Geometry Questions

3 Evaluate the trig function with exact values 1 sin 7 7 4 6 3 2 COS 3 tan 5TT 3

cose 5 13 Sketch the triangle represented then find the sine tangent ratios

A 30 60 90 triangle has a hypotenuse of 7 2 Find the other sides Be careful

Proving That Alternate Interior Angles Are Congruent Read Explain 1 Explain2 and complete Your Turn 1 adapted from Lesson 4 2 Show all your work EXPLAIN 1 Alternate Interior Angles Theorem If two parallel lines are cut by a transversal then the pairs of alternate interior angles have the same measure Example 23 45 Given p q line p parallel to line q Prove m23 m25 Two Column Proof of the Alternate Interior Angles Theorem Statements Example Complete the proof by writing the missing reasons Choose from the following reasons You may use a reason more than once Refer to the reason bank below 1 pllq 2 23 and 26 are supplementary 3 m23 m26 180 4 25 and 26 are a linear pair 5 25 and 26 are supplementary 6 m25 m26 180 7 m23 m26 m25 m26 8 m43 m25 Reason Bank Substitution Property of Equality Reasons Same Side Interior Angles Postulate 1 2 3 4 5 6 7 8 Linear Pair Theorem P Definition of Supplementary Angles 9 1 4 3 5 6 At 8 7 Subtraction Property of Equality Given P 9

13 and complete Your Turn 1 3 adapted from Lesson 4 2 Angle Pair Relationships Same Side Interior Angles Postulate If two parallel lines are cut by a transversal then the pairs of same side interior angles are supplementary Alternate Interior Angles Theorem If two parallel lines are cut by a transversal then the pairs of alternate interior angles have the same measure Corresponding Angles Theorem If two parallel lines are cut by a transversal then the pairs of corresponding angles have the same measure Example Suppose m 1 140 Show how to find m25 m21 mz5 by Corresponding Angles Theorem Using the Substitution Property substitute 140 for mz1 to obtain m25 140 mz1 m25 140 mz5 Corresponding Angles Theorem Substitution To find the measure of mzJKN 2 Two parallel lines are cut by a transversal Use Angle Pair Relationships to find mzJKN By definition JKN and ZMNK are same side interior angles mzJKN mzMNK 180 7x 1 11x37 180 18x 36 180 18x 216 x 12 Same Side Interior Angles Theorem Substitution Combine Like Terms Addition Property of Equality Division Property of Equality 7x 1 we can substitute 12 for x mzJKN 7 12 1 85 So m2JKN 85 M 4 3 5 6 8 7 K 7x 1 11x 37 N R P 9 L P

2 Without using a calculator find the exact value of the expression tan 3 8

Given p q Prove m24 m28 Two Column Proof of the Vertical Angles Theorem Statements 1 pllq 2 24 and 26 are alternate interior angles 3 m24 m26 4 26 and 28 are vertical angles 5 m26 m28 Angles Theorem Refer to the reason bank below 6 m24 m28 Reason Bank Substitution Property of Equality Vertical Angles Theorem Reasons THE RE 1 Given 2 3 4 5 6 Definition of Vertical Angles Alternate Interior Angles Theorem 4 3 5 8 7 P 9 Definition of Alternate Interior Angles

Lesson 4 2 Homework HW Complete problems 1 8 for independent practice When you are finished check the solutions with your teacher 1 Identify the relationship shown below Corresponding Angles Alternate Interior Angles Same Side Interior Angles Consecutive Interior Angles Alternate Exterior Angles 3 Identify the relationship below Corresponding Angles Alternate Interior Angles Same Side Interior Angles Consecutive Interior Angles Alternate Exterior Angles 2 Identify the relationship shown below Corresponding Angles Alternate Interior Angles Same Side Interior Angles Consecutive Interior Angles Alternate Exterior Angles 4 What is the measurement of the missing angle 65

2 Without using a calculator find the exact value of the expression tar

Your Turn 1 Suppose mz4 36 Show how to find m25 2 Two parallel lines are cut by a transversal Use Angle Pair Relationships to find m BEF 0 D A H 3 Two parallel lines are cut by a transversal Use Angle Pair Relationships to find x 5 6 8 7 B 1 4 3 3x 58 7x 1 E 9 5x K G 5 85 FL

