Geometry Questions

In circle Q ZRQS ZSQT U R T Which statement must be true ORT UT O ZRQT ZRST O RQL QT ORS ST

Chords DE EF and FG are congruent F E D 56 5 67 C 75 H G Determine the following measures mFG mZECF 0

The minor arc measures of circle Z are shown in the figure T 54 U 78 54 Y N V 71 71 X 32 W Use the drop down menus to complete each statement Angle UZT is congruent to angle Angle VZW is congruent to angle

Which figure shows a line tangent to the circle 6 9 3 5 10 5 LO 5 3

CB is tangent to OA at point C Find the radius A T T 5 C 8 B CB LAC by the radius tangent theorem so ZC is a right angle AABC is a right triangle so apply the Pythagorean theorem Use the steps and solve for the radius r 1 2 82 r 5 2 2 642 10r 25 39 10 54 25 64 35 89 10

LM is tangent to ON at point M L M 66 N Determine the following angle measures m M mZL O

B Check A E C D N V Y X W Given OA OV what congruency statements can you make Check all that apply OBCZY BEZX CB YZ OZDAB ZZVX DE WX BEZX

Given OO with central angles ZAOC ZBOD Prove AC BD A B C D Complete the missing parts of the paragraph proof Proof are We know that central angles congruent because it is given We can say that segments AO CO BO and DO are congruent because Then by the congruency theorem we know that triangle AOC is congruent to triangle BOD Finally we can conclude that chord AC is congruent to chord BD because

E B F In the figure ABCD is a lattice and AEFG is a square A AEFG 9 cm and Since IABI 4 cm is known C

Find the x and y coordinates of the terminal point for the angle estion 4 4 on the unit circle

8 C T 4 Points O Law of Sines O Law of Cosines b 15 75 25 a DETAILS LARPCALC11 6 2 032 NVA Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle a 10 b 16 C 650 B MY NOTES ASK YO Solve if possible the triangle If two solutions exist find both Round your answers to two decimal places If a triangle is r enter IMPOSSIBLE in each corresponding answer blank Y

An automated machine is calibrated to fill bags of pretzels so that each bag weighs 8 ounces A worker at the factory believes the machine is not filling the bags to the correct weight She randomly selects 40 bags of pretzels and after weighing them calculates their mean weight to be 8 4 ounces Write null and alternative hypothesis to describe this situation 1 point O H p 8 H p 8 OH 8 H 8 OH 8 4 H 8 4 H 8 H H 8

Determine a general formula or formulas for the solutions to the following equation Then determine the specific solutions if any on the interval 0 2x sin 201 A 8 OB 0 O c 9 OD 0 OE There is no solution What is are the solution s to the equation sin 20 1 on the restricted interval 0 2x Select the correct choice below and if necessary fill in the answer box within your choice k or 8 k k0 kor 8 ecces kor 0 kor 8 kor 8 A 8 E Use a comma to separate answers as needed Simplify your answer Type an exact answer using a as needed Use integers or fractions for any numbers in the expression

The solids are similar Find the surface area of solid B Prism A 17 in S 346 in Prism B 34 in The surface area of solid B is square inches

Solids A and B are similar Use the given information and scale factor k from solid A to solid B to find the surface area of solid B Prism A has a surface area of 805 square feet and the and k The surface area of solid B is square feet 5

3 2 1 0 1 1 117 A 63 0 1 2 3 4 C 63 63 5 B 6 E 117 G 8 7 63 F 9 10 11 12 Figure 8 4 Explain why the parallelograms are congruent in terms of rigid transformations 5 Explain why the parallelograms are congruent in terms of corresponding angles and sides 6 Use notation like ABCD A B C D to state how the parallelograms are congruent Note that there c multiple correct ways to write this AMRG AKPS 7 Draw a picture that matches this situation

