2D Geometry Questions and Answers

mplify the following log 2 x log 2 x 4 elect one a log x b c d 4 log2x 8 log 2x 2log 2x

the following graph of a function modeling damped harmonic motion Find the equation for the function pictured in terms of y and 1 Assume that a factor of e provides the desired damping effect and that the graph has no vertical or horizontal shifts 4 2 2 Enable Zoom Pan t

onvert the following to logarithm form 4 16 lect one a log 42 16 b log 2 16 4 O c log 4 16 2 O d log 16 4 2

Find a 8 of a geometric sequence if the first few terms of the sequence are given by 1 3 9 27 Select one O a 2 187 O b 7 880 OC 1 934 O d 3 405

What operation s would you perform on the longer leg across from the 60 degree angle of a 30 60 90 triangle to get the length of the hypotenuse Divide by 2 multiply by 2 Multiply by 2 Divide by 3 multiply by 2 Divide by 2

1 point The sine of 72 degrees is 0 95 What s the cosine of 18 degrees 1 0 95 0 8 0 05

Step 1 of 2 Identify the shape of the more basic function that has been shifted reflected stretched or compressed Answer 3 Points MM MM Keyboard X

17 1 point B 1 Which construction is shown Rhombus Copy an Angle Perpendicular Bisector Perpendicular Through a Point C

Which of the following can only be used after you prove triangles are congruent Alternate Interior Angles CPCTC Substitution Reflexive

1 point Which of the following can be used in this picture with no additional information needed Vertical Angles CPCTC Substitution Alternate Interior Angles

6 5 ft Surface Area 13 ft 5 ft

6 1 point Given DF ER DH EG and DF ER Prove H is the midpoint of FG Statements DF EH DH EG 1 LDFHLEHG and LDHF LEGH ADFHAEHG Reasons Given Given 2 3 FH HG 4 H is the midpoint of FG 5 Which statement belongs in space number 3 AAS The triangles are not congruent HL ASA

8 1 point Which construction could this be Inscribed Equilateral Triangle Inscribed Star Inscribed Octagon Inscribed Square

Verify each identity 1 tan x tan x 4 COS X cos 2x sin xcsc x

18 1 point B This is the first step in which construction Inscribed Octagon Inscribed Triangle Inscribed Hexagon Inscribed Square

13 1 point M P Statements MObisects PN and ZP ZN PO ON N Given Prove MP NO Reasons 1 MObisects PN and P ZN 2 Vertical Angles 4 5 3 A MOP A QON MP NO Which choice belongs in space number 3 ZMPOZNQO LOMP LONQ PMO ONIO

1 point Which of the following can be used when two triangles share a side Reflexive Vertical Angles Alternate Interior Angles Substitution

O B C 1 4 1 3 B C D A D The distance from B to B is 6 and the distance from A to B is 2 What is the scale factor 3 4

Circle H has a radius of 9 inches in Points M and N are on the circle and form the sector MHN The central angle ZMHN in Circle H measures 115 Determine the area of the sector Express your answer in terms of and round to the nearest hundredth if needed

The area of a sector with a diameter of 12 feet ft is 62 8 square ft Calculate the approximate measure of the central angle of the sector in degrees

Consider these five data values 10 14 15 16 20 The mean is 15 0 and the Standard Deviation is 3 6 Now look at these values 10 11 15 19 20 Without doing any calculations what will happen to the standard deviation even though the mean is still the s Select one a The SD will be smaller because 11 and 19 are farther from the mean than 14 and 16 were b The SD will be smaller because the new values effect the range c The SD will be larger because the new values are close to each other d The SD will be larger because 11 and 19 are father from the mean than 14 and 16 were

Johnny was fishing Bass and caught these 5 fish Fish lengths 4 6 7 8 10 The mean is 7 0 based on his catches he calculates an estimated Standard deviation called the Sample Standard Deviation Remember to use Bessel s Correction

Scores on a test are normally distributed with a mean of 200 and a standard deviation of 12 Find the probability a randomly selected student scored less than 218 Select one a 0 75 b 0 90 C 0 45 d 0 93 If the average salary of a computer programmer is 71 800 with a standard deviation of 13 000 approximately 97 800 of the programmers make over

The mean always has a z score value

4 The smaller cone is removed from the larger cone Determine the volume of the figure to the nearest tenth 3 6 12 8 empl

5 Determine the volume of the composite figure Round to the nearest tenth 5 mm 4 mm 2 mm last season att et barot sgil altamo s o lo employ

Y 4 C Figure ABCD is a parallelogram Points X and Y are placed so that BX DY and CDJ XY The area of BXYC is 71 5 square units What is the area of ABCD O 99 square units O 110 square units O 126 square units O 143 square units