5 What is the value of b b 7 Solve for x X 4x 1 157 45 salta inship b tal B 1 zounidony G b 51 il noy nad W X nowomoll E 518 lun wred gim 8 Solve for x x 4 O 5x 2

Corresponding Angles Theorem If two parallel lines are cut by a transversal then the pairs of corresponding angles have the same measure Example 21 45 2 Name the four pairs of corresponding angles Then write an equation which shows that each of the angles has the same measure The first one is done for you Corresponding Angles 21 and 25 24 and 2 and 2 and Alternate Interior Angles Equation m21 m25 24 and 26 m and mz mz Alternate Interior Angles Theorem If two parallel lines are cut by a transversal then the pairs of alternate interior angles have the same measure Example 24 26 m2 1 m2 3 Name the two pairs of alternate interior angles Write an equation that shows that the angles have the same measure m2 Equation m24 mz6 5 m2 7 2 1 4 3 8 7

4 1 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson Checkp below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 Which of the following groups of angles match the given property Select two that apply A E C LDEA and LCEA form a Linear Pair D LFEB and BED form a Linear Pair 60 F D B A LCEA is congruent to ZDEB through the Vertical Angles Theorem B LFEB is congruent to ZDEA through the Vertical Angles Theorem

angles are supplementary The first one is done for you Same Side Interior Angles 23 and 26 24 and 2 lifelong Geometry A LEARNIND mz Equation m23 m26 180 m2 Credit 3 1 2 4 3 5 8 7 L4L Geometry A 2020 6 Page 14

HW 1 Identify the relationship between ZA and ZB lb work Complete problems 1 8 for independent practice b When you are finished check the solutions with your teacher keres Vertical Angles Complementary Angles Supplementary Angles 3 Identify the relationship between ZA and ZB a Vertical Angles Complementary Angles Supplementary Angles 2 Identify the relationship between LA and LB Vertical Angles Complementary Angles Supplementary Angles 4 What is the value of b b b 64

c Graph f f and y x on the same coordinate axes The graph of y x is shown using dashed line Choose the correct graph below A OC O Q B D L

D G N PR 9 A AV 77 Congruence Stmt 250 Congruence Stmt h Congruence Stmt A Reason Reason Reason 7 10 U V W A Y X Congruence Stmt A Reason 8 11 M Congruence Stmt A Reason K 12 D Congruence Stmt 4 Reason F E LE AN

ANGLE ANGLE SIDE In 3 4 find the length of the indicated side d x x y y and use a protractor to measure the indicated angles Mark congruent angles and sides If the triangles are congruent write a triangle congruency statement by AAS 3 A CB FD C B 8 6 4 2 4 6 8 8 6 4 2 0 2 m C m E Congruence Statement 4 6 8 F E m A m F 4 JQ 8 6 4 2 W F FM 8 64 4 2 2 4 02 4 8 m W M Congruence Statement 6 m F R 9 m R m J

Congruence Stmt Reason E U V W VA Y X 0 J gruence Stmt Congruence Stmt Reason 11 M Congruence Stmt K L V M Congruence Stmt Reason 12 D Congruence Stmt E F

13 G H Reason E Congruence Stmt 14 Z Congruence Stmt Reason B 15 N Congruence Stmt Reason R

4 Write a congruence statement remember order is important and state the appropriate postulate SSS SAS ASA SAA for you reason If the triangles cannot be proved congruent write not possible 3 W B 1 2 A J Congruence Stmt Reason S 0 T Congruence Stmt Reason U M N Congruence Stmt Reason 5 W AV X Congruence Stmt Reason X Congruence Stmt Reason 6 M Congruence Stmt Reason R N 55 4 C IC n M 120

What is the value of Round answer to nearest whole number 20 o 12

Directions You will be designing a city map using the guidelines listed below You will be graded on content creativity and neatness Guidelines 1 Your city must have two streets that are parallel to each other and one street that intersects the parallel streets You must name all of these streets after streets in your city 2 Your city has a hospital that is on one of the exterior angles Draw and name the hospital 3 The school is alternate exterior to the hospital that is in your city Draw and name the school 4 The school and the pet shop are at corresponding locations Draw and name the pet shop gas station 5 The pet shop and the gas station are at alternate interior locations Draw and name the 6 The gas station and the park are at same side interior locations Draw and name the park 7 The park and the grocery store are at alternate interior locations Draw and name the grocery store 8 The grocery store and the restaurant are at vertical locations Draw and name the restaurant 9 The restaurant and your house are at alternate exterior locations Draw and name your house ric ent ivity ess 50 points 25 points 25 points 5 points for each guideline that was correctly followed Does your drawing look like a city Did you take the time to make your buildings look good and your streets look good Are they origi Is it colorful Did you use a straightedge to draw your streets Did you write neat and spell correctly

