Geometry Questions

Use the circle below S 71 R 46 X T 8 Find mZSTR a 23 b 152 c 142 d 92

Use the circle below for questions 8 10 E D A 52 B C 4 Find mED a 52 b 38 5 Find mAC a 38 b 52 6 Find mBCD a 38 b 52 c 142 c 90 c 148 d 308 d 308 d 308

Use the diagram below for questions 1 3 U P V IT S R 1 Which of the following is a radius B US C RT A PV D PQ 2 Which of the following is a tangent B US C RT A PV D PO 3 Which of the following is a central angle A ZPVU B ZUST C ZOUS D ZUSR

A tank in the shape of a hemisphere has a diameter of 18 feet If the liquid that fills the tank has a density of 84 8 pounds per cubic foot what is the total weight of the liquid in the tank to the nearest full pound

5323 19AM Question 3 The figure below is a triangular prism What is the volume of the prism if the area of its base is 14 square centimeters 18 cm A B uddan C D 32 cubic centimeters 126 cubic centimeters 252 cubic centimeters T25 Geometry 34 A 324 cubic centimeters

Square RSTU is shown below with a line AB drawn through its center If the square is dilated using a scale factor of and a line is drawn through the center of the new dilated figure what relationship will that line have with line AB in the drawing below 10 points S A T B

am How do we know that alleles actually separate during gamete formation A Scientists are unsure whether the alleles separate B Zygotes will not reach maturity if the alleles do not separate C If the alleles did not separate recessive alleles would never reappear

A 55 pound box sits on a ramp with 24 incline So the box experiences a force of 55 pounds straight down into the earth 4 Find the magnitudes of the force vector perpendicular to the ramp FL pounds and the force vector parallel to the ramp F pounds Round to at least 1 decimal place

G Z E U 4 Explain the relationship between point Z and the triangle Justify with the applicable theorem 5 If the length of GU is 18 units what is the length of GZ Show all your calculations and unit measurements 6 If the length of ZT is 4 8 units what is the length of OT Show all your calculations and unit measurements

22 Describe the transformations a y 2x 5

r answer to two decimal places if necessary The slanted sides of the trapezoid are 12 4 mm long 12 mm 19 mm 25 mm 20 mm

Graph the given parent function after the set of transformatic 1 2 3 5 1 f x 3 2 2 2 7 4 2 f x 1 2

8 5 pts Openstax 6 5 253 A cone shaped tank of depth H has a cross sectional area that increases with its depth A Show that the work to empty it is half the work for a cylinder with the same height and base r h H

A balloonist is directly above a straight road 1 9 miles long that joins two towns She finds that the town closer to her is at an angle of depression of 39 and the farther town is at an angle of depression of 32 How high above the ground is the balloon 399 1 9 mi Not to scale 320 The balloonist is about miles above the ground Round the final answer to two decimal places as needed Round all intermediate values to four decimal places

Find the surface area and volume of the following solids 1 5 cm 6 cm 8 7 cm

In order to maintain a healthy weight an average adult dog that weighs 17 kilograms must consume 13 grams of dog food per kilogram of its body weight each day A specialty pet store sells dog food by the cup where 6 cups of dog food weighs 558 grams About how many cups of dog food should the dog consume each day in order to maintain a healthy weight A 0 40 B 2 17 C 2 38 D 0 42

One rectangle is framed within another Find the area of the shaded region if the frame is 1 unit wide

Ho The shift and reported symptoms are H The shift and reported symptoms are not This hypothesis test is a right tailed Part 2 of 4 Part 2 4 Part 3 of 4 Find the P value Round your answer to four decimal places The P value is 0 2439 Determine whether to reject Ho test independent independent

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