2D Geometry Questions and Answers

Questions 23 25 refer to the following information A team of scientists measures the volume of various samples of different gases with a constant pressure of 0 1 atm and a constant temperature of 610 K The graph below plots the volume of each sample against the amount of the gas 23 Volume liters 2 88 89 90 120 100 80 60 40 20 last0 Volume Amount Relationship Among Samples of Gases 0 5 1 1 5 Amount moles 2 Sample S 2 5 The Ideal Gas Law predicts that at this pressure and temperature the volume of an ideal gas can be modeled by the equation V 50n where V is the volume in liters and n is the amount of the substance measured in moles Assume that the relationship is valid for greater amounts of the substance than are shown in the graph A mole is approximately 6 022 102 molecules According to the data provided what is the volume in milliliters of Sample S A 8 104 B 2 x 10 C 8 x 10 D 4 x 10 There moles of vol A 25 B li

Question 8 1 point N M 14m L 21 82 26 9 80 43 64 10m K What is the length of segment LN

26 Let the polynomials fand g be defined by f x 3x 6x 11x and g x 8x 15x 7 Which of the following polynomials is divisible by 3x 7 A j x 2f x g x B k x f x g x C m x f x 2g x D n x f x 3g x

A car factory that operates 24 hours a day and 7 days a week produces one car every 20 minutes How many cars does the factory produce in 3 days

A scientist estimates that the water level of a lake is dropping by 2 25 inches per year If this trend continues how many years will it take for the wate level in the lake to drop by 27 inches

4a j 7a 3 4b k 7b 3 In the equations shown above j and k are constants jis k plus 1 which of the following is true 1 3 A a is b plus B a is b minus D 1 3 C a is b minus 1 a is b minus 3

P Q y R Given the right triangle PQR above which of the y following is equal to X A cos P B cos Q C tan P D tan Q

B A C D Group A Group B Total 21 38 4 50 Number of Times Watching the News per Week Never 3 4 Total 21 50 38 100 7 4 11 1 2 The table above shows the results of a survey in which 100 people were asked how often they watched the news Group A consisted of people who were registered voters and Group B consisted of people who were not registered to vote If one person is randomly chosen from among those who watch the news fewer than three times a week what is the probability that the person was a member of Group A 14 13 27 18 21 39 More than 4 11 12 23 50 50 100 in the graph A made in

2 Determine the value of DE and EF to the nearest SI bns 0 011 saunatagyd or al 3 algasin dgh to woln 3 C 70

STRETCH IT In triangle JKL below mzJ 58 2 and JK 5 4 What is the relationship between JK and the angle Adjacent Opposite or Hypotenuse J 18 biswau 2900 K

An airplane is on a heading of 075 at 250 km h and an 85 km h wind is blowing from 300 Determine the resultant velocity of the airplane using Cartesian vectors and state the groundspeed and bearing of the resultant

tch a graph from factored form include zeros and bounces bends crossing nts o x 2 x 6 x 4

1 Calculate the son of interior ongles of a heptagon 7 gon 3 Solve for x 5 2 regular 15 gon 4 Solve for x 1 5

A triangle is placed in a semicircle with a radius of 9 mm as shown below Find the area of the shaded region Do not round any intermediate steps Round your final answer to the nearest hundredth and be sure to include the correct unit If necessary refer to the list of geometry formulas 19 mm 0 mm Xx mm mm

O Points 0 of 1 Opomba is sitting on a sled on the side of a hill inclined at 30 The combined weight of Ojemba and the sled is 100 pounds What is the magnitude of the force required fir Mandisa teep the sk Miding down the hill SA

Justin is filling a container with unit cubes Each cube measures exactly 1 cubic inch He places the first 9 cubes on the bottom of the container as shown below 3 inches B 3 inches How many unit cubes in total must Justin use to fill the container C 3 inches D 9 unit cubes 36 unit cubes 18 unit cubes 1 cubic inch 27 unit cubes

