Geometry Questions

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

2 Kiran bought a wedge with a central angle radians and radius 3 inches What is the area top surface of this wedge

HO A circle has a radius of 20 ce angle that measures 216 dec the arc defined by this centra Write your final answer in tem Keep n as a symbol in the a

Construct the circumscribed circle for triangle ABC Show explain your reasoning A

B 57 A C BL is tangent to the circle centered at A Find the measure of angle BCA Explain or show your reasoning

O B 50 A a circle centered at point O Angle AOBmeasures 50 degrees What is the measure of angle ACB 25 degrees 40 degrees 50 degrees 100 degrees

In the rectangle below AE 2x 1 BD 3x 7 and mZEBC 27 Find CE and m ZAED A D B C CE m AED

15 The graph shows a transformation of the function f x sin x 30 35 20 5 0 5 B y 25 sin y 50 sin 15 10 If g x represents the transformed function what is the correct equation for g x A y 25 sin 2 10 7 5 y 50 sin 5 10 15 30 10

te the density of a 3D figure any final answer ALL WORK must be shown in order to receive full credit Directions Complete the following questions by showing all work and annotations Keep work residents and the shaded region represents the surrounding water what is the population density of the village 1 The below shape represents a rectangular town with a width b of 6 miles If the circular village has 1 275 in person per square mile a 45 1 b 0 02 C 11 3 d 67 6 b a

2 The town Roundaway NJ can be modeled with a circle with a diameter of 50 miles has a popul 25 504 Blockhead NJ can be modeled with a square with a length of 40 miles has a population of 22 340 Determine which of the two towns has a greater population density

1 A company manufactures cylindrical containers that each have a volume of 6 cubic feet For a new container design the company plans to keep the same height for the container and double the radius V 6 ft

The medians of APQR are PT QU and RS They meet at a single point V In other words V is the centroid of APQR Suppose QV 10 RS 39 and VT 10 Find the following lengths Note that the figure is not drawn to scale A P S U Q T R PV 0 QU VS

The medians of AJKL are JN KP and LM They meet at a single point Q In other words Q is the centroid of AJKL Suppose KP 36 JQ 22 and LQ 16 Find the following lengths Note that the figure is not drawn to scale M P K 10 N JN QM QP 8 08 X

Which of the following sets of angles are not congruent Linear Pair Alternate Exterior Vertical Alternate Interior

10 1 point 2nd base Pacher s mound 90 2 feet 90 3 feet 180 feet 1ot base Foul Bre X Home plato A baseball diamond is actually a square with side lengths of 90 feet In a game a runner tries to steal second base How far must the catcher throw from home plate to secon base in order to get the runner out 90 feet

Fill in the blank 7 95 107 106

Which of the following constructions must you know how to do in order to construct a circumscribed circle for a given triangle duplicating a line segment inscribed quadrilateral perpendicular bisector angle bisector

P B 2 3 P ANB 1 6 What will P A have to be for A and B to be independent GORY 5 6 1 2 1 4 11 12