1 Just the importance of cvil engineering 2 Write down the properties of bricks 3 Briefly explain physical and chemical clasification of rocks 4 Describe the types of bricks and elaborate them 5 Discus the geological clasification of rocks

Description Common Shares Contibuted Surplus Recained Eamnings Cash Debit Earnings Per Share Revenue Debt to Equity Ratio 5 040 000 545 000 7 015 000 Credit 12 600 000 Place only one T in each row below indicating the impact of the share reacquisition journal entry on the following financial statement metrics Positive Negative Not No Impact Determinable

Description Common Shares Contibuted Surplus Recained Eamnings Cash Debit Earnings Per Share Revenue Debt to Equity Ratio 5 040 000 545 000 7 015 000 Credit 12 600 000 Place only one T in each row below indicating the impact of the share reacquisition journal entry on the following financial statement metrics Positive Negative Not No Impact Determinable

add the current expense to expenses expenses append int line colors gold yellowgreen lightcoral lightskyblue green red plot the pie chart plt pie expenses labels categories colors shadow True colors autopct 1 1f startangle 140 set the axis as equsl plt axis equal display the chart plt show 1000 235 5600 800 480 758 Ligue 1 Ment Gas Sample Output Files imput Car Payment input txt Mic RON clothing

10 A function has a vertical asymptote at x 3 and is concave up when x 3 Determine lim f x and explain your reasoning

Description Common Shares Contibuted Surplus Recained Eamnings Cash Debit Earnings Per Share Revenue Debt to Equity Ratio 5 040 000 545 000 7 015 000 Credit 12 600 000 Place only one T in each row below indicating the impact of the share reacquisition journal entry on the following financial statement metrics Positive Negative Not No Impact Determinable

When the common stock is reacquired at cost higher than issue cost requires a Debit to Loss on Repurchase of Common Shares Option B is correct This done when Par Value method is used Journal Entry for reacquisition of Common Shares in above case will be Credit Account Titles and Explaination Treasury Stock Loss on Repurchase of Common Shares Cash Debit Par Value based on Avg issued price Excess Paid to reacquire over and above par value Total Amount Poid to reacquire shares Explanation is written in Debit and Credit Coloums to understood what values are written Now Also note in the case when shares were initially issued at price higher than par value Then instead of using Loss on Repurchase of Common Shares Account we will use credit balance of Addition Paid in Capital It will be debited instead of Loss on Repurchase of Common Shares Hope you understood the concept if any query feel free to ask in comment section

Stars appear to be white to the naked eye because they emit a mixture of all colors of light However when photographed stars show a range of colors due to their different surface temperatures The coolest stars emit primarily red light while hotter stars emit more blue light This is because hotter stars emit more energy and this energy is released in the form of shorter wavelengths of light such as blue and violet The color of a star can be determined by measuring its spectrum which is the distribution of light that it emits across different wavelengths The wavelength at which the intensity of light reaches a maximum is called the peak wavelength Wien s Law relates the peak wavelength of a star to its surface temperature Surface Temperature 2 98 10 6 K Peak Wavelength nm Where the peak wavelength is measured in nanometers nm and the temperature is measured in Kelvin K For example the Sun has a peak wavelength of about 500 nm Using Wien s Law we can calculate that its surface temperature is about 5800 K The following table shows the relationship between star color and surface temperature Color Red Orange Yellow White Blue Surface Temperature K 3000 3000 5000 5000 6000 6000 7500 7500 Export to Sheets Astronomers use the color of stars to classify them into different types The most common classification scheme is the Morgan Keenan system which divides stars into seven spectral classes denoted by the letters O

Description Common Shares Contibuted Surplus Recained Emings Cash Debit Earnings Per Share Revenue Debt to Equity Ratio 5 040 000 545 000 7 015 000 Credit 12 600 000 Place only one T in each row below indicating the impact of the share reacquisition journal entry on the following financial statement metrics Positive Negative Not No Impact Determinable

