Geometry Questions

Find all solutions of the following equation sec x 4 0 Select the correct answer where k is any integer 5TT 3 TU 3 TL 3 TC 3 TU 3 KIT 2k KI 2k 2 3 2 T 3 2 3 KI 2k KT 4 3 2k 4T 3 5TL 2k 2k 3 ki 5TT 3 k

Find the values of the trigonometric functions of t if cos t 3 and the terminal point of t is in quadrant III 5 sin t O sin t 4 5 sin t cos t 4 5 4 5 3 5 3 BR tan t E 5 cos t cos t EL 4 tan t cot t 3 3 5 tan t 4 3 4 cot t 4 3 cot t 3 4 3 4

Find the perimeter of the following figure with the indicated dimensions Use 3 14 Round your answer to the nearest hundredth if necessary 3 67 ft 1 62 ft 7

The graph shows how the path of a stream of water changes when the hose is held at two different angles Scale 1 unit 1 f Nozzle beld at 60 angle Nozzle held at 30 angle 6 5 4 3 2 1 1 2 3 4 5 6 7 a At which angle does the stream of water shoot up higher 60 How much higher X ft b At which angle does the stream of water shoot out farther 30 How much farther x ft

In 17 18 Find the value then find the measure of each angle 17 7x 12 R 101 12 T 3x 28 S 18 In 19 Use a two column proof to find the value of the variable Justify each statement 19 m RST 10x 12 and m USV 32 x 32 X 3x 75 Statement m RST 10x 12 and m USV 32 x Reason Given

Roll the Die C X Let s implement your randomization plan Roll the die below and assign treatments to each of the nine cows shown in the picture below by marking or circling each cow eyes marking place a circle around the cow crosses marking place an X over the cow no marking underline the cow Below is the randomization plan you proposed on the previous screen You can go back and make changes to your plan if you need To use a 6 sided die to randomly assign each cow in a herd of 50 cows to one of three treatments artificial eyespots cross marked or unmarked you can follow these steps 1 Label the die Assign two faces e g 1 and 2 for the artificial eyespots treatment Assign two faces e g 3 and 4 for the cross marked treatment Assign two faces e g 5 and 6 for the unmarked treatment 2 Roll the die for each cow in the herd By following this labeling

Find the exterior angles of the double triangle 30

In 16 Use a two column proof to find the value of the variable Justify each statement 16 m VST 11x and m RST 50 x R T S U Statement m VST 11x and m RST 50 x Reason Given

In 14 15 Find the value of the variable then find the measure of each angle 14 15 15x2 9x 10 154 3x 7

Question Answer Angst of s Watch Video From the observation deck of a skyscraper Bentley measures a 48 angle of depression to a ship in the harbor below If the observation deck is 969 feet high what is the horizontal distance from the base of the skyscraper out to the ship Round your answer to the nearest tenth of a foot if necessary Submit Answer Show Examples G

Question Watch Video Answer Attempt 1 out of 2 Show Examples From a hot air balloon Ian measures a 30 angle of depression to a landmark that s 1250 feet away measuring horizontally What s the balloon s vertical distance above the ground Round your answer to the nearest tenth of a foot if necessary G

Question Watch Video Answer Attempt 1 out of 2 Show Examples From a hot air balloon Adriel measures a 22 angle of depression to a landmark that s 743 feet away measuring horizontally What s the balloon s vertical distance above the ground Round your answer to the nearest hundredth of a foot if necessary

Question Answer Attempt 1 out of 2 Watch Video Mamadou leans a 18 foot ladder against a wall so that it forms an angle of 75 with the ground What s the horizontal distance between the base of the ladder and the bottom of the wall Round your answer to the nearest tenth of a foot if necessary foot Show Examples

uestion Watch Video Answer Attempt 1 out of 2 Show Example he angle of elevation to a nearby tree from a point on the ground is measured to be 74 How tall is the tree if the point on the groun 4 feet from the bottom of the tree Round your answer to the nearest tenth of a foot if necessary

Question A boat is heading towards a lighthouse whose beacon light is 113 feet above the water The boat s crew measures the angle of elevation to the beacon 11 What is the ship s horizontal distance from the lighthouse and the shore Round your answer to the nearest tenth of a foot if necessary Answer Attempt 1 out of 2 Watch Video Show Examples

