Geometry Questions

3 Find m PST Q P S 11x 3 5r 9 T H

From the last problem we figured out that x 12 23 38 24 83 25 59 Now it is time to describe some of the other angle relationships m2MAY Select all that apply 23 24 28 25 24 25 142 0121 by the Angle Addition Postulate M B 3 Q S A R

Find the area of the regular octagon below Round to the nearest centimeter Be sure to label the unit 3 cm 2 5 cm

Find the approximate value of using the trapezoidal rule with four subdivisions Draw a graph to illustrate The estimated value is Give your answer accurate to four decimal places This answer is an x dx 3 under estimate over estimate Explanation of answer above because the function is concave up because the function is concave down because the function is increasing because the function is decreasing

ind the area of the regular pentagon below Round to the nearest meter Be sure to label the unit 4 9 m 7 1 m

If A B and I are collinear and AC 24 find AB and BC A 2 x 5 B X 2 C

Given AC bisects LCAB 60 Prove LDAB 120 L DAB A D C B

Given LADBE LCBD LCDB LABD Prove AABRE D ACDB A D B

The two triangles below are similar 15 I 36 40 10 104 K X 40 18 104 30 20 W Complete the similarity statement AUK A What is the similarity ratio of the first triangle to the second triangle Simplify the similarity ratio and write it as a proper fraction improper fraction or w number

8 Which triangles are congruent and by what theorem you can just give the names no proof needed for this one Find x and y A E 2x ry B 4x 10 D Sx 15 C F

Given CD is a median AC BC Prove LACD LBCD A D B

Find the supplementary angles A C 2x 30 5x10 D B LADC and LCDB

A Find x y and z if LABC ADEF 5 x E Z 11 F

2 3 Indicate three different bases for the following three congruent triangles and draw in the perpendicular height for its base on each shape Now measure in centimetres to one decimal place for each triangle the base and its corresponding perpendicular height and use the table provided to calculate the area of the triangle using the formula Area of A base X1 height A ABC Triangle Base A B C B3 A2B2C2 B1 C3 C A2 B2 Perpendicular height Area C

70 99 a Enter the values of the exterior angles for this quadrilateral in the table and calculate the sum b Drag the points to create two new quadrilaterals and complete the table for both of these c Move to the next slide and do the same for a pentagon What do you notice What do you wonder A B C Sum of Angles

Which side lengths form a right triangle Choose all answers that apply A 2 3 4 8 3 17

What other polygon do you see in the design What is the polygon with the most number of sides that you can find in this design

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