Geometry Questions

2 Anton will be constructing a segment bisector with a compass and straightedge while Maxim will be constructing an angle bisector with a compass and straightedge Describe the similarities and differences between their construction steps

The equation for line s can be written as y x 4 Line t which is parallel to line s includes the point 3 2 What is the equation of line t Ver en espa ol Write the equation in slope intercept form Write the numbers in the equation as simplified proper fractions improper fractions or integers pla

1 2 3 Graph the function h x 2x 1 4 5 6 X

1 Tie 2 Graph the function h x 2x 1 6 3 Co 6 4

EDis a secant BCis tangent to circle A at point B E A b B D a C If b 45 and c 4 then a C units

For problems 8 10 solve the triangles Round to the nearest tenth 67 V 49 50ft

Prove the identity Cos Statement sill Note that each Statement must be based on a Rule chosen from the Rule menu To see a detailed description of a Rule select the More Information Button to the right of the Rule Validate COEX sil Rule Select Rule 3 0 J X 0 6 3

latch the equation with the surface it defines Also identify the surface by type paraboloid ellipsoid etc 4z x Which graph below shows the surface OA OA Ellipsoid OB Elliptical cone OC Paraboloid OD Hyperboliod OB O C

nd the component form of the unit vector obtained by rotating the vector 0 1 210 counterclockwise about the origin Choose the correct answer below OA 2 2 OC 1 OE 2 2 2 2 2 2 OB OD OF 1 2 2 2 2 3 2 1 31 22

eltaMath Back New Problem Show Solution Ms Bodner Simplifying Fractions Jul 17 2 11 21 PM Simplify the following fraction 3 Answer rogress Submit Answer Report Bug 05 23 75 100 75 1 3 5 15 25 25 100 1 2 420 225 50 100 75 100 3 4 01 13 13 15 20 11 21 90 21 1 3 90 on I 4 8 7 21

Watch help video Solve for 2 Round to the nearest tenth if necessary 48

Match each symbol to the corresponding vocab words from set theory CCB a Intersection An B AUB AC b Union c Subset d Complement

Set A is the set of factors of 24 set B is the set of even natural numbers less than 25 and set C is t set of even natural numbers less than 13 The universal set U is the set of natural numbers less than 24 Use the sets given below to answer questions a g A 1 2 3 4 6 8 12 24 B 2 4 6 8 10 12 14 16 18 20 22 24 C 2 4 6 8 10 12 U 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 What is An B

Use the complement of calculate the indicated probabilities One pile of cards contains the number 2 through 6 in red hearts A second pile of cards contains the numbers 4 through 8 in black spades Each pile of cards has been randomly shuffled If one card from each pile is chosen at the same time what is the probability that the sum will be less than 12

The numbers 1 through 30 are written on slips of paper that are then placed in a hat Students draw a slip to determine the order in which they will give an oral report Event A is being one of the first 10 students to give their report Event B is picking a multiple of 6 If you pick first calculate each of the indicated probabilities P A

If the radius of a circle is 6 Inches then the area of a sector bounded by a 100 arc is Round the answer to the nearest tenth of a square Inch square inches

Terrance wants to determine the height z of a nearby tree He stands 29 feet from the base of the tree The measure of the angle of elevation from Terrance s feet to the top of the tree is 53 Select all of the following that can be used to find the height of the tree x 29 sin 531 A B C D E F I E 29 sin 37 29 cos 53 29 cos 37 x 29 tan 531 P 29 tan 37 A

20 The given cylindrical container is used to fill the fish tank a rectangular prism with water 3 in 8 in 24 in containers 24 in 12 in What is the least number of full cylindrical containers needed to completely fill the fish tank

16 Determine whether the triangles are similar A 12 64 B 16 A The triangles are not similar B The triangles are similar by AA similarity The triangles are similar by SAS similarity D The triangles are similar by AAS similarity D 9 64 C EA 12 F

13 Examine parallelogram QUAD below D 6x 12 Q B x 11 Select all of the following values that are correct A2 13 cm Q 114 D m U 54 E mZA 126 F m D m D 66 52 1 A U

5 Find the value of a that makes AOLD AAGE E x A 3x 5 58 D 2 36 x 15 L G

Use the figure below to find RT M RT 4x 1 A R 3x 3 T

Order the side lengths of the triangle from shortest top to longest bottom A E 40 11 AB BC B 50 C

Which additional Information would be necessary to prove that ATOY ACAR using the Side Angle Side Congruence Thec Y T 2T LC B ZY ZR TY CR OY AR A C R

15 As modeled below a movie is projected onto a large outdoor screen The bottom of the 60 foot tall screen is 12 feet off the ground The projector sits on the ground at a horizontal distance of 75 feet from the screen 60 12 75 0 Determine and state to the nearest tenth of a degree the measure of 8 the projection

9 B 7x 1 Select all that apply A m BAC 62 A C D Using the figure above which of the following angle measures are correct Bm ABC 61 D cm BCA 48 9x 11 m BCD 132 14x 6

8 00 APIG shown below undergoes a dilation by a scale factor of through a center point at the origin to produce AP I G 6 5 PI G 8 16 7 1054 6 10 W t 0 1 2 3 4 5 6 7 8 x 23 2 3 4 5 567 8 Select all of the statements that are true A P 2 1 BI 0 0 CG 1 3

