Geometry Questions

Solve for x Round to the nearest hundredth when necessary logsx4 2 5

Solve the following equation and find the value of x for which the logarithm is defined logx 4x 3 2 Select one a 2 b 1 O c 3 d 4

Solve the following equation log 9 27 x elect one a 2 3 b 3 2 c 4 3 d 3 4

Solve for x x log 2 2 Select one O a 1 2 Ob 2 OC 0 O d 1

For loga y to be defined a y 0 b a 0 a 1 Select one O True False

Which group shows the values in the order from greatest to least Select one a log 10 In 10 log e In 1 b In 1 log 10 In 10 log e Oc log e In 10 log 10 In 1 Od In 10 log 10 log e In 1

The logarithm log x 5 2x is defined for x 3 Select one True False

If f x 1 then find the value of the function at x 0 Select one a undefined Ob 0 O c 10 d 1

Simplify 3lne Select one O a 3 b In 3 c 3x Od 1

Find the value of log681 Round value to the nearest hundredth place

When applying the change of base theorem to find log 75 there are several methods for determining the value Choose all that apply Select one or more a log75 log5 b log15 C d log5 log75 In75

Use Cramer s rule to compute the solutions of the systems x1 x2 3 3x1 2x3 0 x2 2x3 2

True O False Question 8 The eight elements of reasoning are not just fundamental they are universal True 1 5 pt

Find the value of x Round the length to the nearest tenth 22 16 m Not drawn to scale O 14 8 m 6m 6 5 m 42 7 m X

A pyramid with three regularly side S ABC know m BSC 60 degree Through BC make a perpendicular line H with AS Height of the pyramid is 2root2 Find the slice of H with the pyramid

As shown in the diagram below the radius of a cone is 2 5 cm and its slant height is 6 5 cm 6 5 2 5 How many cubic centimeters are in the volume of the cone 1 12 5m 3 30 0m 2 13 5 4 37 5m No Work No Credit Please show

Triangle ABC with vertices at A 0 0 B 3 5 and C 0 5 is graphed on the set of axes shown below 0 1 23 m Which figure is formed when ABC is rotated continuously about AC P FG 3

13 A company makes a table for 15 and sells it for 19 What is the percentage of markup

Find the value of x Round the length to the nearest tenth 10 yd 23 6 yd 5 1 yd 4 6 yd 11 yd Not drawn to scale 25 X

Green Township to the main road Expressway East so that drivers can travel between Green Township and Metro City in the shortest possible time The direct north south distance from Green Township to Expressway East is 35 miles and the total east west distance between Metro City and the point directly south of Green Township on Expressway East is 70 miles See diagram which is for illustrative purposes only and not to scale 35 70 Al The speed limit on the new road will be 35 mph and the speed limit on Expressway East is 60 mph a How far to the west of Metro City should the new road from Green Township connect to Expressway East to enable drivers to make the trip in the least amount of time If necessary round result to 1 decimal place miles b What is the total time that the trip from Township to Metro City will take If necessary round result to 1 decimal place

Write the ratios for sin A and cos A A 10 sin A Not drawn to scale sin A sin A 26 sin A 24 10 26 24 10 24 26 24 B cos A cos A cos A cos A 24 26 10 26 10 24 10 26

A slide 4 1 meters long makes an angle of 350 with the ground To the nearest tenth of a meter how far above the ground is the top of the slide X 07 1 m 2 4 m 3 4 m O 5 0 m 4 1 m 35

Find the lengths of the missing sides in the triangle Write your answers as integers or as decimals rounded to the nearest tenth 8 X Ox 45 Not drawn to scale Ox 11 3 y 8 Ox 5 7 y 6 9 Ox 8 y 11 3 x 6 9 y 5 7

Find the value of x and y rounded to the nearest tenth X 45 y 34 30 x 24 0 y 139 3 Ox 24 0 y 46 4 x 48 1 y 46 4 x 48 1 y 139 3

All of the above Use of data facts and experiences O Concepts and theories Question 12 One develops as a critical thinker by Taking command of one s thinking All of the above Continually distinguishing between assumptions and inferences Realizing that our purposes may be inconsistent at times

O False Question 10 1 5 Monological problems are ones for which there are definite correct and incorrect answers and definite procedures for getting those answers True

Find the slope through the given two points 4 5 and 6 1 Find the slope of the line that passes through the given two points 1 6 and 2 6 Find the slope of the line that passes through the given two points 2 3 and 4 7 Find the slope and the y intercept of the given line y 4x 11 line that passes Find the slope and the y intercept of the given line 3x 4y 36 Find the slope and the y intercept of the given line 9x 6y 9 Find the equation of a line with the given slope and y intercept Slope 4 y intercept 0 3 Find the equation of a line with the given slope and y intercept Slope 5 y intercept 0 2 Graph using the slope and y intercept y 3x 7 Graph using the slope and y intercept y 6x 7 Graph using the slope and y intercept 2y 4x 10 Graph using the slope and y intercept 2x 3y 15

2 3 05 Ibu find the value EN 0 41x 4 12 540 0 of LAY Solve its

Match each scatterplot shown below with one of the four specified correlations 0800 O OOO 00 88888 00 a Q a 0 99 b 0 26 c 0 12 d 0 82

Find AM in the parallelogram if PN 15 and AO 6 The diagram is not to scale M P O 15 O 12 O 7 5 N

O is the midpoint of circle CHEF EH is extended and cuts the circle CGEO at G CFE x 10 1 10 2 10 3 10 4 Prove that 180 2x Prove that EF CH Prove that ACGH AFGE N N E If EH HG 5 3 determine the value of EF HC X 1

