Geometry Questions

13 The diagram below shows parallelogram ABCD with diagonals AC and BD intersecting at E B C E X D A What additional information is sufficient to prove that parallelogram ABCD is also a rhombus 1 BD bisects AC 2 AB is parallel to CD 3 AC is congruent to BD 4 AC is perpendicular to BD

5 in 3 in Volume 6 in 9 in 2 in

14 Find the area of the shaded region 9 cm

Let 2 1 1 B 1 2 3 A 0 02 2 13 2 points Part c 6 points Part d Evaluate each of the following if possible If it is not possible justify your answer Show all your work 4 points Part a Evaluate CD 3AT 3 points Part b Evaluate Evaluate DB Evaluate 8E tr CD I C 2 D 2 1 1 E 3 E 2 6 BC 4 2

21 In parallelogram PQRS QP is extended to point T and ST is drawn S R 1 130 2 80 P If ST SP and m R 130 what is mZPST 3 65 4 50 T

gths 4 Will be used later as a theorem In triangle ABC let D be a point on BC and let E be a point on AD Prove that Let ABE ACE BD CD ABD U ACD V PBD u PCD v BD CD ABP x ACP y a Which theorem states that U V t t V t t b Conclude that Uv uV i e u x v u v y Then conclude the desired poult

33 Find two values of for the trigonometric equation cos 0 9135 Round your answer to the nearest degree 24 156 B 24 336 204 336 156 204

Which is the best name for the quadrilateral with vertices at 2 2 5 2 1 5 and 2 1 A parallelogram B rectangle C rhombus D square

Triangle ABC has coordinates A 1 3 B 2 0 and C 4 1 The image of the triangle after a sequence of transformations is triangle A B C where A 5 3 B 4 0 and C 2 1 Write a sequence of transformations that takes triangle ABC to triangle A B C yt 5 4 A 3 21 B 6 5 4 3 2C1 34 2 4 5 6 A C B 1 2 3 4 5 x

Elizabeth was playing with a spinner that has 3 equal areas numbered 1 2 and 3 Elizabeth spun the spinner 100 times and 23 of the 100 spins came up as a 3 She wanted to see how likely a result of 23 threes in 100 spins would be with a fair spinner so Elizabeth used a computer simulation to see the proportion of threes in 100 spins repeated 100 times assuming a probability of of spinning a 3 Create a 95 confidence interval based on the data from the simulation to the nearest hundredth and state whether the observed proportion of threes is within the margin of error of the simulation results 1 Mean 0 331 SD 0 048 0 2 0 25 ooooo oooooo 0 3 0 35 Proportion of Threes 0 4 0 45 0 5 Note don t use percents for the interval or sample proportion The confidence interval based on the simulation is observed proportion of threes of is spinner s simulation so the of the fair

linder 6 c m Surface Area 12 cm

Rectangular Prism Surface Aras Surface Area of Rec WWE 13 mm

C 2 Suppose V is a vector space that contains vectors u u us and us If u 2 0 which of the following would be a set that spans V Select that all applied 244 S ui uz ui ui S ui u u Sa ui ui ui S u u u 0 S 0 S

Find the surface area of following 6 cm 7 cm 4 cm 12 cm 8 cm 8 cm

In the circle below IK is a diameter Suppose m 1J 44 and mLIJL 28 Find the following a m JIK 0 b m 2 KJL X

Round Tree Manor is a hotel that provides two types of rooms with three rental classes Super Saver Deluxe and Business The profit per night for each type of room and rental class is as follows Room Type I Type II Super Saver Deluxe Business 30 Rental Class 20 35 30 40 Type I rooms do not have high speed Internet access and are not available for the Business rental class Round Tree s management makes a forecast of the demand by rental class for each night in the future A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class The demand forecast for a particular night is 160 rentals in the Super Saver class 60 rentals in the Deluxe class and 50 rentals in the Business class Round Tree has 100 Type I rooms and 120 Type II rooms a Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types Is the demand by any rental class not satisfied Explain If demand materializes as forecast there will be rooms not reserved in th Select Super Saver Deluxe Business b How many reservations can be accommodated in each rental class Super Saver Deluxe Business ss