Question Solve for 2 Round to the nearest tenth if necessary x 1 94 72 J

uestion Express tan K as a fraction in simplest terms L 47 M 17 K

4 Suppose a large population has an unknown mean and a known standard deviation 0 4 4 How many individuals should be randomly sampled from this population so that the sample mean is within 0 75 unit of with 95 confidence Answer Previous Answer 133 Q Search Return to overview H hp Jy

Given a stained glass window with 1 29 inches and d portion of the window Note Not to scale Area 1 d 85 1 d square inches 55 inches find the area of the stained glasse

Use the traditional method to test the given hypothesis At the a 0 05 significance level test the claim that a population has a standard deviation of 20 3 A random sample of 18 people yields a standard deviation of 27 1 O There is not sufficient evidence to warrant rejection of the claim that the standard deviation of the population is equal to 20 3 O There is sufficient evidence equal to 20 3 support claim that the standard deviation of the population is O There is sufficient evidence to warrant rejection of the claim that the standard deviation of the population is equal to 20 3 O There is not sufficient evidence to support the claim that the standard deviation of the population is equal to 30 3

the perimeter add each side 2 Find the area of a circle 3 Find the volume of the L x W x H

Find the measure of the indicated angle 1 A This is the only question in this section Question Find m A Answer Attempt 1 out of 2 A

A pyramid was built about 2590 BC Its original height was 518 feet 11 inches but due to loss of its topmost stones it is now shorter Find the current height of the pyramid using the information given in the figure on the right The current height of the pyramid is feet CHCEC 38 8 45 52 the final newer Thed to two decimal places as needed

For problems 1 and 2 let z y be a point on the unit circle with the corresponding angle 0 2 7 1 Use the given information to find tan 8 5 points cos 8 0

2 Let 0 6 a Find y 5 points b Sketch the unit circle and on it indicate the point z y as well

3 A cosine function has the given properties Amplitude 3 phase shift a Write the function in the form y Acos z d where A 0 3 points b What is the domain of the function 3 points c What is the range of the function Use interval notation 3 points d Sketch one period of the graph starting at z 0 Clearly label each intercept and other key points such as max and mins 2

7 In 5 8 Find the value of the variable then find the measure of each angle 5 1 4z 10 32 10y 52 6 8 4x 1 7x 3 7 9x 4 113

Statement ZMON 4x 17 and m2QOP 67 Reason Given

In 1 3 Use the given figure and write a two column proof to find the value of the variable justify each step 1 NIH 10x 5and m2MJK 3x 30 Reason Given Statement m NJH 10x 5 and m MJK 3x 30

N 2 mZMON 4x 17 and mZQOP 67 M M 3 m AEC 23x 83 and m DEB 5 12x 5z 9 D E K B In 4 5 Find the value of the variable then find the measure of each angle 4 8z Statement mZMON 4x 17 and m QOP 67 Statement mZAEC 23x 83 and mZDEB 5 12x 5 4x 1 65 Reason Given Reason Given

3 1 LA20 Er 1 TRIGONOMETRIC RATIOS USING SIN COS AND TAN In 4 6 find sin R cos R tanR Write each answer as a fraction and as a decimal rounded to three decimal places 4 R 6 T 30 T 15 sin R cos R n R 25 2 S 5 S sin R cos R opposite A for adjacent or H for hypotenuse from the indicated angle 3 tan R 24 26 10 R 16 S sin R cos R 34 A

The figure shown is a rhombus HJ has length 6 FG has length 10 Find the length of FJ E H 6 J I

8 Graph the equations below to form the figure Label the coordinates of the vertices 1 y x 2 y 3x 9 3 y 2 x 4 y 5 10 10 5 10 4 points 10 4 points

3 Points A 5 3 and B 7 6 lie on AB Points C 7 6 and D 1 10 lie on CD Which statement is true a AB CD b AB 1 CD C AB CD are the same line d AB CD intersect but are not perpendicular Using the same information from the problem above which statement is true about the length of the segments a AB CD b AB CD c AB CD d Not enough information is given

7 Graph the equations below to form the figure Label the coordinates of the vertices 10 3 y 4 2 3 y 2 x 1 y 1 x 4 x 5y 10 10 4 points a How many sets of parallel sides does the figure have Show calculations to justify your answer 4 points b How many right angles does the figure have Show calculations to justify your answer 1 point c Does the figure have 4 congruent sides Show calculations to justify your answer d What is the most precise name for this figure 4 points 2 points

