2D Geometry Questions and Answers

3 In the accompanying diagram of the circle below SW 6x WQ Determine the value of x 12x PW Fu R 9 and WR 8 2 4 12x 2

equation that is perpendicular to y 2x 3 and passes through the point 5 3 6 A1 Spiral Write an

5 SAT Question Equivalent Expressions Which of the following is equivalent to 12x a b C 1 8x 3x 4 2x 3x 1 2x 3x d 1

are 5 and 2 7 8 04 Review Find the hypotenuse of a right triangle when the legs

x Let x y be defined as follows x y 2xy 2 y x If a b 0 and b 0 which statement COULD be true x X X A X B 5 of 10 X D E a 5 b 1 5 C a 1 b 1 a 2 b 1 13 50 a 0 b 1 a 3 b 3

2 In circle G above mzJ 2x 18 and mIH x 63 Determine the mZHGI H O

2 In the diagram above diameter AB bisects chord CD at point E in circle F If AE 5 and FB 10 determine the length of CE in simplest radical form E F

wor 1 In the circle below FC 10 FB x 10 EF 6 and DF 5x a What is the value of x LU HOLL b Which segment above is the greatest in length a FB b FC A m Diagram is not drawn to scale

4 In the diagram YOU DO ROUND 2 3 In the accompanying diagram of circle O chord CD bisects chord AB at E CE 2 and AB Determine the length of ED A E 0 B

6 In the diagram above DF AF DE is a diameter that bisects CB at F If the circles area is 144 ne length of CB in simplest radical form D A LL F B

8 Find the length of TV T C 14 7 6 A S x 12 V

5 In the diagram above of circle 0 chord AB bisects chord CD at E If AE of CE in simplest radical form 8 and BE 9 find the lengur B EU

1 In circle A shown DF 8 EF 9 BF x 17 and CF x 15 Determine the le 13 beskra A F E

find the exact value of sin 2a 8 if a sin 3 and tan Please show your work Do not waste your time inputting the 32

Tues 4 25 Assignment Surface Area Find the Total Surface area of the cylinder 15 cm 4 cm Prisms Cy

A 82 O O sin 82 34 sin 82 34 sin 82 34 sin 82 27 F sin B 27 sin C 27 sin B 82 sin B 34 27 34 B

1 Part 0 5 Part 1 of 5 2 An equation of an ellipse is given a Identify the center of the ellipse b Identify the vertices c Identify the endpoints of the minor axis d Identify the foci e Graph the ellipse Express numbers in exact simplest form x 2 3 25 16 3 1 4

Question 30 2 points Identify the inequality that represents the graph O 3 2 y x X y x 3 2 3 45 2 3 5

Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long Round to the nearest whole degree 36 54 46 44

Find the surface area of the pyramid hint you must find the slant height first 20 ft 30 ft 30 ft ft 2

What is the total surface area of the cylinder to the nearest square inch 9 in 14 in in

Find the surface area of the following cone OOO C A 9 7 km C 13 2 km OA OB O C UD 32 km 1 km B 6 5 km D 15 3 km

4 cm 5 cm 3 cm The surface area is

Find the surface area of the cone hint you must find the slant height first Round to the nearest hundredth 9 mm 20 mm mm

Which pairs of rectangles are similar polygons Select each correct answer 0 0 40 m 13 m 15 m 5 m 8m 5 2 m 3 m 2 5 m O 1225 m 18 m 144 m 6m 3 5 m 4 5 m 1 2 m 1 5 m

Trigonometric Ratios For Exercises 1 3 find sin A cos A and tan A 9 1 2 C X45 4 Hap OPP X F 7 375 48 5 12 For Exercises 4 9 find the value of x Round to the nearest tenth 5 sin 45 W sin 35 odj B W X 5 5 W 5 5 sin 45 5 5 W X 5 5 sin 35 7 8 A 8 9 6 10 Skylar drew two triangles that share a side and labeled the two portions of the base w and x Then he solved for w and x as shown Are his calculations correct Explain 11 X 4 6 5 23 45 10 A OB 3 X 1 8 11 A wire makes a 70 angle with the ground and is attached to the top of a 50 ft antenna How long is the wire Round to the nearest foot 6 9 25 5 5 B W 60 70 8 54 47 45 B 35 x 50 ft

A patrol car is parked 30 feet from a long warehouse see figure The revolving light on top of the car turns at a rate of 34 revolutions minute How fast is the light beam moving in ft sec along the wall when the beam makes angles of 0 30 0 60 and 0 75 wi the line perpendicular from the light to the wall a 30 b 60 0 y ft ft sec ft sec c 0 75 Round your answer to two decimal places

atic aph each quadratic inequality Find the missing coordinates Ay x 6x 3 2 y x 3 x 5 vertex y int 0 41 point 5 0 7 6 5 4 3 2 1 1 2 3 5 6 0 1 2 x intercepts 0 0 vertex y int 0 point 2 7 6 5 3 2 1 0 6 5 4 3 2 1 2 1 2 3 3 y 2 x 2 6 vertex 2 6 y intercept 0 Circle each point that is a solution to the given system of inequalities and cross off those that are not 5 TERE 6 39 4 132 2 2 1 0 6 5 4 3 2 1 1234 0 1 2 3

The cross section of a nuclear power plant s cooling tower is in the shape of a hyperbola Suppose the tower has a base diameter of 162 meters and the diameter at its narrowest point 40 meters above the ground is 54 meters If the diameter at the top of the tower is 108 meters how tall is the tower

ven that f x sin x g x cos x h x tan x F x csc x G x sec x and H x cotx Find f 135 What point is on the graph of f Find G 135 What point is on the graph of G Find h 135 What point is on the graph of h

How many rectangles can you make that will fit on a 4 x 4 geoboard such that none of them are congruer 8 X rectangles

Plot the point whose coordinates are 3 0 5 Select one Oa O b 4 t A O C Od

etermine the directrix of the conic with polar form the directrix is x 1 3 3 cose

ch of the following is not a polar equation of a cc ect one a b C r 1 1 sin Oe r 1 2 cos r 3 d 1 1 2 cos 0 r 1 2 cos 0

A lamp has the shape of a parabola when viewed from the side The lamp is 24 centimeters wide and 18 centimeters deep How far is the light source from the bottom of the lamp if the light source is placed at the focus 24 cm 4 cm 18 cm Light source 18 cm 12 18 24 cm 0 0 cm 12 18

Set up the form for the partial fraction decomposition Do not solve for A B C and so on 4x 14 x 8 3x 4 010

onstruct a simple graph with vertices T U V W X Y whose degrees are 2 2 1 1 2 2 That is the edge set

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

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

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

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

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 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

Write sin 49 in terms of cosine sin 49 COS O

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