Geometry Questions

ven is the Midpoint of WY VYZ ve WX AYZX W 3 Complete the Two Column Proof Statement 1 X is the Midpoint of WY1 2 VW YZ 3 XWXY 4 YXZ Reason BiUFont Family 2 13 Definition of a Midpoin 4 Explain why we are unable to finish this proof establishin that AVWX AYZX AA A

Initial Point 8 3 Answer Terminal Point 6 1

Use y X Find the critical values Enter your answers as a comma separated list Find the critical points x y x y x y x x 5 36 and its derivative dx dy 5x x 3 x 5 36 relative maxima relative minima smallest x value Find the intervals on which the function is increasing Enter your answer using interval notation largest x value Find the intervals on which the function is decreasing Enter your answer using interval notation horizontal points of inflection Find the relative maxima relative minima and horizontal points of inflection If an answer does not exist ente x y DNE x y x y to find each of the following DNE DNE X X

14 An observer in the top of a lighthouse determines that the angles of depression to two sailboats directly in line with the lighthouse are 3 5 and 5 75 If the observer is 125 feet above sea level find the distance between the two boats Show your main steps 5 points y 3 5 X 5 75 125 f 25 f

Use the given information to prove that ARST AUVT R 1 S T Statement Validate U Given RST is a right angle LUVTIS a right angle ST VT Prove ARST AUVT Reason Reason Send To Proof Send To Proof Send To Proof Send To Proof olo 2

Find the 3 cube roots of 64cis B 4

2 Describe in words and a simple sketch the solid given by the following inequalitie a 0 p 2 0 6

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2011 48384 53829 56147 58882 60358 62108 60655 62202 62766 62328 58193 55773 53345 44421 a Make a graph of the data use graph paper label completely and choose the correct axis for th independent x and dependent y variables b Find the slope between 1940 and 1945 c Find the slope between 1960 and 1965 d Find the slope between 1995 and 2000 e Add a trend line to the graph f Estimate the vertex and explain its meaning in context and it is Select an answer g Estimate both x intercepts and explain their meaning in context The smaller of the 2 x intercepts is at x and it is Select an answer The larger of the 2 x intercepts is at a Select an ancwor and it is

Write the standard form of the equation of the hyperbola subject to the given conditions 3 Vertices 2 1 6 1 Slope of the asymptotes The equation of the hyperbola in standard form is 00 0 0

Consider the following two loans for P 7 500 Loan A 5 year loan annual interest rate of 7 monthly repayments of 148 51 Loan B 3 year loan annual interest rate of 10 monthly repayments of 242 00 On which loan will you pay the least interest Select the correct answer below Loan A O Loan B

The grade of a road is its slope written as a percent Find the grade of the road shown 22 feet Find the slope of the line 3 feet OA The slope of the line is m GCLER Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer Type an integer or fraction The grade is Round to one decimal place as neede Ay

A ladder leaning against a building makes an angle of 78 degrees with the ground TF foot of the ladder is 5 feet from the building How long is the ladder

32 10 X Solve for x Round to the nearest tenth

Write the given exponential equation in logarithmic form a 1 11

Using the accompanying Home Market Value data develop a multiple linear regression model for estimating the market value as a function of both the age and size of the house State the model and explain R2 Significance F and p values with an alpha of 0 05 Click the icon to view the Home Market Value data State the hypotheses for the multiple linear regression test Ho B B Bk 0 H at least one B is not 0 State the model for predicting MarketValue as a function of Age and Size where Age is the age of the house and Size is the size of the house in square feet MarketValue Age Size Type integers or decimals rounded to three decimal places as needed 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 30 34 30 33 34 33 33 35 30 33 33 32 34 31 33 35 34 32 31 33 27 26 27 29 27 27 28 27 27 29 27 26 25 29 26 29 29 n 1911 1873 1775 1926 2095 1719 1930 1775 1649 1902 1574 1767 2284 2475 1602 2179 1689 1692 1699 1507 1461 1639 1652 1460 1496 1525 1750 1547 1446 1476 1456 1424 1566 1691 1600 1860 109546 95240 94024 102765 104103 89395 99587 91901 85292 102626 93173 86919 109475 112782 83189 113072 95140 82756 85589 80433 77312 77934 87887 79055 80074 90368 89532 81663 87724 86582 91652 78861 87398 91541 82412 87520