C B3 90 34 3 56 2 A 5 4 3 2 1 D E 11 10 1 0 1 56 2 90 343F 4 Figure 7 2 3 1 Explain why the triangles are congruent in terms of rigid transformations 2 Explain why the triangles are congruent in terms of corresponding angles and sides 3 Use notation like ACATADOG to state how the triangles are congruent Note that there are

h A cylindrical can has the following properties height h 21 6 cm and radius r 6 cm The company that makes this can wants you to minimize the materials needed surface area to create their can while maintaining the same volume Determine th

The height of a radio tower is 350 feet and the ground on one side of the tower slopes upward at an angle of 10 a How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 160 feet from the base of the tower b How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a point 160 feet from the base on the flat side

10 M 1 3 4 Find the formula for the graph of the function f x given in the graph above f x

Prok m 2 A landscape modeler uses a 3D printer to create plastic forms that will eventually be transformed into model trees The forms consist of a right square pyramid with base edges 6cm and a height of 10cm In the center of the base is attached a cylinder with a diameter 2cm and height of 3cm a Find the total surface area of the plastic form b Find the volume of the plastic form

1 point Find a possible formula for the trigonometric function graphed below Use x as the independent variable in your formula f x help formulas 5 18

1 point Question 30 S a ath y sin x X a Write an expression involving the variable a and h for the slope of the line segment joining S and T in the figure above Slope an expression involving the variables a and h b Evaluate your expression for a 1 6 and h 0 2 Round your answer to two decimal places a value rounded to two decimal places Slope

nts 763268 take 13 Given the similar prisms pictured below with the measure of one pair of corresponding sides The surface area of prism 1 is 104 in and the volume of prism 2 is 1625 in 1 Find the volume of prism 1 2 Find the surface area of prism 2 11111 4 in Prism 1 10 in Prism 2

Use the point slope formula to write an equation of the line that passes through form if possible The equation of the line is 0 0 0 8 X and has an undefined

1 point Assume that sin A sin B in the figure Find exact answers for each of the values below not decimal approximations All angles are given in radians and your answers should be in radians a If A then B b If A 1 1 then B help numbers help numbers sintet

Graph the solution to the following system of inequalities x y 2 y x 2 1

Complete the table by solving the parallelogram shown in the figure The lengths of the diagonals are given by c and Round your answer to two decimal places b a 45 a 55 0 b C C d d 80 0 O 4

Show that sin 0 O A O B O C 100 Which of the following four statements establishes the identity O D 1 82 cos 20 cos 40 sin 40 sin 0 sin 40 sin 0 1 cos 20 2 sin 0 sin 0 1 cos 20 3 2 8 1 cos 20 2 sin 0 sin 0 c 1 cos 20 2 2 11 3 8 1 2 3 8 2 cos 20 cos 40 cos 20 1 2 8 cos 40 1 cos 20 cos 40 8 3 1 1 82 cos 20 cos 40

Use a tree diagram for the following K a Find the number of ways 2 letters can be choosen from the set U V W if order is important and repetition is allowed b Reconsider part a if no repeats are allowed c Find the number of combinations of 3 elements taken 2 at a time Does this answer differ from part a or b GELLD a The number of ways to select 2 letters from the set U V W if order is important and repetition is allowed is

retractable awning above a patio lowers at an angle of 50 from the exterior wall at a height of y 11 feet above the round No direct sunlight is to enter the door when the angle of elevation of the sun is greater than 70 see figure What the length x of the awning Round your answer to two decimal places ft y ft 70 Suns rays

4 Find the height of triangle DEF 9 m B 11 m E 13 m

Problem 6 Solve for the missing sides and angles b 3m

AXYZ T 1 R axis D AABC Draw A XYZ 02 9 the graph below if it is the case that T PENCIL THIN V 12 11 10 9 4 BLACK 6 5 20 2 A 12 114 10 9 8 7 6 5 4 2 B N M p S 99

6 Check if the triangles given below are similar Specify which triangles are similar Also write which method you used to decide similarity i e SSS SAS a E D LO b PQ SR 3 cm Angle P and S are 90 degrees B