1a If there exist any solutions find the all solutions of the following congruences i x 2x 35 0 mod 27 ii x ux 44 0 mod 49 b Investigate the solututions of the following congruences If there are any solutions or not i x 461 mod 773 ii x 219 Mod 383

5 A rectangular town has an area of 900 miles In the town the reservoirs and ponds have an area of 224 miles If the total number of people living in the town is 6 513 determine the population density ppl mi ppl a 7 2 b 9 6 29 1 c d 0 1 mi2 ppl mi2 ppl mi

2 Two square towns with the given populations are shown below surrounded by water Which of the two towns has a greater population density 20 000 4 miles 35 000 7 miles

6 Jan wants to move to one of the towns below He wants to live in the one that has less people around him Which town should he move to Why 18 000 6 miles 24 000 8 miles

Consider the following function Step 1 of 2 Identify the general shape of the graph of this function Answer 8 x 2 3 X L Ay 66666666 Ay x

3 The mass of the object above is 400 grams Determine the density of the object 7 in 2 3 in

O Determine which figure has the greater density 9 cm 9 cm 6 cm 400 kilograms 3cm 10 cm 475 kilograms

4 SAT Question The system of equations below has solution x y What is the value of x a 3 b NIN 2 C 4 d 6 1 2Y 4 1 x 2y 2

1 SAT Question The density d of an object is found by dividing the mass m of the object by its volume V Which of the following equations give the mass m in terms of d and V a m dv b C d m DID m V d m V d

For f x 1 2 x 2 the slope of the graph of y f x is known to be 6 121 at the point with x coordinate 3 Find the equation of the tangent line at that point

Mei and Anju are sitting next to each other on different horses on a carousel Mer s horse is 3 meters from the center of the carousel Anju s horse is 2 meters from the center After one rotation of the carousel how many more meters traunlod than Aniu

Identify the values that make the proportion statement true 225555 22 29 21

professional cyclists burn a mean of less than 6900 calories during the annual Monaco Endurance Race This would be an improvement on the previously accepted value of 6900 calories In a sample of 13 randomly selected professional cyclists the sample mean number of calories the cyclists burn during the race is 6833 with a sample standard deviation of 773 calories Assume that the population of numbers of calories burned by professional cyclists during the race is approximately normally distributed Complete the parts below to perform a hypothesis test to see if there is enough evidence at the 0 05 level of significance to support that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6900 a State the null hypothesis H and the alternative hypothesis H that you would use for the test Ho 0 11 0 The value of the test statistic is given by 1 Jn Student s t Distribution Step 1 Enter the number of degrees of freedom Step 2 Select one tailed or two tailed O One tailed O Two tailed 10 05 is the value that cuts off an area of 0 05 in the right tail Step 3 Enter the critical value s Round to 3 decimal places b Perform a hypothesis test The test statistic has a distribution so the test is a test Here is some other information to help you with your test Step 4 Enter the test statistic Round to 3 decimal places 0 4 03 Since the value of the test statistic lies in the rejection region the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6900 0 2 BE Since the value of the test statistic lies in the rejection region the null hypothesis is rejected So there is enough evidence to support the claim that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6900 H Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is rejected So there is enough evidence to support the claim that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6900 O 0 Osa Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is not rejected So there is not enough evidence to X 0 020 0 0 0 0 X X c Based on your answer to part b choose what can be concluded at the 0 05 level of significance about the claim made by the sports science group O S X 2 A M

ationships ework 2 If a 1479 what is the value of b Show work and name the angle relationship a 4 If COB measures 104 determine the value of BOD DOA and COA

Angle 1 Ifa 38 what is the value of b Show work and name the angle relations I Complementary Angle 3 a 380 3 If AED mea measure of relationsh

