Geometry Questions

Find the length of the leg If your answer is not an integer leave it in simplest radical form Select one a 24 24 Ob 12 2 288 d 2 3 C 45

Find the length of the hypotenuse 45 Select one a 18 b 6 C 12 3 2

A rectangular lot is 165 feet long and 90 feet wide How many feet of fencing are needed to make a diagonal fence for the lot Round to the nearest foot

Find the length of the missing side Leave your answer in simplest radical form Select one 10 ft a 206 ft b 2 74 ft c 26 ft 14 ft Time le

Find the length of the missing side Select one a 8 b 64 C 23 O d 4 17 15

Determine if the function in the graph is one to one 4 A The function is one to one B The function is not one to one Determine if the function in the graph is one to one A The function is one to one B The function is not one to one Determine if the function in the graph is one to one R

Determine the leading coefficient for the rational y 10 8 3 6 8 10

0 1 pt10099 Details A communications tower is located at the top of a steep hill as shown The angle of inclination of the hill is 79 A guy wire is to be attached to the top of the tower and to the ground 94 m downhill from the base of the tower The angle formed by the guy wire is 9 Find the length of the cable required for the guy wire 79 length of guy wire 9 94 m NOTE The picture is NOT drawn to scale m Enter your answer as a number your answer should be accurate to 2 decimal places

1 point 3sin x tan x 3 sin x 0 Find all angles in radians that satisfy the equation For each solution enter first the angle solution in 0 or 0 2 depending on the trigonometric function then the period When 2 or more solutions are available enter them in increasing order of the angles e g x 2 2k or x 3 2 k etc Note You are not allowed to use decimals in your answer Use pi for X or X or V

BY USING MATHEMATICA SOFTWARE 1 Given four points 0 1 1 2 2 2 and 3 1 with no order Plot a control polygon connecting four given points to generate the following cubic B zier curve DA a h c d e

Next question You can retry this question below Points A and B are separated by a lake To find the distance between them a surveyor locates a point C on land such than ZCAB 44 3 Find the distance across the lake from A to B C Get a similar question 459 yd distance B 315 yd NOTE The triangle is NOT drawn to scale yd 1 44 3 Enter your answer as a number your answer should be accurate to 2 decimal places Question Help Worked Example 1 A

core 0 7 3 7 answered 3 o Question 3 Details Submit Question 0 1 pt100 99 Find c if a 2 7 mi b 3 83 mi and ZC 41 9 degrees Enter c rounded to 3 decimal places C mi Assume LA is opposite side a LB is opposite side b and LC is opposite side c Question Help Video

3 3 43 3 3 a 10 pts Find the matrices A6 and A8 A 2 b 10 pts Use the matrices found in part 1 to find A 4 Question 3 20 points Let A be a 2 x 2 matrix

Question 9 0 1 pt100 99 Details 31 A pilot is flying over a straight highway He determines the angles of depression to two mileposts 5 3 mi apart to be 31 and 45 as shown in the figure 5 3 mi 450 A B NOTE The picture is NOT drawn to scale Find the distance of the plane from point A distance from A mi Find the elevation of the plane height mi Enter your answer as a number your answer should be accurate to 2 decimal places Question Help Worked Example 1

A 2x 16 L C I E F J 3x K H B D

Find a constant h for which the vectors 3 and h are orthogonal 6 pts

At what point do the curves r t t 5 t 35 t and r s 7 s s 2 s intersect x y z Find their angle of intersection 0 correct to the nearest degree 0

In the circle below suppose m VUX 204 and mZUVW 95 Find the following a mZVUX b m ZUXW ZVUX 0 ZUXW

Use the Unit Circle below to evaluate each trig function Rather than give a numeric value write your answer using the appropriate coordinate label shown in the figure m n o p q r s t kl u v ij w x g h v z e f c d a b o COS sin 3 3T COG 3 sin 5T 6 COS 7 3 4 sin 5T 3

1 A 6 10 B e D E A B C do rusal 3 DE AE AB 6 cm BC 10 cm Yukar daki verilere g re AE ka cm dir A 6 2 B 6 3 C 9 2 D 12 E 12 2

6 B 10 A 8 X T ki ember K ve L noktalar nda kesi mi tir T te etin de me noktas d r PB PL PT P PA 8 cm AB 10 cm oldu una g re PT x ka cm dir A 9 B 10 C 12 D 15 E 16

Which of these is an equation of one of the asymptotes of the function f x 7 sec X x X X x 32 8 2 1 2 4 sec 1 2 xXx 1 x 4 None of the above

7 Construct an angle with measure equal to 2 m MOV mZVOR Label It ZHGJ

Complete the proofs below by filling in the missing statements and reasons 19 Given 21 and 22 form a linear pair 21 23 Prove 22 and 23 are supplementary Statements 1 21 and 22 form a linear pair 2 21 and 22 are supplementary 3 m 1 m2 180 4 21 23 5 m 1 m 3 6 m 3 m2 180 7 22 and 23 are supplementary 1 2 3 4 5 6 7 Reasons 3 2

Evaluate the flux integral SF ds where F x y z x 1 y 2 3 and C is the outward upward oriented half sphere z 9 x y 0 z 3

28 Given WY XZ Prove WX YZ 1 WY XZ 2 WY XZ 3 WX XZ WZ WY YZ WZ 4 XZ YZ WZ Statements 5 WX XZ XZ YZ 6 WX YZ 7 WX YZ 1 2 3 4 5 6 7 W X Y Reasons

