Geometry Questions

An artist designed a badge for a school club Figure ABCD on the coordinate grid below shows the shape of the badge D C 4 3 2 111 M Y The badge is enlarged and plotted on the coordinate grid as figure JKLM with point J located at 4 7 and point M located at 2 3 Which of these could be the coordinates for point L 1 point

12 Give a proof You will use all of the blanks Given OLENS and ONGTH Prove ZE is supplementary to T Statements 2 3 5 6 Reasons 1 2 3 5 6

17 50 T K 80 E S 60 65 ATSR 169 156 F R

The area of circle Z is 64 ft N T r Area 7 What is the value of r O r 4 ft O r 8 ft O r 16 ft O r 32 ft

W 8 X O 7 10 N Line segment WX is the radius of circle X and line segment ZY is the radius of circle Y Points W X C Y and Z are all on line segment WZ What is the area of circle C which passes though points W and Z O 81 units O 164 units O 324 units O 1296 units

In the figure angle ZYX is measured in degrees The area of the shaded sector can be determined using the formula N mZZYX 360 X T Which best explains the formula O The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector O The central angle measure of the sector divided by the total angle measure of a circle multiplied by the circumference of the circle will yield the area of the sector O The central angle measure of the sector multiplied by the area of the circle will yield the area of the sector O The central angle measure of the sector multiplied by the circumference of the circle will yield the area of the sector

The diagram shows one way to develop the formula for the area of a circle Pieces of a circle with radius rare rearranged to create a shape that resembles a parallelogram Since the circumference of the circle can be represented by 27 and the area of a parallelogram is determined using A bh which represents the approximate area of the parallelogram like figure O A 27 r O A 2 r 2 A 2 r 1 A 3 2 r

8 feet 3 feet C Garden A circular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet What is the approximate area of the path alone Use 3 14 for T O 172 70 ft O 178 98 ft O 200 96 ft O 379 94 ft

Fiona draws a circle with a diameter of 14 meters What is the area of Fiona s circle O 7 m O 14 m O 28 m 49 m

20 9 What is the area of the shaded sector of the circle O9 units O 27 units 81 units O 162 units

D 3 5 C E B F The radius of circle C is 6 units and the measure of central angle ACB is radians What is the approximate area of the entire circle square units What is the approximate area of the entire sector created by central angle ACB square units What is the approximate area of the shaded region only square units

Arc LM on circle O has a measure of 40 M Which statements are true Check all that apply The central angle measure created by the shaded region is 40 The central angle measure created by the shaded region is 20 The ratio of the measure of ZLOM to the measure of the whole circle is 9 Circle O can be divided into a total of 9 sectors equal in area to sector LOM Circle O can be divided into a total of 10 sectors equal in area to sector LOM

12 11 1 10 9 8 765 2 3 4 What is the sector area created by the hands of a clock with a radius of 9 inches when the time is 4 00 O 6 75 in O 20 25 in O 27 in O 81 in

C A 217 11 T Use the diagram to answer the questions What is the area of the circle in terms of pi units What is the measure of the central angle of the shaded sector What is the area of the shaded sector rounded to the nearest whole number units

What is the approximate circumference of the circle What is the height of the parallelogram What would be the approximate length of the parallelogram if the base were completely straight What would make the estimation of the circle s area more precise What is the area of the circle used to create the parallelogram like shape to the nearest tenth of a square unit 3 AW M

N X 20 3 Y If the radius is doubled what is the effect on the area of sector XYZ O The sector area will be times greater O The sector area will be 2 times greater O The sector area will be 2 times greater 3 The sector area will be 4 times greater

4 72 M N What is the ratio of the sector area to the area of th entire circle 00 0 2 04

Timothy built a base for a circular tabletop The base can support a tabletop with a radius of at least 6 inches but not more than 23 inches What is the smallest possible area of the tabletop that will fit on Timothy s table base Round the answer to the nearest whole square inch square inches What is the largest possible area of the tabletop that will fit on Timothy s table base Round the answer to the nearest whole square inch square inches

The canopy of a parachute is a semicircle with a radius of 13 feet A company that is making parachutes for a Fourth of July celebration wants each parachute to be made from equal parts of red white and blue fabric Approximately how much fabric of each color will be needed to make a single parachute canopy 88 5 ft O 88 5 ft2 O265 5 ft OCE E 42

B A 5 O 4 9 1561 O D Which statement is true regarding the two shaded sectors of circle O Explain O The area of sector AOB is greater than the area of sector DOC because the central angle measures are equal O The area of sector DOC is greater than the area of sector AOB because the radii are equal O The area of sector AOB is equal to the area of sector DOC because the central angle measures are equal The area of sector AOB is equal to the area of sector DOC because the radii are equal

M N 6 L The measure of central angle MNL is radians and the measure of the entire circle is 2 radians The ratio of the measure of the central angle to the entire circle measure is The area of the entire circle is The area of the sector is units VTT units

Which statements are true Check all that apply The ratio of the measure of the central angle to the measure of the entire circle is 5 2 The ratio of the measure of the central angle to the measure of the entire circle is 5 2 The area of the sector is 250 units The area of the sector is 100 units The area of the sector is more than half of the circle s area mZRQP 5 radians radius 10 units R

An engineer is designing a parabolic reflector The area of aperture A is equivalent to times the square of the diameter D If the engineer wants the area of aperture to be at least 15 square feet which of the following inequalities could be used to determine the diameter OA 15 D 4 OB 15 VD O C 15 OD 15 TD

Scientists are examining a substance that has a half life of 10 years The table represents the amount in grams of the substance after x half life cycles X g x 2 750 3 375 4 187 5 5 93 75 6 46 875 What is the average rate of change over the interval 4 6 Round to the nearest hundredth if necessary A 140 62 grams per half life cycle B 70 31 grams per half life cycle C 35 16 grams per half life cycle D 23 44 grams per half life cycle