In triangle ABC ZA is a right angle and mZB 45 Find BC If your answer is not an integer leave it in simplest radical form O 10 2 ft B A Not drawn to scale O 20 ft O 10 ft C O 20 2 ft 10 ft

2 Let ABC be a right angled triangle such that ZA 90 AB AC and let M be the mid point of the side AC Take the point P on the side BC so that AP is vertical to BM Let H be the intersection point of AP and BM 1 Find the ratio of the areas of the two triangles AABH AAHM 2 Find the ratio BP PC

What is the value of x given that AE BD A ES D 099 10 7 2 03 10 11 26 11 7 C

6 If m CDF 3x 14 mZFDE 5x 2 and mZCDE 10x 18 find each measure 7 If m LMP is 11 degrees more than m NMP and m NML 137 find each measure LA f M P N P D mZLMP mZNMP 8 If mZABC is one degree less than three times m ABD and m DBC 47 find each measure B C D F 9 If QS bisects LPOT mZSQT 8x 25 m POT 9x 34 and mZSOR 112 find each measure Q FC D E S G H m CDF m FDE m CDE T R 10 If ZCDE is a straight angle DE bisects ZGDH mZGDE 8x 1 mZEDH 6x 15 and m CDF 43 find each measure m ABD m ABC E x mZPQS m PQT mZTOR X m GDH m FDH mZFDE

Evaluate the following logarithm without using a calculator log 9 3 Select one a 1 4 b 4 c 1 d 2

32 1 1 3 2 1 1 2 A y 2x 5 B y 2x 1 6 x 3x 3 1 2 3 The equation of this line is y 2x 3 Which of the following shows a way that we could change the equation to shift the line downward

Let s say every one of the eight cubical cells in the picture has a side length of 10 metres If this net of cubical cells is folded up into a tesseract and you start moving through the cubical cells in the direction of the arrow how far have you moved when you return to your starting point Answer

4 Given SABC A B C be the midpoint of the Si des BC CA ond AB respectively and let D be the foot of the perpendiculur from A onto BC a Let Lim that perpendiculos from b Compute be B bisects the respective P feet of the O oto C A A B Prove AD this is not I between Lm the engle and BC

In the rhombus m 1 15x m 2 x y and m 3 30z Find the value of each variable The diagram is not to scale 3 2 1 Ox 12 y 84 z 6 O x 12 y 174 z 3 x 6 y 84 z 3 Ox 6 y 174 z 6

The Venn diagram shows the number of students in an eighth grade class taking art and drama as their electives What is the probability of a student chosen at random taking either of these subjects as an elective 8th Grade Art 34 78 OA 107 SOB OC 92 107 15 107 14 Drama 44 15

If A t t 1 ti 11 1 What is the condition for the linear transformation TA to become onto 2 Find the value of t that becomes rank A nullity AT

Suppose you invest 4900 in an account with an annual interest rate 12 compounded monthly 1 each month Use this information to complete the table below Round to the nearest cent as needed Month 1 2 3 4 5 Starting Balance 4900 4949 5048 47 Question Help Video 1 Interest on Starting Balance 49 50 99 Ending Balance 4949 5048 47

Which figure can have the same cross section as a sphere 1 21 R

Linear Regression Christmas Trees The following table gives the total number of live Christmas trees sold in millions in the United States from 2004 to 2011 Source Statista com t number of years since 2004 In 2008 there were approximately 28 2 0 O C total number of Christmas trees sold in the U S in millions 1 Use the TABLE to determine the number of live Christmas trees sold in the year 2008 C 0 27659t 29 77411 x 2 27 1 4 28 6 6 28 2 27 7 30 8 2 Determine the linear regression equation that models the set of data above Use the indicated variables and proper function notation Round to the nearest hundredth as needed million live Christmas trees sold in the U S 3 Interpret the meaning of the slope of your rounded regression model From 2004 to 2011 the number of Christmas trees sold in the U S increased by approximately 0 2786591 x million trees each year 4 Use the REGRESSION EQUATION to determine the number of live Christmas trees sold in the year 2008 In 2008 there were approximately 30 85573 x million live Christmas trees sold in the U S 5 Your answers to parts 1 and 4 should be different Why is this the case The data are linear The regression equation gives a more precise answer than the value from the table The data are linear The regression equation gives only an approximation of the actual value not the exact value The data are not perfectly linear The regression equation gives a more precise answer than the value from the table The data are not perfectly linear The regression equation gives only an approximation of the actual value not the exact value

Find the measurement indicated in each paral 13 EW x 3 WG 2x 14 Find EW E F W D G

Let 2 X 1 3 1 Y 1 11 2 5 0 31 V 2 13 x 1 U 1 W 2 02 a 3 marks XYT T b 2 marks 2Y I3 c 4 marks tr W V 2 1 2 1 0 1 0 Evaluate each of the following if possible If it is not possible justify your answer Show all your work

In parallelogram DEFG DH x 2 HF 2y GH 4x 3 and HE 5y 1 Find the values of x and y The diagram is not to scale D Ox 8 y 5 Ox 6 y 4 Ox 4 y 6 Ox 5 y 8 H I R E

In the parallelogram mZKLO 78 and m MLO 42 Find m KJM The diagram is not to scale J O 120 O 110 078 60 L K

The function shown below is f z We are interested in the transformed function g x 2f 2 a Describe all the transformations g z has made to f z shifts stretches etc b NEATLY sketch the transformed function g z and upload your graph as a PDF document below You may use graph paper if you want Be sure to label your vertical and horizontal scales so that I can tell how big your function is N