2D Geometry Questions and Answers

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

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

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

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

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

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

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

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

In a right triangle the side adjacent to angle has length 3 79 meters and the hypotenuse has length 6 19 meters What is the cosine of the angle cose i e Textbook and Media

Some questions make use of the Interactive Graphing Tool in order to draw a parabola using two points Click the icon to view instructions for the Interactive Graphing Tool Draw a solid vertical parabola overlaying the dashed parabola on the graph Use the vertical parabola tool button on the graphing palette to draw a solid vertical parabola Place the first point at the vertex of the parabola shown as the solid dot on the graph and place the second point at another location on the parabola shown as the dashed curve on the graph Click to enlarge graph Careful Be sure to use a second point that is exactly on the parabola causing the dashed curve to be completely covered 8 6 A 4 P 8 Ay 6 9 1 2 14 6 48 40

For the function find the points on the graph at which the tangent line is horizontal If none exist state that fact y 2x 8 List all the points where the tangent line is horizontal Select the correct choice below and if necessary fill in the am A The point s at which the tangent line is horizontal is are Type an ordered pair Use a comma to separate answers as needed B The tangent line is horizontal at all points of the graph C There are no points where the tangent line is horizontal

8 A girl 160 cm tall stands 360 cm from a lamp post at night Her shadow from the light is 90 cm long How high is the lamp post 6104

5 Your new job requires you to calculate the material costs for manufactured goods One of goods you manufacture is a fabric sample in the shape of a circle Given the formula A Tr find the 2 area A of the fabric sample whose radius r is 6 2 x 105 m Write your answer in scientific notation Use 3 14 for T A m

If you already know lal and lvl then the formula a xv2 gives a convenient way to ind the curvature Use it to find the curvature and radius of curvature of the curve r t cost t sin t i sin t t cos t j t 0

O GRAPHS FUNCTIONS AND SYSTEMS Finding the slope and y intercept of a line given its equation in Find the slope and the y intercept of the line 7x 2y 10 Write your answers in simplest form slope 0 y intercept 8 08 X Undefined

A car has wheels with a 8 inch radius If each wheel s rate of turn is 3 revolutions per second find the angular speed in units of radians second 3 n 8 24 3 n 6 3r

Find a solution to the equation sec B 12 csc 29B 10

1 Find the length of arc s in the diagram below To the nearest tenth 8 in 60 S

1 If DE is the perpendicular bisector of AC which of the following statements is not true A BD BE OZABD CBD OAB BC AD CD D B E C

4 Find the height in centimeters of a square pyramid with a volume of 455cm and a base edge length equal to the height Give the approximate answer rounded to 2 decimal places

2 A tent is in the shape of a right pyramid with a square floor The square floor has side lengths of 8 feet If the height of the tent at its center is 6 feet what is the volume of the tent in cubic feet

graph of the hyperbolic paraboloid 2 x 9z Choose the correct graph of the hyperbolic paraboloid OA O C OB O D y

Determine the graph of the paraboloid z x 9y Choose the correct graph of the equation OA B O C Y

5 In the diagram below a plane intersects a square pyramid parallel to its base Which two dimensional shape describes this cross section 6 A solid metal prism has a rectangular base with sides of 4 inches and 6 inches and a height of 4 inches A hole in the shape of a cylinder with a radius of 1 inch is drilled through the entire length of the rectangular prism Find the volume of the entire rectangular prism Find the volume of the cylinder 4 in 4 in What is the approximate volume of the remaining solid in cubic inches 6 in

find the area of segment coloured in red A D 400m A B 340m B D 260m triangle is above centre point G A weat wosk

m 1 N L Find the measure of each marked angle in the figure when m1 3x and m2 2x 10 2 u m t C O S

B a 80 b 120 16z 12 E 2z 4 D c 12 d 141

9 Which is mVXU a 15 W a 105 b 120 9x 18 X V T 15x U 3x 21 c d 122 5 126

anu 0 H Not drawn to scale Given m HJF 84 are shown Which statement if true would help prove that quadrilateral FGHJ is inscribed in Circle O and why a m JFG 84 for a quadrilateral inscribed in a circle adjacent angles are congruent b m JFG 96 for a quadrilateral inscribed in a circle adjacent angles are supplementary c m FGH 84 for a quadrilateral inscribed in a circle opposite angles are congruent d m FGH 96 for a quadrilateral inscribed in a circle opposite angles are supplementary

12 What is m XYZ a 83 166 b 979

16 Write the equation of a circle with center M 7 10 and radius 2 a x 10 y 7 4 b x y 7 10 4 c x 7 10 4 d x 7 10 2