Geometry Questions

Three business partners Shelly Ann Elaine and Shericka share R150 000 profit from an investment as follows Shelly Ann gets R57 000 and Shericka gets twice as much as Elaine How much much money does Elaine receive A R 124 000 BR 101 000 C R 62 000 DR 31000

In the figure A B C and D are points of tangency calculate x a 20 d 36 B A 130 b 60 778 D D c 40

Determine the leading coefficient for the rational function graphed below Write as a reduced fraction with no spaces

0 t A 0 0 2 3 1 00 0 Compute e by summing the power series

90 B 26 26 A D C Drag the RED and GRE below Then solve the following situation algebraically on the whiteboard below ZABD and ZCBD form a linear pair and have EQUAL measure m ZABD CHF Submit

11T 6 Use the x y coordinates in the figure to find the value of tan or state that the expression is undefined Select the correct choice below and if necessary fill in the answer box to complete your choice O A 11x 6 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize the denominator OB The expression is undefined tan 1 3 2 2 3 1 2 2 3 2 1 0 2 1 2 2 0 1 0 1 T 3 T 166 1 0 1 3 2 2 3 1 2 2 3 2 2 7 2 3 2 X

Find the first fundamental form of polar coordinate of xy plane First fundamental form of plane is x noso y rsino x y roso asinos

0 3 Find the area of the composite figure below Be sure to label the unit 6 in 9 in 11 in 9 in 11 in

Find the value of x in the isosceles triangle shown below 80 83 8 80

What is the area of this figure 6 mm 12 mm 4 mm 5 mm 5 mm 5 mm 5 mm 4 mm t 11 mm 7 mm 5 mm 12 mm

A 8 12 8 Determine the following cardinalities n A n C 19 n An C n AUB 21 n AUBUC n An BnC Help 7 7 Video B

If these are the degrees for the top of a hat measuring 7 5 8 I needed to know what the degrees for 7 7 1 8 7 1 4 7 3 8 7 1 2 7 5 8 7 3 4 and 8 would be So I just needed to know the degree of each angle at those measurements Hat 75 8 62 5 Degrees 55 degrees 62 5 Degrees 62 5 Degrees a 55 degrees 62 5 Degrees

Use the Pythagorean Theorem to find the value of x to the nearest tenth if necessary X 14 13

Use SOH CAH TOA to find the value of x to the nearest tenth 7 8 34

Solve the triangle with the given measures a a 3 4in b 2 6in and C 48 b a 6 b 8 c 10

BD OC CD and AB I OD B 36 m COD D m OCD O C

The distance from the star S to the planet X is approximately 148 700 000 kilometers km The distance from S to the planet Y is approximately 57 900 000 km The elongation angle a is the angle formed between the line of sight from X to S and the line of sight from X to Y See the figure on the right Suppose that the elongation angle is 13 Use this information to find the possible distances between X and The larger distance from X to Y is Do not round until the final answer km Then round to one decimal place as needed

11 If ARST is isosceles find mZS 15x 31 R T 9x 11 S

If AB CD find the measures of angles x y z 9 1 C x 140 B D

3 Find LDAB and ZCAB D A X 30 x 30 E B

2 Find m DAB if AC bisects LDAB A D 2x 40 x 7 B

1 Find the volume of the prism 7 ft 7 ft 240 ft 343 ft 251 ft 232 ft 7 ft

Marcus has a balance of 2 800 on his credit card The credit card has an annual interest rate of 15 compounded monthly 1 25 each month Marcus uses his credit card for various expenses throughout month and at the end of each month makes a 325 payment Use this information to complete the table below Round to the nearest cent as needed Month 1 2 3 4 5 Prior Balance 2800 2806 09 1 25 Interest on Prior Balance 35 99 Additional Charges 378 280 216 477 Monthly Payment 325 325 325 325 Ending Balance 2800 2806 09

Given AB II CD AB CD Prove AE CE A D E B

Suppose you borrow 1000 at a 12 annual interest rate compounded monthly 1 each month At the end of each month you make a 100 payment Use this information to complete the table below Round to the nearest cent as needed Month 0 1 2 3 4 51 S Prior Balance 1000 910 819 10 1 Interest on Prior Balance 10 9 10 8 19 Monthly Payment 100 100 100 Ending Balance 1000 910 819 10 727 29

Suppose you invest 3800 in an account with an annual interest rate 6 compounded monthly 0 5 each month At the end of each month you deposit 325 into the account Use this information to complete the table below Round to the nearest cent as needed Month 1 2 3 4 LO 5 Prior Balance 3800 4489 72 Question Help D Video 0 5 Interest on Prior Balance 24 19 Monthly Deposit 325 325 325 325 Ending Balance 3800 4489 72

of the two triangles ABC and DEF are similar Find the measure of AB A B 3 6 OAB 1 28 AB 1 66 AB 2 5 AB 8 4 E C 3 6 7 8 D 4 9 F

