Geometry Questions

5 In the diagram below MNPQ is a parallelogram whose diagonals are perpendicular Prove MNPQ is a rhombus M Q R N P

Given that CDEF is a trapezoid with CD FE list all pairs of supplementary angles C

Weights in grams of apples are normally distributed with a mean weight of 110 and a standard deviation of 5 5 grams An apple is selected at random Which has the greatest probability Select one a The apple weighs less than 75 grams b The apple weights between 95 and 100 grams c The apple weighs between 115 and 120 grams d The apple weights greater than 150 grams

The faces of a normal die are numbered from one to six Three such dice are used in an experiment The first one is thrown and the number shown on the top face is a five The second and third dice are then thrown Calculate as a fraction the probability that All three numbers shown are odd Select one a 2 3 b 1 2 Oc 1 6 d 1 4

Complete the equations which represent the relationship between polar and rectangular coordinates r sin tan x y Choose Choose Choose r 2 xr V 4

Rewrite the vector components using the unit vector form 7 13 3 U 13 3

6 Quadrilateral ABCD has vertices at A 0 6 B 4 1 C 4 0 and D 8 7 Prove that a ABCD is a rhombus using the distance formula b The diagonals of ABCD are perpendicular a

3 An isosceles triangle ABC has legs of length 24 and a vertex angle that measures 36 Determine the length of its base BC to the nearest tenth A 24 36 24

If 7 points are found on a circle how many triangles can be drawn using any 3 of these points as vertices Select one a 210 b 44 C 35 Od 38

Given the polar equation r 1 5sing Select one O a x 24y 30y 9 0 O b x 26y2 15y 9 0 Oc 24y x 15y 9 0 d None of these which is the rectangular equation

Graph the circle x2 y2 2x 8y 19 0 Ty Select one a 5 Ob 10 10 10 10 x

A rope is used to support a flag pole The rope is attached to the top of the 42 ft pole and attached to the ground 15 1 ft from the base of the pole How long is the rope Select one a 140 6 ft O b 44 6 ft OC 49 6 ft d 33 6 ft

If a 5 4 and ka 30 24 then k 9 8 7 6 5

A lighthouse is 46 m in height A boat s captain determines that the angle of elevation from his boat to the top of the lighthouse is 19 How far is the boat from the lighthouse Select one a 119 m b 145 m c 134 m d 186 m

A sailor is sailing around three islands She travels 2 6 km from Island A to Island B She then turns 55 and travels 2 9 km to island C How long is the last leg of the trip from Island C to Island A Select one a 1 3 km b 2 6 km OC 8 5 km d 2 9 km

Use your calculator to find the measure of the angle to the nearest degree tan 9 1

6 In trapezoid ABCD shown below AB DC BC LDC and sides have lengths as shown a Determine the measure of ZD to the nearest degree b Find the length of AD in simplest radical form D A 7 in 5 in B 3 in C

A boy who is 5 feet 6 inches tall casts a shadow that is 8 feet and 3 inches long What is the measure of the angle of elevation of the sun A as shown in the picture Round to the nearest degree Be careful with your units in this problem

How far from the base of a building must the bottom of a 15 foot ladder sit for it to make a 52 angle with the ground Round to the nearest tenth of a foot 15 ft bo

5 A person sights a boat from 235 feet above sea level as shown If the angle of depression from the man to the boat is 21 then determine the boat s distance to the edge of the cliff to the nearest ten feet 235 ft 21

A long wire is attached to the top of a 175 foot tall electrical transmission tower If the wire needs an angle of 65 with the ground then how long must it be Round your answer to the nearest foot feet 65 make 175 feet person sights a boat from 235 feet above sea level as shown If the angle of depression from the man to boat is 21 then determine the boat s distance to the edge of the cliff to the nearest ten feet

Verify the identity Simplify at each step 9 cos x 9 sin x 9 cos 2x x 9 cos x 9 sin x 9 cos x sin x 9 cast 1 sin x

Consider the angle shown below whose vertex is at 2 2 5 A circle with a radius 1 7 units long is centered at the vertex of the angle and the terminal point at 3 4 3 46 9 Preview 4 3 4 3 46 F 2 2 5 3 2 Y a The terminal point is how many units to the right of the center of the circle units Preview b The terminal point is how many radit to the right of the center of the circle radi Preview c Therefore the radian measure of the angle is 3 5 I

gra Hint Graph the vectors on graph paper then draw the resultant vector Select one a b Vectors choose the image which best represents the difference of u v

Given a 61 43 4k and b 3i xj 9k find x when a b 2

The figure below shows quadrilateral ABCD and a line of reflection A B C R 9 x y 8 7 6 5 4 3 2 B x y C 4 5 6 7 Determine the coordinates of A B C and D using only reasoning that is without folding x y 1 2 3 D 1000 00 8 T 9