2 Determine the volume of the composite figure Round to the ne 4m 3 m the 2m 451 637 in

What is the measure of each exterior angle of a regular hexagon 000 40 60 72

8 Calculate the volume of the 3D figure 12 in 13 in

Z Rhombus WXYZ is graphed on a coordinate plane What is the perimeter of the rhombus 16 units O 20 units O 24 units O 28 units

A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm 14 cm What is the approximate area of the hexagon O 224 cm O 336 cm O 448 cm O 672 cm

HOW 2 Determine the volume of a cone with a dia of 10 in and a height of 4 in Round to the nearest tenth Draw the figure first

3 Calculate the volume of a pyramid with a base area of 10cm and a height of 5cm

An interior angle of a regular polygon has a measure of 108 What type of polygon is it pentagon O hexagon O octagon O nonagon

Galina is finding the area of triangle RST To do so she follows the steps in the table Step Draw a rectangle around triangle RST Step Find the area of the rectangle 2 Step 3 Find the area of the three right triangles created by the sides of the rectangle and the intersection with each vertex of the triangle Step Subtract the area of the right triangles from the area of the rectangle To solve the problem using these steps what are the dimen ns of the rectangle she should draw R 5 3 2 5 4 3 2 1 24 3 5 S O2 units by 4 units 3 units by 4 units 19 F Funits T 3 4 5 X

Four interior angles of a pentagon measure 88 118 132 and 100 What is the measure of the fifth interior angle 82 O 92 O 102 O 112

A regular octagon has an apothem measuring 10 in and a perimeter of 66 3 in 10 in What is the area of the octagon rounded to the nearest square inch O88 in O 175 in O 332 in O 700 in

A square has an apothem measuring 2 5 cm and a perimeter of 20 cm What is the area of the square rounded to the nearest square centimeter O 13 cm O 25 cm O 50 cm O 100 cm

A regular hexagon is shown 12 in b C What is the measure of the radius c rounded to the nearest inch Use the appropriate trigonometric ratio to solve O 6 in O 10 in 14 in O24 in

The base of the right triangle drawn in the regular octagon measures 0 7 cm 1 9 cm 0 7 cm What is the perimeter of the octagon 11 2 cm 14 1 cm O 15 2 cm 20 8 cm

The area of the regular hexagon is 169 74 ft2 7 ft What is the perimeter rounded to the nearest tenth O 24 2 ft 28 3 ft O 48 5 ft O 56 8 ft

Bianca calculated the height of the equilateral triangle with side lengths of 10 tan 30 h 8 7 h A 30 Then she used the formula for area of a triangle to approximate its area as shown below bh 10 8 7 43 5 units2 5 Calculate the area of the equilateral triangle using the formula for area of a regular polygon and compare it to Bianca s answer The apothem rounded to the nearest tenth is units The perimeter of the equilateral triangle is Therefore the area of the equilateral triangle is or approximately 43 5 units V The calculated areas are units

Manuel wants to buy a window shade to cover the window and frame shown The window is in the shape of a regular octagon The radius of the window including the frame is 2 ft and the measure of each edge of the octagonal frame is 1 52 ft Window 1 52 ft What is the approximate area of the window that nee to be covered including the frame O2 ft O 7 ft O 11 2 ft O22 5 ft

A community pool that is shaped like a regular pentagon needs a new cover for the winter months The radius of the pool is 20 10 ft The pool is 23 62 ft on each side To the nearest square foot what is the area of the pool that needs to be covered O192 ft O 960 ft O 1 921 ft 3 842

A regular pentagon has an apothem measuring 3 cm and a perimeter of 21 8 cm 3 cm What is the area of the pentagon rounded to the nearest tenth O 13 8 cm O 17 3 cm O 32 7 cm O 69 0 cm

A hexagon has a radius measuring 23 cm What is the approximate area of the hexagon O 686 6 square cm O 793 5 square cm O 1374 4 square cm O 1587 0 square cm

A regular pentagon has a perimeter of 60 cm B A D What is the measure of angle CBD What is the length of segment CD cm Which trigonometric ratio can be used to compare Bo to CD using angle CBD What is the approximate length of BC cm What is the approximate length of BD GM

Probability and Counting 6 A fair die is rolled once Let A be the event of rolling a number less than 4 Let B be the event of rolling an even number A 4 1 Draw a Venn diagram 2 What is the probability of event A P A 3 What is the probability of event B P B 4 What is the probability of A and B P AnB 5 What is the probability of A or B P AUB

The floor of a gazebo is in the shape of a regular octagon The perimeter of the floor is 72 feet The distance from the center of the octagon to one of the vertices is 11 8 feet What is the approximate length of the apothem 3 feet What is the approximate area of the floor of the gazebo square feet 3