Mason is building a 3 D model of a house for a project His model consists of a triangular prism on top of a rectangular prism as shown in the diagram 5 in 8 in 14 in Which measurement best represents the total volume of Mason s model house in cubic inches Answer A 1 218 in 3 3 B 1 323 in 9 in C 1 638 in 3 D 5 040 in 3 X X X

Consider AXYZ in the figure below The perpendicular bisectors of its sides are TS US and VS They meet at a single point S In other words S is the circumcenter of AXYZ Suppose VS 66 YZ 82 and ZS 110 Find XS UZ and VY Note that the figure is not drawn to scale X VO Y S T DU Z XS UZ VY X A 0 U

Which polygon is a concave octagon

2 Evaluate sin 240

Consider ADEF in the figure below The perpendicular bisectors of its sides are XW YW and ZW They meet at a single point W In other words W is the circumcenter of ADEF Suppose YW 42 DZ 62 and FW 70 Find EY DW and DE Note that the figure is not drawn to scale Y W Z X E D F EY DW DE 0 X

The regular hexagon has a radius of 4 in 4 in What is the approximate area of the hexagon O 24 in Q 42 in O 48 in O 84 in

In the regular nonagon shown what is the measure of angle x O 36 O 40 O 45 60

The area of the regular pentagon is 6 9 cm 1 38 cm What is the perimeter O2 cm 5 cm 10 cm 20 cm

T A 70 O 100 C B The image shows a quadrilateral inscribed in a circle Select all true statements Select all that apply The arc from Bto D passing through Cmeasures 70 degrees The arc from A to Cpassing through I measures 200 degrees Angle BCD measures 140 degrees The sum of the measures of the arcs from Ato C one passing through B and the other passing through D is 350 degrees Angle CDA measures 80 degrees Angle CDA measures 100 degrees

An equilateral triangle has an apothem measuring 2 16 cm and a perimeter of 22 45 cm 2 16 cm What is the area of the equilateral triangle rounded to the nearest tenth O2 7 cm O 4 1 cm O 16 2 cm O24 2 cm

A section of a rectangle is shaded The area of the shaded section is 63 square u What is the value of x O9 units O 11 units 18 units 21 units

Consider quadrilateral JKLM below 17 6 54 L K

133 D 102 170 117 F E What is the measure of ZB2 O 98 O 108 O 118 O 128

A regular pentagon is shown 10 cm What is the measure of the radius c rounded to the nearest hundredth Use an appropriate trigonometric ratio to solve O 5 88 cm 08 09 cm O 12 36 cm O 17 01 cm

B Figure ABCD is a parallelogram Two trapezoids are created using line segment XY such that AX CY What is true about the areas of the trapezoids O Each area is equal to half of the area of ABCD The area of AXYD is less than the area of BXYC O O The area of AXYD is greater than the area of BXYC Each area is equal to the area of ABCD

in K buto N 2 H 3 2 G 5 1974 C4 B A 5 6 X How does the area of triangle ABC compare to the area of parallelogram GHJK O The area of AABC is 2 square units greater than the area of parallelogram GHJK O The area of AABC is 1 square unit greater than the area of parallelogram GHJK O The area of AABC is equal to the area of parallelogram GHJK O The area of AABC is 1 square unit less than the area of parallelogram GHJK

In the rectangle below AE 4x 7 CE 6x 1 and mZEDC 54 Find BD and m ZEAD A D E B C BD mZEAD 00

3 QUESTIONS ON THIS SLIDE Several different cheeses are for sale The cheese comes in wedges shaped like sectors of a circle All of the wedges are the same height 1 Mai bought a wedge with a central angle of 45 degrees and radius 10 centimeters What is the area of the top surface of this wedge

R 12 L 81 age shows 2 circles The circle with center B is a dilation of the circle with center Ausing scale factor 2 Select all true statements Select all that apply The circumference of the circle centered at Bis greater than the circumference of the circle centered at Aby a factor of 2 The ratio is greater than the ratio by a factor of 2 The value of Bis greater than the value of a by a factor of 2 The angle marked a measures radians The angle marked B measures In 811 radians