Given the vector 6 12 6 12 1 with a directional angle of

17 Solve for the surface area and volume of the composite figure made of a right cone and hemisphere half sphere 15 points 10 in 13 in

Given a vector begins at 3 and ends at 2 1 then the components of the vector are 4

formation is given about AABC Determine if the information gives one triangle two triangles or no triangle Solve the resulting triangle s Round the ngths of sides and measures of the angles to 1 decimal place if necessary c 12 b 5 B 38 There is no triangle that can be formed from the given information O There is one unique triangle that can be formed from the given information A a O There are two triangles that can be formed from the given information Triangle 1 S E

Solve the triangle For the sides give an expression for the exact value of the length in terms of sine and approximate to I decimal place Part 1 of 3 A B 64 Part 1 3 Part 2 of 3 Skin Part Check b 71 118 6 sin cos 97 4 a 00 B Save For Show Transcribed Text

Given the information a vector has length 8 with South direction it would be drawn from the the point 0 6 the origin anypoint and extend

i 8j 4w 6i 3j 3w I i 7 6 5 4 3 W

0 This is a vector wit 2 03 magnitude direction

each circle 2 2 1 x 1 y 3 2 2 3 x 1 y 4 2 x 2 y 1 16 2 4 x y 3 25 4 9

6 x 1 y 3 4 y 6 5 4 3 2 1 6 5 4 3 2 1 11 2 31 0 45 6 6 5 4 3 2 1 4 7 x 2 y 1 16 y 6 5 4 3 2 1 6 5 4 3 21 1 0 11 2 3 4 5 6 8 x 1 y 4 9 y 6 5 4 3 2 1 0 N F1 2 6 5 4 3 2 1 31 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 9 x y 3 25 ya 0 1 2 3 4 5 6 1 1 2 3 4 5 6 X A 1 2 3 4 5 6 X

2 Diameter of 12 3 Diameter of 22 For problems 4 10 write the equation of the given circle 4 Center 12 7 Radius 4 5 Center 2 14 Radius 5 6 Center 12 10 Radius 7 7 Center 6 4 Radius 8 8 Center 3 13 Diameter 2 9 Center 1 3 Diameter 8

problems 8 10 Leave your answers in terms of pi 240 14 in 315 19 12 16 ft 12 ft

with a diameter of 14 inches 3 A sector that is two thirds the area of a circle with a radius of 10 yards For problems 4 7 find the area of each sector Write your answer as a decimal rounded to the nearest tenth 4 5 6 60 10 in 3 m 150 3x 4 cm

Find the value of the variable 24 A X D B Answer T 40 13 Find the value of the variable S C

the standard equation of the circle in the graph Center 4 0 4 5 et one a x 4 2 y2 25 0 x y 25 C x 4 2 y2 25 d x y 16 e the standard equation of the circle in the graph 2 1 4 1

of the following statements is false one Every chord is part of a secant Every diameter is part of a secant Every diameter is a chord Every chord is a diameter the standard equation of the circle in the graph one 012 o 212 19

Which is the equation of a circle with center 2 3 and radius r 5 Select one O a x 2 2 y 3 25 b x 2 2 y 3 25 c x 2 y 3 10 d x 2 2 y 3 10 Which is the equation of a circle with diameter AB where A 5 4 and B 1 4 Select one a x 5 2 y 4 10 b x 5 y 4 100 c x 2 2 y2 25 d x 2 y 5

arc Leave your answers in terms of pi 8 9 315 150 3r 8 cm 19 ft 13 ft

2 Find the distance around one fifth of a circle with diameter of 14 inches 3 Find the distance around five sixths of a circle with diameter of 20 yards For problems 4 7 find the length of the darkened arc Round your answers to the nearest tenth 4 5 6 11 ft 315 270 3x 13 ft 16 ft

the figure below what is m C D B elect one a 50 b 15 c 35 30 d 65 N d 7 5 the figure below what is the value of z 4 elect one a 2 9 Ob 8 75 c 5 6 E 100

Which of the following is the graph of x 2 2 y 1 9 elect one a b C d Lify FRE 2 O

What is the equation of the circle with center 0 0 that passes through the point 8 3 Select one a x y 73 b x y 55 c x 8 2 y 3 55 d x 3 y 3 73 Check

degrees the measure of arc FH is 138 degrees and the measure of arc HB is 20 degrees Find the measure of FPD 3 points P B E 9 In the diagram below the measure of arc SQ is 106 degrees and the measure of arc PR is 120 degrees Find the value of x 3 points

X 6 X 4 12 12 Find the value of x 3 points S x 5 N x 8 M K 4