A DCM boost converter is to be designed to operate under the following conditions 18 V V 36 V 5 W Pload 100 W V 48 V fs 150 kHz You may assume that a feedback loop is in place that changes the transistor duty cycle as necessary to maintain a constant output voltage of 48 Design the converter subject to the following specifications The converter should operate in the discontinuous conduction mode at all times To ensure an adequate design margin the inductance L should be chosen such that K is no greater than 75 of Kerit at all operating points Given the above requirements choose the element values to minimise the peak inductor current The output voltage peak ripple should be less than 1V Specify a The inductor value L b The output capacitor value C c The worst case peak inductor current peak

Create a Python program called expenses py that uses matplotlib to plot a pie chart showing how much money use percentages is spent on the following expenses Rent Gas Food Clothing Car payment Misc A sample pie plot is provided below Save your plot as a png file called expenses png and submit it with the Python program Expenses September 2022 Savings Car Payment 17 0 15 0 30 0 8 0 14 0 10 0 Rent 6 0 Clothing Gas

A cruise ship maintains a speed of 12 knots nautical miles per hour sailing from San Juan to Barbados a distance of 600 nautical miles To avoid a tropical storm the captain heads out of San Juan at a direction of 38 off a direct heading to Barbados The captain maintains the 12 knot speed for 11 hours after which time the path to Barbados becomes clear of storms a Through what angle should the captain turn to head directly to Barbados b Once the turn is made how long will it be before the ship reaches Barbados if the same 12 knot speed is maintained a The captain should head through an angle of Do not round until the final answer Then round to one decimal place as needed Barbados 600 O 38 San Juan

A Python program that impements a graph using an adjacency matrix A Python a program that implements a graph using an adjacency list Vertex 0 3 2 1 Vertex 1 2 0 Vertex 2 1 0 Vartay 4

For the below problem you will need to reference the Kodak Anthropometry pdf file provided on Canvas Neatly show all work for partial credit 1 A desk is 30 inches tall The desk chair has a seat height of 20 inches For keyboard work it is recommended that resting elbow height be between 1 inch above and 2 inches below the J key on the keyboard Using the Kodak data what percentile range of males and what percentile range of females will fit this workstation Assume that the J key is 0 5 inches above the desk and that a footrest is provided for workers with shorter legs easurement TANDING 1 Forward functional reach a Includes body depth at shoulder b Acromial process to functional pinch c Abdominal extension to functional pinch Abdominal extension depth B Waist height 3 Popliteal height 9 Leg length Tibial height 5 Knuckle height 5 Elbow height Shoulder height B Eye height Stature D Functional overhead reach ATED 1 Thigh clearance height 2 Elbow rest height 3 Midshoulder height 4 Eye height 5 Sitting height normal 5 Functional overhead reach 7 Knee height Males Females 50th 1 1 50th percentile S D percentile S D 32 5 31 2 26 9 24 4 9 1 41 9 41 3 17 9 29 7 43 5 45 1 5 8 9 5 1 9 29 2 2 2 28 1 1 7 24 6 24 5 31 0 34 1 50 6 21 3 17 2 41 4 3 5 0 8 2 1 2 1 1 1 1 6 1 8 2 5 56 6 57 6 64 7 68 7 12 6 69 9 2 6 82 5 3 3 2 4 3 1 24 0 6 1 3 1 2 1 4 15 3 3 1 1 1 0 1 9 23 8 8 2 40 0 38 8 16 5 28 0 40 4 42 2 51 9 56 3 39 6 63 8 64 8 78 4 4 9 9 1 22 8 29 0 32 2 47 2 20 1 16 2 39 6 1 5 27 2 30 7 35 0 1 7 25 7 29 5 34 1 13 22 6 25 6 29 3 2 6 19 1 24 1 29 3 0 8 7 1 8 7 2 0 37 4 40 9 2 2 35 8 39 9 0 9 15 3 17 2 Population Percentiles 50 50 Males Females 5th 50th 95th 1 6 1 4 2 7 38 5 25 9 28 8 38 0 42 0 43 6 54 4 59 7 49 8 55 3 61 6 56 8 62 1 67 8 60 8 66 2 72 0 61 1 67 1 74 3 3 4 74 0 80 5 86 9 2 7 48 4 2 6 2 2 2 4 2 8 0 5 1 2 4 3 7 3 1 0 21 4 1 2 27 4 5 3 9 3 23 6 29 9 10 2 44 7 44 5 19 4 31 9 45 8 48 6 1 6 32 0 34 6 2 6 43 6 48 7 1 0 18 7 20 7 0 7 15 1 16 6 1 7 37 3 40 6 5 11 4 26 1 32 8 37 4 54 8