What is the value of x in the triangle ABC if the given triangles are similar A C 5 cm O 10 cm O 12 cm 16 cm 10 X B E 14 cm D 7 cm F

a Apply the Brute force algorithm to find the minimum cost Hamiltonian circuit on the graph below 10 Marks 9 9 s 6 5 15 14 N H 10 8 12 g 30 20 h b If a sequence has a first term of an 12 and a common difference d 7 Write the formula that describes this sequence Use the formula of the arithmetic sequence Hint Use the brackets for subscripts eg for an you can use a n 5 Marks GRA

CR Geometry B GP 5 Which is the angle of depression from the top of the waterfall to Jim 8 5 6

Find a matrix P such that PTAP orthogonally diagonalizes A Verify that PTAP gives the proper diagonal form Enter each matrix in the form row 1 row 2 where each row is a comma separated list A P PT AP 0 10 10 10 5 0 10 0 5 2 1 1 1 3 2 2 1 0 0 0 0 15 0 0 0 15 X

10 miles Q Eric walks around a man made circular lake pictured above four times How far in miles has he walked Eric has walked a total of miles Use 3 14 or the button on your calculator Round your answer to the nearest tenth Question Help Worked Example 1 Video

3 Which is the angle of elevation from the boat to the lighthouse 1 2 1 1 1 3 1 1 4

An angle measures 12 degrees less than three times it s supplement x Find both angles algebraically Check the measure of the smaller angle below Angle smaller larger total Measure Correct X X X

8 m Perimeter Area 3 m 7 m 5 m I xm m Question Help Message instructor

Figure A shows their paths and the locations where they each catch a Pokemon Note The small squares in the grid have side lengths of one yard and areas of 1 square yard Figure A Dolores start Marianne The red vertical line represents the path Dolores walked How far did Dolores walk before she caught a Pokemon yards The blue horizontal line represents the path Marianne walked How far did Marianne walk before she caught a Pokemon yards What is the distance between the spot where Marianne caught a Pokemon and the spot where Dolores caught a Pokemon yards

m21 2x 3 m25 4x 7 H These angles are which are always X m41 m45 angles Diagram not to scale N P M4 2 1 3 4 A 5 T R

12 m 2 m Perimeter Area 10 m 4m m E Question Help Worked Example 11 Video 1

A rectangular swimming pool has a length of 32 feet a width of 11 feet and a depth of 6 feet Round answers to the nearest hundredth as needed a How many cubic feet of water can the pool hold cubic feet b The manufacturer suggests filling the pool to 95 capacity How many cubic feet of water is this cubic feet

Find the perimeter and area of the figure pictured below 8 m Perimeter H Area 3 m fr 5 m m m Question Help Message instructor

12 2cm EA 80m A b Find the values of X and y 12cm 13 5 a What scale factor is applied to triangle A to create triangle B Explain your reasoni B 6 F B X

5 In the two triangles pictured below m A m D and m B m E Using a sequence of translations rotations reflections and or dilations show that AABC is sim to A DEF

You may use a calculator and your reference chart 1 Select all the true statements for triangles ABC and XYZ B A ZA ZX B ZX ZC AB C XY A BC D AC 12 Similarity End of Unit Assessment BC XZ YZ XZ 20 16 C X 3 Y 5 4 Z

8 cm D 2 cm E A X 12 cm b What is the length of XF Explain your reasoning C F B a ABCD is a parallelogram and EF is parallel to AB What triangles are similar to triangle AEX Show your thinking

Polygon ABCD is congruent to Polygon WXYZ Find x and then m BCD and m XYZ D x A 9x 11 B m2 BCD m XYZ C Z Y 11x13 Note Always make sure the value of a produces positive angles W

Polygon ABCD is congruent to Polygon WXYZ Find x and then AB and WX A x D 4x 10 AB WX B C Y Z X 6x 4 Note Always make sure the value of a produces positive lengths W

2 Let F R R be given by f x y x ay x y 3ry a Why is f differentiable b Find dF z c Find and interpret dF 2 1 d Find and interpret dF 2 1 3 1

Find the value of x in the figure P R 7x 5 x 47 Q S

x 8x 12 0 a Write the equation in vertex form by completing the square b What is the vertex axis of symmetry and what direction does it open Explain what each of these parts of the graph are c Use your vertex form to solve the equation What do the solutions represent d Use the quadratic formula to solve the given equation How do your answers compare e Evaluate the two methods used to solve which do you

Find the measure of the missing angle in the following figure if the two lines cut by a transversal are parallel 60