle ABC AD is the perpendicular bisector of BC AB 25 AC 3x 5 and mLADC y 35 What method can be used to verify the triangles are congruent Find the value of x and y 4 What method can be used to verify the triangles are congruent If RQ 5x 2 RS 3x 8 and PQ 2x 4 find the value of xand all sides 3y 6 O x 4 2 Triangle ABC and DEFhave the following properties ABDE BC EF and LB LE If AB 27 BC 4 DE 7x 3y and EF 2x y What method can be used to verify the triangles are congruent Find the value of xand y N A B D C

Find the length of LM K LM 16 N 10 12 L M 0 Write your answer as a whole number or a decima

Find the length of GH F I GH 5 8 2 G J H Write your answer as a whole number or a decima

If GH GJ m GIH 6b and mZGIJ b 60 what is mZGIJ G H J I

If JK 9w 67 and GI 2w 12 what is the value of w G H I

V is the midpoint of UW and S is the midpoint of TW If TU z and SV 2z 45 what is the value of z W V S

R is the midpoint of QS and U is the midpoint of QT If ST p 53 and RU p 4 what is the value of p Q S R U

QS is a midsegment of APRT If PT v 22 and QS v 7 what is the value of v T S P Q R 20

RT is a midsegment of ASUV If UV y 6 and RT 2y what is the value of y S R V T U

Determine what ADDITIONAL INFORMATION would be necessary to prove the two congruent using the suggested postulate or theorem with the given information NC RO NC RO 13 Given ZN ZV and NG VI Use SAS Postulate Mark the pairs of sides and angles that you use complete the congruence between the triangles and choose SSS SAS ASA AAS or HL as the reason 15 ANCO A by 14 Given VK LIK NS L GS and ZV ZN Use ASA Theorem THE SN HNAK THINS 17 ATHA A 19 APIE A P is the midpoint of IS IE ES H by by O E 16 AKGI A ZK ZN GI bisects ZKGN 18 AGIVA GV bisects LIGE GV bisects LIVE 20 ATEUA TE TR ZTUE ZTYR by K by G by G I U K N

bel AMNO and AXYZ Indicate the additional pairs of corresponding parts that would have to be proved congruent in order to use the given postulate or theorem to prove the triangles congruent 8 9 ZNLY and NO YZ by ASA V 20 ZZ and ZM ZX by AAS 10 ZNZY and ZM ZX by ASA 11 Given AABC ADEF AB 15 BC 20 AC 25 and FE 3x 7 find x 12 Given AABC ADEF DE 10 EF 13 DF 16 and AC 4x 8 find x

Then identify the transformation Graph the Image R S T to check on to write the rule that maps each preimage to its your answer The coordinate rule is The transformation is Preimage P 4 2 Q 1 3 R 3 3 P Q R Image Preimage R 4 3 S 1 3 T 4 1 Bike Image R 1 1 S 4 1 T 1 3 R 2 Draw the image of each figure under the given transformation Record the coordinate of the Image P Q R on th table sty x y x 1 y 2 P t 5 R S 0 O 5 S