Geometry Questions

valuate r v w 0 2 0 1 5 2 2 4 4 w 2011 10 RAMMERI ANT

Type the equation of the given graph in the form y Asin Bx or y Acos x 0 Type an equation Use integers or fractions for any numbers in the equation 4

equations x x x x t y y y y t where 0 st s 1 describe the line segment that joins the points P x Y and P x Y Use a graphing calculator or computer to draw the triangle with vertices A 1 1 B 5 4 C 1 6 Find the parametrization including endpoints and sketch to check Enter your answers as a comma separated list of equations Let x and y be in terms of t F AB BC

A ship leaves Port A and travels 73 km due west to Buoy C It then adjusts its course 66 northward It travels 123 km in that direction until it reaches Port B What angle with respect to due west could the ship have used to travel directly from Port A to Port 82 See the figure below The figure is not drawn to scale Port B 123 km 66 Buoy C 23 km Port A Carry your intermediate computations to at least four decimal places Round your answer to the nearest tenth of a degres

You are on a fishing boat that leaves its pier and heads east After traveling for 25 miles there is a report warning of rough seas directly south The captain turns the boat and follows a bearing of S35 W for 14 2 miles a At this time how far are you from the boat s pier b What bearing could the boat have onginally taken to arrive at this spot 142 MA

For the function f x 3 sinx 1 give the ampl midline vertical shift and graph the function Your graph should show at least one period with 5 accurately plotted points 3 Amplitude Period Horizontal shift Midline Graph Tr Lo 2111 20

Test the claim about the difference between two population means and 2 at the level of significance a Assume the samples are random and independent and the populations are normally distributed Claim 0 01 Population statistics 3 2 0 1 7 Sample statistics x 14 n 30 X 16 n 27 Ha H1 H Determine the standardized test statistic Z Round to two decimal places as needed Determine the P value P value Round to four decimal places as needed What is the proper decision OA Fail to reject Ho There is enough evidence at the 1 level of significance to reject the claim OB Reject Ho There is not enough evidence at the 1 level of significance to reject the claim OC Reject Ho There is enough evidence at the 1 level of significance to reject the claim OD Fail to reject Ho There is not enough evidence at the 1 level of significance to reject the claim

A tower that is 175 feet tall casts a shadow 151 feet long Find the angle of elevation of the sun to the nearest degree 151 ft 175 ft The sun s angle of elevation is Do not round until the final answer Then round to the nearest whole number

5 5 ft 74 10 ft feet zearn Richland School Di Find the height of the top of the goal post rounded to the nearest tenth of a foot

C 16 O O A 108 sin 108 40 sin 108 16 sin 108 40 sin 108 40 sin B 16 sin B 32 sin C 16 sin C 108 40 B

To calculate the cost of painting his silo a farmer must find its height The farmer uses a cardboard square to line up the top and bottom of the silo as shown in the diagram below Approximate the height of the silo DR

The vertices of AABC represent the buoy markers that form the legs of the course for a swim race What is the distance from marker C to marker A Round your answer to the nearest tenth of a meter 60 O 130 5 m O 148 4 m O 175 9 m O 269 5 m 200 m 40 B

In order to meet ADA Americans with Disabilities Act requirements a wheelchair ramp must have an angle of elevation of no more than 4 8 A builder needs to install a ramp to reach a door that is 2 5 feet off the ground 11 Is 20 feet long enough for the straight line distance of the ramp to meet the requirements What angle of elevation will this ramp have A 20 foot ramp will have an angle of elevation of approximately

You hike 210 meters up a steep hill that has a 31 angle of elevation as shown in the diagram A 210 m 31 b B a C Give each side and angle measure rounded to the nearest whole number a mZB III

3 7 01 You are planting a garden in the shape of an equilateral triangle as shown in the diagram You want to find the area of the garden to determine how much topsoil you will need 60 6 ft 6 ft 30 6 ft 19 Substitute the values of b and h in the formula A 2 b 1 b h for the area of the garden

A roof has a cross section that is a right triangle The diagram shows the approximate dimensions of this cross section Find the height h of the roof Round your answer to the nearest tenth 20 ft The height of the roof is about 23 9 ft feet h 13 ft

35 cos M cos N sin M 37 sin N N 12 HIII 1 T 1 1 1 T

You are holding a kite string in your hand The angle of elevation from your hand to the kite is 53 and the distance to the kite is 300 feet Your hand is 4 feet above the ground How high is the kite Round your answer to the nearest tenth of a foot feet

A 25 foot ladder leans against a wall so that it is 20 feet high at the top The ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up How much higher is the top of the ladder now Hint L t 15 2x be the distance from the base of the ladder to the wall 2x Save Exit The top of the ladder is feet higher now L

An 80 foot rope from the top of a tree house to the ground forms a 45 angle of elevation from the ground How high is the top of the tree house Round your answer to the nearest tenth of a foot feet

Find the value of b Round your answer to the nearest tenth B 40 10 12 A

Find the area of AABC with side lengths b 9 and c 14 and included angle A 145 Round your answer to the nearest tenth The area of the triangle is about square units

24 6 27 Which of the following trigonometric ratios are correct 20 b X cos 20 cos 20 sin 20 Otan 20 Osin 20 a 1 X tan 20 b X X X b a X X b a

Write sin 49 in terms of cosine sin 49 COS O

Classify a triangle with each set of side lengths as acute right Acute or obtuse Right Obtuse