Because of prevailing winds a tree grew so that it was leaning 6 from the vertical At a point d 40 meters from the tree the angle of elevation to the top of the trees is a 28 see figure Find the height h of the tree Round your answer to one decimal place h

7 Which shows the length of the darkened arc 7 5x 1 5x 15x G3T S zoom in 60 7 FORMULA n S 3 2 r 360 F H S

6What is the degree measure of RTU F 32 HD 238 G212 D 248 zoom in 32 S 6

In circle E with m DEF 78 and DE 20 find the area of sector DEF Round to the nearest hundredth F D E

Using the digits 0 to 9 at most one time each place a digit in each box such that the central angle is greater than 120 degrees C Central angle Inscribed angle Circumscribed angle 0 O D D Check

The table below gives percent of flights that were delayed and on time during good and bad weather Good weather Bad Weather 17 5 32 5 Delayed 7 5 On Time 42 5 Given these percentages during bad weather is it more likely that your flight will be delayed or on time How much more likely It is 30 more likely to be delayed It is 15 more likely to be delayed It is 30 more likely to be on time It is 15 more likely to be on time

1 What is the m C B A 25

The table below gives the typical number of days of rainfall in Fall and Spring in Death Valley California Fall Event F Spring Event S Rain Event R 7 No Rain or Dry Event D 115 Given the fact that it rained one day in the Fall or the Spring how much more likely is it that the day it rained was in the Fall o 1 13 122 244 01 6 116 265

Team A and B love to play pickup basketball There are no fouls and no three pointers so all shots are worth 2 points The only problem is Team A always wins They typically play games to 100 and Team B loses by 10 points That is the typical final score is Team A 100 Team B 90 So they decide to increase the point value of each basket for Team B to 2 2 points Based on the typical results above what effect is this most likely to have The teams will tend to score the exact same number of points O Team A will still tend to win by 1 point instead of 10 Team B will now tend to win by a margin of 1 point Team B will now tend to win by 10 points

At certain times of the year about 70 of airline flight delays are caused by bad weather During those times about 50 of all flights experience bad weather and about 25 of all flights are delayed Given these percentages if the weather is good what is the probability that your flight will be delayed About 15 About 20 About 35 About 30

In baseball a player pitches a ball from the mound to a catcher behind the plate A pitch that passes over the plate above the batter s knees and below his chest is a strike All other pitches are balls provided the batter does not swing at them or hit them foul The table below breaks a sample number of pitches into strikes and balls over the plate and not over the plate Over plate Event C Not over plate Event D Strike Event A 10 0 Ball Event B 5 20 Which conditional probability below is either inaccurately described or inaccurately calculated The probability that a pitch not over the plate is a strike is zero So P AID 0 The probability that a pitch not over the plate is a ball is 1 So P BID 1 The probability that a pitch over the plate is a strike is 10 15 So O The probability that a pitch over the plate is a ball is 5 10 So P BIC 0 5

A simple dart target has two concentric circles The larger circle has a radius of 4 The smaller circle has a radius of 2 The scoring should correspond to the relative difficulty of hitting the inner circle and the outer ring How many more points should a player receive for landing a dart in the inner circle as opposed to the outer ring The player should receive 4x times as many points The player should receive 2x times as many points The player should receive 9 times as many points The player should receive 3 times as many points

Convert the following to polar coordinates where angles are given in radians Give one representation with r 0 and one representation with r 0 6 pts each A Give rounded to 1 decimal place The point 3 5

A park in the shape of a quadrilateral ABCD has ZC 90 AB 9 m BC 12 m CD 5 m and AD 8 m How much area does it occupy

Let 1 3 2 and w 1 4 5 a Determine W 3 pts b c e d Determine 3 v 3 pts Determine 3 pts Find the unit vector in the direction of 3 pts Determine the dot product of and W 3 pts Angular coordinates Determing the angle between the vectors and w 3 pts