6 Plot Figure ABCD given the points A 1 3 B 1 8 C 3 3 and D 1 2 10 S 10 10 Loid 4 points O on TBS HAW Ame d What is the most precise name for this figure 10 a How many sets of parallel sides does the figure have Show calculations to justify your answer 1 point b How many right angles does the figure have Show calculations to justify your answer 1 point c Does the figure have 4 congruent sides Show calculations to justify your answer Irbe 2 points 2 points

2x 3y 4 and passes through the point 1 3 ay 3 x 1 by 3 x 1 y 3 x 1 d y 3 x 1 2 3 4 b c y x d y 5x 17 Which equation represents a line parallel to the y axis x 5 y 10 Which statement is true 2x Points A 5 3 and B 7 6 lie on AB Points C 7 6 and D 1 10 lie on CD a AB CD b AB 1 CD c AB CD are the same line d AB CD intersect but are not perpendicular c AB CD d Not enough information is given 3y 2x 4 33 Using the same information from the problem above which statement is true about the length of the segments a AB CD b AB CD 5 Below the equations of lines A B and C are given Determine whether each statement is true or false Line A y x 2 AIC WAS ALB Line B y 6 x 7 1 point each Line C 4x 5y 5

he given point on the unit circle find the six circular function values for s 8 X 17 the value of x or y as appropriate Then assumin X 0 Type an integer or a simplified fraction www

Graph the rational function Answer parts 1 through 7 below X 1 Select the symmetry of the function O The function is symmetric about the y axis O The function is symmetric about the origin O The function has no symmetry about the y axis or the origin 2 Find the y intercept Select the correct choice below and fill in any answer boxes within your choice OA The y intercept is Type an integer or a simplified fraction OB There is no y intercept 3 Find any x intercepts Select the correct choice below and fill in any answer boxes within your choice OA The x intercept s is are Type an integer or a simplified fraction Use a comma to separate answers as needed OB There are no x intercepts 4 What are the x coordinates of the vertical asymptote s Select the correct choice below and fill in any answer boxes within your choic OA x Use a comma to separate answers as needed COL OB There are no vertical asymptotes 5 What is the y coordinate of the horizontal asymptote Select the correct choice below and fill in any answer boxes within your choice OA y OB There is no horizontal asymptote 6 Type the y coordinate for each of the following points 2 2 4

3 Which ordered pair does not fall on the line formed by the other three Hint graph the points to the right 1 16 18 2 12 12 3 9 10 4 3 6 RDBTSNFO7654 Y 20 19 18 17 16 15 14 13 12 11 10 9 8 7 32 2 1 0 F 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 X

estion 8 estion 9 estion 10 T corresponds to x Then findcos x andsin and state which functions are undefined for The point on the unit circle is Type an ordered pair Type an integer or a simplified fraction 1 0 2 0 1 0 0 1

4 The point on the unit circle is Type an ordered pair Type an integer or a simplified fraction 1 0 2 0 1

Lets 1 5 correspond to the point x y a Determine the quadrant where x y is located b Determine whether sins and cos s are positive or negative a Choose the correct answer below A Quadrant III B Quadrant II OC Quadrant IV D Quadrant I b is the value of the function cos 1 5 positive or negative Positive Negative Is the value of the function sin 1 5 positive or negative Negative O Positive

aces Dx where b 0 Determine the equation of the

50 Find the length of the pulley belt shown in Fig 2 87 if the belt crosses at right angles The radius of each pulley wheel is 5 50 cm C Fig 2 87

Let sec A 2 with A in QIII and sec B 5 with B in QII Answer exactly Find sec A B

and closer to the given angle than any other coterminal angle Give the quadrant of the angle if applicable A 103 Choose the correct graph below where the curve on each graph traces the angle beginning at the positive x axis and ending at the ray OA OB 100 B 48 103 F

coterminal with the given angle The correct expression is 315 Type an equation using n as

complementary angles with measures 3x 5 and 4x 31 The angles are Simplify your answer Type an integer or a fraction Type your answer in degrees Do not include the degree symbol in your answer Use a comma to separate answers as now

mea inal with A in degrees not equal to the given measure of the least positive angle that is The measure of the least positive coterms Simplify your answer