30 Given 21 and 23 form a right angle 21 and 22 are complementary Prove 22 43 Statements 1 21 and 23 form a right angle 2 21 and 23 are complementary 3 21 and 22 are complementary 4 22 23 1 2 3 4 A Reasons D C

Complete each proof 18 Given 3 2x 7 29 4x Prove x 4 Statements Reasons

In the diagram O is the centre of the circle with radius OC ABCD is a cyclic quadrilateral N is another point on the circle such that BC is parallel to ON OE bisects chord BC at Eu GC is a tangent to the circle at C GC and ON are produced to meet at F C 20 D B 150 10 1 Calculate with reasons the size of 10 1 10 10 1 2 D 10 1 3 C 10 1 4 D 10 2 OECF is a trapezium with OF 3y and EC 2x Using the formula below determine the length of OE in terms of x and y if the area of OECF y x Area of a Trapezium sum of the parallel sides x1 height 2 2 2

swer each of the following questions about transformations a Write the equation of a function that has been transformed up 4 adn right 3 from its parent function b In the function f x 3x4 8 what does the 3 coefficient tell you c In a function how do you determine if there is a horizontal stretch compression

Write the complete factored form of fix 1x 3x 7x 7x 3 zeros 1 33 1x 0 Type your answer in factored form Use integer

If the mBC 47 cm when the m BAC 60 what is the area of the sector of the circle defined by ZBAC and BC 12 cm 24 cm D A C B 144 cm 2 47 cm

Ed 16 5 O B LL F M FB is tangent to the circle shown Given FB 12 and AF 8 what is Al O 18 10

In circle W m VWX 119 Solve for x if mVX 12x 27 If necessary round your answer to the nearest tenth V W X

8 2 5 12 Determine critical points draw the phase line and sketch the solution y 4 y dx

G is an enlargement OT Find the centre 5 scale factor 5 O 5 G G D 5

Find the measure of ZPQR List in sequence with reasons the angles you had to find along the wa o determine the required angle M 50 N S 17 P 80 R O

f x x 2 The vertical stretch by 2 then the vertical shift up by 3 The vertical shift up by 3 then the vertical stretch by 2 Reflect Are the resulting graphs the same Does the order in which we apply the graph transformations matter This phenomenon is sometimes called the Socks then shoes vs Shoes then socks problem

Apply transformations in the column below that correspond to your chosen function to get new functions Use the button in the upper left corner of the page to add a new line for each of the transformations below Your subsequent graphs will be displayed in different colors Graph Transformations f x x2 The vertical stretch by 9 The vertical shrink by 9 The horizontal stretch by 3 The horizontal shrink by 3 Now consider the reflection question below You are not required to answer the question but pause to think about

3 Estimate a polynomial for the sine function using the points sin0 0 sin 1 2 1 and sin 0 Hint rewrite as points in x y form to look more like the last problem Use your result to estimate sin 7 3

Nine square tiles are laid out on a table so that they make a solid pattern Each tile must touch at least one other tile along an entire edge The squares all have sides of length 1 a What are the possible perimeters of the figures that can be formed The perimeter is the distance around the figure b Which figure has the least perimeter These figures have perimeters of 18 units and 16 units respectively a What are all the possible perimeters of the figures that can be formed The perimeter is the distance around the figure Use the Show Work learning aid to provide related calculations and additional reasoning to support your answer Use a comma to separate answers as needed b Which figure has the least perimeter A a 3 by 3 square B a pyramid with a base of 5 tiles a middle row of 3 tiles and a top row of 1 tile OC a 1 by 9 rectangle OD a figure with a base row of 4 tiles a middle row of 4 tiles and a top row of 1 tile

Determine what additional information is required in order to know that the triangles are congruent by ASA Postulate V G O ZV 21 O VH GI O ZIGH ZVHG O VG HI H I

Determine whether the triangles are congruent If so name the postulate or theorem that justifies your answer If not T explain U S R O The triangles are congruent by the AAS Postulate O The triangles are not necessarily congruent Not enough information provided O The triangles are congruent by the SAS Postulate The triangles are congruent by the ASA Theorem 27

Write an equation a in slope intercept form and b in standard form for the line passing through 1 7 and perpendicular to 3x 7y 1 a The equation of the line in slope intercept form is Type your answer in slope intercept form Use integers or fractions for any numbers in the equation

The graph of a linear function f is shown a Identify the slope y intercept and x intercept b Write the equation that defines f The slope is Type an integer or a simplified fraction Ay 61 10 8 64 2 44 6 B E

In the figure AABC ADEF Solve for x X O x 1 5 O x 6 F O x 4 x 5 5 8 B E 160 160 16 3 D C

1 point Given the function f x 3x 4x 1 find the following a the average rate of change of f on 2 6 b the average rate of change of f on x x h

Find the measure of the arc C C 146 E B mDE A

A WXY is a right triangle W 34 17 A True B False X 17

Use the following problem to answer questions 48 50 Find the dilation image AA B C of AABC with center at the origin 1 and k 48 A a 1 2 b 9 18 c 18 9 d 2 1 49 B a 0 1 b 9 0 c 1 0 d 0 9 50 C a 18 0 b 2 0 c 0 18 d 0 2