Q1 Step 1 enter all data with the reference names in excel sheet Step 2 calculating average of the respective columns formulae used average all values in the column Step 3 calculating weighted averages multiplying averages with percentage Final total was 81 80 785 which is grade B Q2 So we will change the values in exem1 and check the total We need to find the least value in exem1 where grade dosen t change so total has to be greater than 79 5 At exem 1 score 70 we get total as 79 585 80 so the least is 70 Grade doesn t change for 6 less points then 76 Q3 So student didn t do any online reviews so avg of online reviews 0 then total will become 77 785 78 so grade will be affected so grade changes to C Q4 Redo assignments that is not exems So they are online reviews projects homeworks quizs if we consider the best possible outcome scoring full marks in these things so there averages will be 100 so changing the average to 100 we get final total 89 2 89 Grade B So he wouldn t increase his grade even if he redo Q5 As there are 20 homeworks and total percentage of homework is 10 Changin one homework dosen t affect at all There is no reason to ask for this as the grade dosen t change for one homework

5 2 determine the exact value coS X COS X Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators

Problem A ship is sailing east At one point the bearing of a submerged rock is 47 20 After the ship has sailed 16 4 miles the bearing of the rock has become 380 40 Find the distance of the ship from the rock at the latter point ZA N G Rock LI

horizontal plane non horizontal plane circular cylinder parabolic cylinder ellipsoid elliptic paraboloid hyperbolic paraboloid cone hyperboloid one sheet hyperboloid two sheets 2 z 6x 2y 3 z y 3x 4 z 3 5 3x 6y 22 4 6 6y z 4

K Write the expression as a product of trigonometric functions cos 10x cos 4x cos 10x cos 4x

B tan given tan tan 2 3x with 2 p Type an exact answer using radicals as needed Rationalize all denominators

10 A function has a vertical asymptote at x 3 and is concave up when x 3 Determine lim f x and explain x 3 your reasoning

Expand the binomial by using Pascal s Triangle to determine the coefficients 6v 3z 4

The following data lists the number of correct and wrong dosage amounts calculated by 32 physicians In a research experiment a group of 19 physicians was given bottles of epinephrine labeled with a concentration of 1 milligram in 1 milliliter solution and another group of 13 physicians was given bottles labeled with a ratio of 1 milliliter of a 1 1000 solution If one of the physicians is randomly selected what is the probability of getting one who calculated the dose correctly Is that probability as high as it should be Correct Dosage Calculation Wrong Dosage Calculation 15 4 Concentration Label 1 milligram in 1 milliliter solution Ratio Label 1 milliliter of a 1 1000 solution P physician calculated the dose correctly Round to three decimal places as needed SLICA Points 0 of 2 3 10 C

Suppose that A and B are angles in standard position Use the given information to find a SIA A 3x 8 17 cos A 3x 13 A 2 B 2 and sin B a sin A B Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

sin 5x 12 5x Choose the correct expanded form of sin using the sum or difference formula for sine 12 5x A sin sin 12 5x B sin sin 12 5x c sin 12 OD sin 5x 12 sin sin K4 3x 54 K4 3x 96 W 3 R6 73 T K sin cos 6 cos 4 sin 6 IS COS sin 3x 4 I os 3 sin 4 COS 3x sin T T T I 4 cos 6 cos 4 sin 6 3x COS cos sin 4 3x 4 W 3 sin 3 5x The exact value of sin 12 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Complete the identity tan x 1 sec Choose the correct answer below OA OC cos a OE OG sin a 1 CSC sin a B csc D cos a OF sec a H sec a

Drag the appropriate labels to their respective targets ions molecules has dissolves in water to give ions molecules or both both NaCl a strong electrolyte HI a weak electrolyte CH3CH OH a nonelectrolyte KNO3 a strong electrolyte glucose a nonelectrolyte H CO3 a weak electrolyte