12 Given m 1 57 mRS 3x 6 mVT x Find mRS 3 points R S T V

9 Given AOLOB and OC bisects ACB Find mAB and mBC 2 points B

4 Given AABC M and N are the midpoints of AC and BC respectively Prove AMNC AABC Proof Statements 1 AABC M and N are the midpoints of AC and BC 2 MN AB 3 ZCMNZA ZCNM ZB 4 AMNC AABC 3 points 1 2 3 4 A M C Reasons N B

11 Given AB OD in circle O mBD 46 Find m 2 and mAQ 2 points A Q O B D

10 Given m 124 mTV x 1 mSR 3 x 1 Find mTV 3 points R S

2 The measures of two supplementary angles are in the ratio 3 12 Find the measure of each angle 2 points X

7 IF mCD 62 and mAB 70 find mZE and mZAOB m E m AOB 1 point E D B A

8 If the measures of the angles of a quadrilateral are in the ratio of 2 4 5 7 find the measure of each angle 2 points

5 Given right AABC with AB 8 3 and m CBD 150 Find AC and BC A 2 points 8 3 B D

12 Given m 1 57 mRS 3x 6 mVT x Find MRS 3 points R S 1 T L

13 Given mAB 114 and mDC 38 Find m 1 point A B D C

3 Given quadrilateral ABCD quadrilateral HJKL If AB 6 BC x HJ 12 and JK x 4 Find x 2 points B A H D L C S

9 Given AO LOB and OC bisects ACB Find mAB and mBC 2 points C 3 O A B

6 Given right ADEF with DE 6 2 and m FEK 135 Find EF and DF D 1 point 6 2 E

1 The measures of two complementary angles are in the ratio 2 7 Find the measure of each angle 2 points 2 x

A D 18 Given Find B Exercises 17 20 AC AD E 12 AB 6 AE 14

What additional piece of information would prove AWZY AMKS similar by SAS W 10 7 8 Y 5 S 4 K

In the figure for Exercises 21 to 24 RS is tangent to the circle at S See Theorem 6 3 7 21 Given Find RS 8 and RV 12 RT HINT Use the Quadratic Formula R T S Exercises 21 24 3

14 Given Find m 1 63 mRS mVT x mRS 3x 6 R 2 Exercises 14 15 T V

Find SR 3 and RQ QSL TV at R a RV b TV 4 T S R W G Exercises 16 17

9 Given Find Tangents AB and AC to OO m ACB 68 a mBC b mBDC c m ABC d MZA C Exercises 8 9 A B A

R T Exercises 3 5 W S 5 Find m RST if mRT m TS 1 4

Find the area of overlap in the two circles below The smaller circle has a radius of 7 97 cm and the larger circle has radius 10 6 cm The distance between the centers of the circles is 11 67 cm 2arccos A 1800 sine c a b 2abcosC D The second box is for you to enter your answer

10 Given Find d m A m 1 mDC a mAB b m 2 72 34 A B Exercises 10 11 D

In the figure for Exercises 7 to 16 O is the center of the circle See Theorem 6 3 5 11 Given Find AE CB 6 EC 3 AD 8 D A E Exercises 7 16 3 B C

In Exercises 25 and 26 CA and CB are tangents 25 Given mAB x Prove m 1 180 X A B Exercises 25 26 X 1

3 Given 2 Find R T Circle O with diameter RS tangent SW chor TS and mRT 26 a m WSR b m RST c m WST W S

12 ar 18 AB is the common chord of OO and OQ If AB each circle has a radius of length 10 how long is OQ A B

13 Given Find OO with AB AC and 72 m BOC a mBC b mAB c m A d m ABC e m ABO B ST A

For Exercises 1 to 8 use the figure provided A B Exercises 1 8 1 If mAC 58 find m B 46 find m 0 3 If mDE 47 6 find m 0 4 If mAC 56 4 find m B 5 Ifm B 28 3 find mAC 6 If m O 48 3 find mDE 7 If mDE 2 If mDE U 47 find the measure of the reflex angle tha

For Exercises 1 to 8 use the figure provided A Exercises 1 8 E LU B D

10 Given Find ST SR is a diameter a mST b mTR c mSTR d m S SR in OQ HINT Draw QT T R

14 Given Find R S Right ARST with RT m STV 150 RS and ST T V 6 2

Exercises 9 12 12 Given Find E Right ADEF with m E EF 12V 3 DE and DE 2 m F and

In Exercises 15 to 19 create drawings as needed