Find the exact value of x X 10 X 6

6 AB is tangent to circles P and Q below If AP 5 AZ x 4 BZ x and BQ 3 Determine the length of PZ in simplest radical form 5 N B

1 AE is tangent to circles D and C If EB x 8 DE 8 AB 6 and AC x a Find DB in simplest radical form b Find the length CB E B

5 In the diagram above AC and AD are tangent to circle B at points C and D respectively If CB 4 and AE 8 determine the length of AC in simplest radical form A E B

4 In the figure d e and fare parallel lines What is the value of x x 20 70

3 8 04 Review A right triangle has one leg that double the length of the other If the hypotenuse is 5 what is the length of each leg

3 In the figure c d What are the measures of 21 and 22 1 2 4 3 5 75 8 7

4 SAT Question Equivalent Expressions Which of the following is equivalent to 3x4 3 a 3 x 1 b 3 x 1 c 3 x 1 x 1 d 3 x 1 x 1 x 1

2 In the accompanying diagram BA is tangent to circle O at A Radii OA and OC are drawn and OC is 2 determine and state the length of AB extended to intersect at BA at B If AO 3 and BC C B

Find the perimeter and area of the figure The perimeter is 66 ft Simplify your answer Type an integer or a decimal The area is Simplify your answer Tyne an integer or a decimal 16 ft 1 1 5 ft 12 ft 12 ft

17 Find the geometric mean of 6 and 48 Solve for x 18 20 24 x 18 20 30 30 X Solut 19 21 3 200 18 24 X V 15 late 17 18 19 20 21 stoc brif barutosta gofapt lonke l euapomn nosta

Determine whether the triangle with the given side lengths is acute right obtuse or not a triangle 8 3 9 10 9 6 12 19 10 21 28 35 Not a A Acute Right Obtuse Not a A Acute Right Obtuse Not a A Acute Right Obtuse Gina Wilson All Things Algebra LLC 2014 2018

Which solid figure is represented by this globe x x X A cylinder B cube C C cone sphere

Solve for x 1 19 3 30 33 X 16 2 4 X 16 5 22 9 2 25 16 1 2 3 4 5 6 7

Organizers of an outdoor concert will use 320 feet of fencing to fence off a rectangular VIP section What is the maximum area that they can fence off 4x X A 6 400 square feet B C 12 800 square feet E 25 600 square feet D 24 000 square feet 3 200 square feet

During strenuous work a human body generates about 2 400 BTUs of body heat per hour If 6 football players are in a gym that is 12 ft x 18 ft 10 ft lifting weights how many BTUs per cubic foot do they produce in 2 hours to the nearest tenth A B C 133 3 BTUs ft3 13 3 BTUs ft3 66 7 BTUs ft3

A rectangular corn field yielded 2 200 000 ears of corn The dimensions of the corn field are 800 yards by 550 yards How many ears of corn per square yard did the corn field yield x x A 25 per square yard B C 10 per square yard 5 per square yard D 50 per square yard

Which solid figure is represented by this soup can x A cone B rectangular prism C cube D cylinder Mer ar Roth Thank Me QUALITY

x Po has a frame that is 9 in x 8 in What is the maximum area the picture can have to fit in the frame A 72 sq in B 81 sq in C 63 sq in D 9 in 96 sq in 8 in

Which solid figure is represented by this globe X 1x A cylinder B cube C cone D sphere G G G

To indirectly measure the distance across a lake Lauren makes use of a couple landmarks at points L and M She measures KO OM and NO as marked Find the distance across the lake LM rounding your answer to the nearest hundredth of a meter M L 95 m Diagram is not to scale 109 5 m 125 m K HANDM

Express your answer to the nearest tenth of a foot Enter your answer in the box 42 8 Part D A In the future Luke has plans to construct a circular storage bin centered at coordinates 50 40 on the plan Which of the listed measurements could be the diameter of a bin that will fit on the plot and be at least 2 feet away from the warehouse Select all that apply 10 feet B D 15 feet 18 feet 22 feet feet 25 feet U139 30 20 0 UT 11 20 2 U121 400 U521 and or 42 8

4 A manufacturer is designing a new container for their chocolate covered almonds Their original container was a cylinder with a height of 18 cm and a diameter of 14 cm The new container can be modeled by a rectangular prism with a square base and will contain the same amount of chocolate covered almonds Chocolate Covered Almonds 14 cm If the new container s height is 16 cm determine and state to the nearest tenth of a centimeter the side length of the new container if both containers contain the same amount of almonds 18 cm Chocolate Covered Almonds A store owner who sells the chocolate covered almonds displays them on a shelf whose dimensions are 80 cm long and 60 cm wide The shelf can only hold one layer of new containers when each new container sits on its square base Determine and state the maximum number of new containers the store owner can fit on the shelf

2 The town of Manchester population 50 000 has the shape of a rectangle that is 5 miles wide and 7 miles long Part A What is the population density in people per square mile in Manchester Round your answer to the nearest whole number of people per square mile Part B The town of Manchester contains a business area in the center of town that has the shape of a disk with a radius of 1 mile If no one resides in the business area what is the population density in Manchester in people per square mile outside of the business area Round your answer to the nearest whole number of people per square mile

5 A scale drawing of Corinne s bedroom floor is shown below All given dimensions are in feet All intersecting line segments shown are perpendicular Corrine wants to completely cover the floor with square hardwood tiles Each tile has a side length of 1 foot and no tiles will be cut How many tiles will Corinne need to cover the floor 5 69 63 C 79 84 11 6 9