The curves of the 2 functions are given as follows f x x 5x 6 g x 4 3x x a b c Determine the 2 interception points of the above curves Hint f x g x 10 marks Find the interception points of f x and g x on the x axis and y axis 12 marks 3 marks Sketch the curves

r Flanagan made a line plot to show the number of hours the 15 students in his class spent doing homework last night 5 O Number of Students Labu 0 5 Number of Students Number of Students Time Spent Doing Homework udents 0 xxxxxxxxx X 1 2 3 4 0 5 5 Number of Hours Time Spent Doing Homework XX 1 5 XXXXXXXX 2 3 4 5 5 5 Number of Hours x 1 5 XXXX Time Spent Doing Homework XXXXXXXXX x 2 3 4 5 5 Number of Hours 1 X 1 X 1 Time Spent Doing Homework of the students spent 5 of an hour doing homework Which line plot could be the one Mr Flanagan made

Which statement is TRUE about a unit cube O O O A C Its volume is equal to 1 unit plus 1 unit B Its volume is equal to 1 unit plus 1 unit plus 1 unit C Suspe Its volume is equal to 1 unit times 1 unit Its volume is equal to 1 unit times 1 unit times 1 unit

At the park there is a pool shaped like a circle A ring shaped path goes around the pool Its inner radius is 11 yd and its outer radius is 15 yd 11 yd 15 yo We are going to give a new layer of coating to the path If one gallon of coating can cover 6 yd how many gallons of coating do we need Note that coating comes only by the gallon so the number of gallons must be a whole number If necessary refer to the list of geometry formulas gallons of coating Espa ol Aa

A rotating light is located 19 feet from a wall The light completes one rotation every 3 seconds Find the rate at which the light projected onto the wall is moving along the wall when the light s angle is 10 degrees from perpendicular to the wall light wall feet per second

Use the graphs below to answer questions 1 4 PROPERTIES OF TRANSFORMATIONS 6 5 4 GIOVANNI D F XAN F 6 5 4 1 F HANNAH B ENT B Describe the transformation represented on Hannah s graph cansione Rotation over y axis ABC A B C er Giovanni s graph write a 1 and a 2 o the 1st and 2nd transformations in the ence of transformations represented by aph Not all choices will be used a Reflection over x axis 5 Translation 4 units right Rotation 180 clockwise Rotation 90 clockwise Translation 4 units left D graph s represent a pre image that is nt to the image and which graph s Is a pre image that is similar to the H G ANDREW 7 I 3 For Andrew s graph write a 1 and a 2 next to the 1st and 2nd transformations in th sequence of transformations represented his graph Not all choices will be used 1 a Dilation by a scale factor of b Rotation 90 clockwise c Translation 6 units up d Dilation by a scale factor of 4 e Translation 6 units left 5 Ricardo will transform a triangle con quadrant II by reflecting over the x axi dilating by a scale factor of 0 5 Which true statement A The image will be in quadrant III

3 5 3 1 6 Solve for x and y Leave answer as a simplified Radical 1 2 X 60 20 30 Y X 5 3 60 30 X Y 4 30 X 6 X 60 30 60 9 14 3 Y X 9

5 How far from the base of the house would you need to place a 15 ft ladde so that it reaches the top of a 12 foot wall Draw a picture then solve

Solve for x Round to two decimals if necessary 13 cm 15 cm X

Identify if the following sides form an acute obtuse or right triangle 11 in 13 in 5 in O a Ob Oc Acute Obtuse Right

45 y Solve for y O a Ob Oc Od 10 5 5 2 10 2 5 3

Solve for x Round to two decimals if necessary X 13 cm 15 cm PREVENT X PLACE

15 10 5 0 5 10 5 10 15 20 Write an equation for the function that is shown by the blue points use x for the input B Submi

1 point Find the centroid x y of the region bounded by X y 5x 6x y 0 x 0 and x 8

Given A 1 0 B 2 4 and C 5 1 Show that ABC is isosceles Find the midpoint M of BC Show that AM is perpendicular to BC Ay B 2 4 A 1 0 M 5 1 x