The graph of f x is shown below 8 6 4 1 2 If g x 10x 2 which statement is true OA The x intercept of g x is less than the x intercept of f x B y A 8 6 4 The x intercept of g x is greater than the x intercept of f x 2 2 4 6 8 2 6 8 X

Jason observed a large art sculpture in a local park and wanted to know its height but the sculpture was much taller than he could measure Jason measured the length of the shadow of the sculpture s highest point to be 15 feet long If the top of a slide in the same park measured at the same time of day has a height of 75 inches and a shadow length of 45 inches how tall is the art sculpture at its highest point OA 30 feet B 45 feet C 20 feet D 25 feet

D 45 24 E What is the area of the shaded sector O 24T O 45T O 72 O 576

Indicate which property is illustrated in Step 3 A commutative B distributive C associative D arithmetic fact Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 5x 1 12x 4 5x 1 12x 4 5x 1 12x 4 5x 12x 1 4 5x 12x 1 4 5 12 x 1 4 17x 5

An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet The yard has 3 sprinkler heads that each cover a circular area with no overlap What is the approximate total area that will be watered O 1963 5 ft O 1963 5 ft O 5890 5 ft O 5890 5 ft

The box plot below represents the ages of campers at a summer camp What can be interpreted from this box plot OB 10 12 14 16 18 Age years O A It can be interpreted that about 50 percent of the campers are from 10 years of age to 14 years of age O C Age of Campers at Summer Camp O D 8 It can be interpreted that about 50 percent of the campers are 10 years of age or older It can be interpreted that about 50 percent of the campers are from 8 years of age to 10 years It can be interpreted that about 50 percent of the campers are 8 years of age or younger of age

If x 28 what is m PQT In the figure above line TQ is tangent to a circle with center S at point Q and chord RQ is a diameter of the circle A 62 B 56 C 68 P D 118 R

Michelle is working on a design for a new building She has built a model of the building according to the client s specifications The height of the model is 15 inches the slant height of the model is approximately 17 inches and the base has a length of 14 inches and a width of 20 inches O A 5 600 cubic inches OB 280 cubic inches 980 cubic inches C W Michelle must order appropriate equipment to heat and cool the building so she must use the model to determine how much space there will be inside What is the volume of her model Round to the nearest hundredth if necessary Note picture not drawn to scale

9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 What is the rule for the transformation from the smaller polygon to the larger polygon O A x y x y 3x 3y OB x y 2x 2y O C x y x y OD x y x y X

Solve for x in the following equation OA 7 O B 72 O C 14 C 14 2x 3

What is the scale factor for this dilation O A OB 1 1 20 1 O C D y 2 9 8 7 6 5 4 3 2 In the dilation shown above the dark colored figure represents the original image and the light colored figure represents the resulting image 0 1 2 3 4 5 6 7 8 9 X

A single six sided die is rolled twice What is the probability of rolling an odd number on the first roll and an even number on the second roll O A B 12 O c 1 4 O D 1 36

Amanda and Steve are preparing for a party Amanda buys flowers from a florist and Steve buys groceries from a supermarket Are the two events dependent or independent Justify the answer The two events are independent because the flowers that Amanda buys affect the groceries that Steve buys The two events are dependent because the flowers that Amanda buys affect the groceries that Steve buys O C The two events are independent because the flowers that Amanda buys do not affect the groceries that Steve buys O D The two events are dependent because the flowers that Amanda buys do not affect the groceries that Steve buys A B

0 S F 25 U AHGE 60 G 35 84 H T

Find the missing length indicated 1 5 6

3r D If tan 0 37 2 a sin 20 FORMULA IS BELOW sin 20 2 sin 8 cos 24 37 find the exact value of each of the following a sin 20 on an exact answer using radicals as needed

37 You want to find this angle 1874 mi You need to find this Discuss within your group 28 Show Transcribed Text Solve the problem for any wind speed and angle Use w for the wind speed and theta for the wind angle Describe but do not try to solve what we would need to do if the

Use the power reducing formulas to rewrite cos 5x in terms of the first power of cosine Simplify your answer as much as possible To indicate your answer first choose one of the four forms below Then fill in the blanks with the appropriate numbers o o o cos 5x cos x cos cos 5x cos x cos cos sx cos x cos 5x cos x OJO 8 X S

A pole leans away from the sun at an angle of 6 to the vertical When the elevation of the sun is 54 the pole casts a shadow 43 ft long on level ground How long is the pole The pole is ft long Round to the nearest foot as needed

ot the complex numbers 3 1 and 1 2 in the complex plane Re X

Select the graph for each system of inequalities below 16 70 4x 4y28 2x ys l A D C B E

Using only the unit circle definition of the sine function find the solution set of the inequality on the given interval 2 2 2 sin x on 0 2x Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is the interval Type your answer in interval notation Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression Os OB The solution set is Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed There is no solution

Find the trigonometric ratio by referring to the figure cot a cot a 30 24 B

25 A plane is steering at S83 E at an air speed of 550km h The wind is from N70 E at 85km h Find the ground velocity of the plane to 1 decimal and include a proper diagram 5 Marks

Question 18 5 two and 2 with multiplicity one There is an ellipse with equation given below x 4 y 16 1 I what are the coordinate of the two foci O none of these answers Question 19 O 0 3 46 and 0 3 46 O 3 46 0 and 0 3 46 O 3 46 0 and 3 46 0

3 46 0 and 0 3 46 O 3 46 0 and 3 46 0 Question 19 Write equation of a line that goes through points 2 3 and 1 5 none of these answers O y 2x 7 Oy 2x 5 O y 2x 5 Question 20 finding the end behavior