D O O 4 D G 84 7 6 6543 2 y 3210 1 2 3 4 5 6 7 8 x 2 3 5 6 7 8 What are the coordinates of D O and G

Lines a and b are parallel Both lines are intersected by transversal p as shown in the Image below What is the value of T 7x 2 4x 9 b

7 Is reflected over the line y a to produce 8 76 N 8 7 64 5 43 2 He 2010 10 1 2 3 4 5 6 7 8 x 4 3 4 in 6 5 y 6 7 8 T What will be the coordinates of N A 5 3 B 5 3 C 3 5

16x 8 B m BAT m CAT A degrees T 4x 8 C degrees own below

4 Given 22 23 and 24 25 Prove 21 25 1 2 3 Fill in the missing proof reasons using the drag and drop responses below 4 5 Statement 22 23 21 22 21 23 24 25 5 23 24 Reason Given Transitive Property of Congruence Vertical angles are congruent DRAG DROP THE ANSWER Given Vertical angles are congruent Supplementary angles are congruent Transitive Property of Congruence Reflexive Property of Congruence XE

6 As modeled below a projector mounted on a ceiling is 3 74 m from a wall where a whiteboard is displayed The vertical distance from the ceiling to the top of the whiteboard is 0 41 m and the height of the whiteboard is 1 17 m 3 74 m 0 41 m 1 17 m Determine and state the projection angle to the nearest tenth of a degree

xtra Practice 1 A quadrilateral has vertices at A 3 1 B 5 9 C 7 1 and D 3 3 Prove that the midsegments form a parallelogram 10 14 lie on a circle with

What is the rate of return when 25 shares of Stock A purchased for 30 share are sold for 825 The commission on the sale is 6 Rate of Return Give your answer as a percent rounded to the nearest tenth Enter

Tax Table Standard Deduction Taxable income Income Tax Rate 0 9 700 9 701 39 475 39 476 84 200 84 201 160 275 Above 160 275 12 200 00 10 12 22 24 32 37 A 48 200 B 38 500 C 26 300 D 36 000 After applying the standard deduction how much of a 48 200 salary is taxable income

This table shows the amount of commission earned for a broker receiving 2 5 commission on sales How much would this agent earn in commission for 1 000 000 in sales Commission Earned Sales in thousands of Commission in thousands of A 40 000 B 400 000 C 25 000 D 250 000 200 5 400 10 600 15 800 20 1000

67 A lake is in the shape of an isosceles triangle as shown in the picture You want to go from point A to point E 4 miles away on the opposite side of the lake in the shortest time possible You can walk at a rate of 4 miles per hour and row a boat at 2 miles per hour How should you proceed You may row a boat from A directly to E but that may not be the shortest time possible or is it Instead you may walk along the shore to a point B and then row a boat from B to E Determine the point B that will minimize the time of your travel A 0 0 B r C 4 2 E 4 0 D 1 2

Graph the hyperbola x 4y 6x 24y 63 0 12 4 124 0 a 9 S 4 NO 10 2 2 12 23 41 4 14 OX X V

V Find an equation of the line L The equation is Tyne an equation Simplify your answer

deo The angle below is the image formed when a figure containing RS is dilated by a scale factor of 5 What is the measure of ZRST R 94 S T

What is the volume of a hemisphere with a diameter of 8 9 cm rounded to the nearest tenth of a cubic centimeter

Match each of the coordinate points on the unit circle with the given angle V 3 1 22 0 1 1 0 2 4 22 3 1 4 2 2 1 2 3 5 2 81 3 4 5 6 7 6 5 25 6 4

Step Prove ABEC ADFA H 5 arallelogram BE 1 AC and DF LAC pa Statement Type of Statement ABCD is a parallelogram BEL AC DF LAC B E Reason Given F C

Give one pair of supplementary angles and one pair of vertical angles shown in the figure below 1 2 3 4 5 6 m 8 a Supplementary angles b Vertical angles X 40 and and 40 40 and 40

Give one pair of vertical angles and one pair of supplementary angles shown in the figure below 7 8 5 6 3 4 12 a Vertical angles b Supplementary angles X 40 and 40 40 and 40 G

For problems 1 and 2 find the value of each variable If your answer is not an integer express it in simplest radical form 1 2 12 7 45 b

points A supplier is late with a delivery which has caused a delay in completion of Derek and Addison s project In which part of their project status report would Derek and Addison discuss this Problems encountered Project overview Impact on budget The delay should not be mentioned

Multiple Concept Example 9 deals with the concepts that are important in this problem A grasshopper makes four jumps The displacement vectors are 1 33 0 cm due west 2 28 0 cm 44 0 south of west 3 20 0 cm 63 0 south of east and 4 23 0 cm 60 0 north of east Find a the magnitude and b direction of the resultant displacement Express the direction as a positive angle with respect to due west a Number i b Number i 72 73 8 Units Units TA 0 7 W Start N S E

You are driving into St Louis Missouri and in the distance you see the famous Gateway to the West arch This monument rises to a height of 192 m You estimate your line of sight with the top of the arch to be 7 71 above the horizontal Approximately how far in kilometers are you from the base of the arch Number Units