M is the midpoint of AB and N is the midpoint of CM Find the coordinates of N A 1 2 M N C 4 6 B 7 3

Find the missing longth indicated LRD O 169 Nona of the other answers are correct 80 220 O 144

Dans chaque cas d terminez la mesure associ e x l aide de l aire donn e B a b A 800 m 61 31 m A 1700 cm 59 cm 67 cm

Find the missing length indicated X 144 169 64 200 36 60

Identify the range of the following exponential function y 82 2 O 0 0 O 2 0 0 2 O 8 00

You are tasked with creating a logo for a company The company wants the logo in a mathematical representation so it can be re created in a variety of mediums Your task is to use a graphing calculator program to create the logo You want to be creative and use as many mathematical equations as you cam Example 50 100 50 50 edit graph on desmos

21 Trapezoid KLMN with vertices K 7 1 L 3 0 M 3 4 and N 7 8 180 about 1 5 K L M N

T By O cy B This is a vector with components 10 12 A

A ala va tu l n B C D E F 49 35 30 53 33 B D E F 49 35 30 53 33 24 18 43 8 55 34 2 36 17 44 24 18 55 43 8 34 36 2 17 44 ww The weights of edges in a graph are shown in the table above Apply the sorted edges algorithm to the graph Give your answer as a list of vertices starting and ending at vertex A Example ABCDEFA

000000000 D CD CE AE AB 14 BE BC BD AC AD 15 B 12 E Q Find the minimum cost spanning tree on the graph above using Kruskal s algorithm Which of the edges below are included in the minimum cost tree 10 A

C 15 00000 ABCDE D 8 14 13 12 B 7 E a Apply the repeated nearest neighbor algorithm to the graph above Starting at which vertex or vertic produces the circuit of lowest cost A

Find the total area of the composite figure Round all calculations to the nearest ter 38 mm Cepatic WILL BE 15 mm

Matt was converting the polar equation into an equivalent rectangular coordinate equation First Matt listed all the true relationships between polar coordinates and rectangular coordinates Analyze his work Step 1 Since tan and tan 1 substituting tan 11 for tan 1 2 4 Step 2 Using the definition of tan 1 tan Step 3 Since tan 1 1 Step 4 x y Matt is in his reasoning

Point Y is a centroid for every problem Solve for the missing segment 1 Find TY TW 18 2 Find TW TY 20 3 YV 7 Find XV 4 UZ 6x 3 UY 3x 10 Find UY T X Z W V

Test Final Exam Study Guide Question list O Question 1 Question 2 Question 3 PASAU K An agent for a residential real estate company in a suburb goal the agent would like to use the size of an apartment Complete parts a through f b Use the least squares method to determine the regress bo h Round to one decimal place as needed Bound to one decimal place as needed

While waiting for your sister to finish her bungee jump you decide to figure out how tall the platform she is jumping off is You are standing 200 feet from the base of the platform and the angle of elevation from your position to the top of the platform is 62 degrees How many feet tall is the platform

The table shows the number of goals made by two hockey players Player A Player B 2 1 3 8 2 1 4 3 1 2 3 1 3 2 2 1 3 6 Find the best measure of variability for the data and determine which player was more consistent O Player A is the most consistent with an IQR of 2 5 O Player B is the most consistent with an IQR of 1 5 O Player A is the most consistent with a range of 7 O Player B is the most consistent with a range of 5

MA 912 GR 3 2 X 7 2 Y 6 4 and Z 3 1 Part A Graph triangle XYZ Part B Find the lengths of the sides Cl

An equilateral triangle is inscr a circle We draw a line through the midpoints of two sides of the triangle Show that the ratio AB BC is the golden Ratio Hint Use the following Axiom If two chords of a circle intersect in a point that divides the first chord into the lengths a and b and the second into the lengths c and d then ab cd A 0 C B C