Geometry Questions

O are points on the circumference of O is the centre of the circle Find the rom the figure given below B C 6112 D me a b 15 35 c 50 d 65 130 e

9x y 225 The center of the ellipse is 0 0 Type an ordered pair vertices endpoints of the minor axis and foci The vertices of the ellipse are 0 15 0 15 Use a comma to separate answers as needed Type an ordered pair using integers or fractions The endpoints of the minor axis are 5 0 5 0 Use a comma to separate answers as needed Type an ordered pair using integers or fractions The foci of the ellipse are Simplify your answer Use a comma to separate answers as needed Type an ordered pair Type exact answers for each coordinate using radicals as needed

Find an equation for the line with the given properties Express your answer using either the general form or the slope intercept form of the equation of a line 1 Slope containing the point 3 3 The equation is

Graph the hyperbola x y 9 Give the domain range center vertices foci and equations of the asymptotes for the figure The hyperbola has a center at 0 0 Type an ordered pair The vertices are Type ordered pairs Use a comma to separate answers as needed

What is the Axis of Symmetry of the following parabola y x 8x 20 Ox 4 X 4 Ox 8 x 8

Find the point P at which the line intersects the plane x 8 7t y 4 7t z 7 10t 5x 4y 2z 13 The point P at which the line intersects the plane is 0 Simplify your answer Type an ordered triple

Which equation of a parabola would pass through all of the points on the graph 54 3 2 1 31 1 3 21 3 4 5 2 3 4 5 y 3 x 3 5 y 0 1 x 3 5 y 0 1 x 3 5 Oy 3 x 3 5

A line passes through the points P 8 7 3 and Q 10 6 4 Find the standard parametric equations for the line written using the base point P 8 7 3 and the components of the vector PQ y z

A lithotripter is based on an ellipse with the equation given on the right Find the distance from the ellipse s center to the kidney stone and to the beam source Use the fact that c a b The distance is Give an exact answer Simplify radicals if possible Lithotripter a machine used to crush kidney stones using shock waves The patient is placed in an elliptical tub with the kidney stone at a focus of the ellipse A beam is projected from the other focus to the tub so that it reflects to hit the kidney stone x y Equation 64 25 A 1

Find the plane determined by the intersecting lines L1 x 1 3t y 2 3t L2 x 1 4s y 1 2s z 1 2t Z 2 2s Using a coefficient of 1 for x the equation of the plane is Type an equation

Select the transformation of the graph of the parent cubic function that result in the graph of g x 3 x 2 1 Select three that apply A Horizontal stretch by a factor of 3 B Horizontal compression by a factor of C Vertical stretch by a factor of 3 D Translation 1 unit up E Translation 2 units left F Translation 2 units right

Graph the following ellipse Give the domain range center vertices endpoints of the minor axis and foci 9x y 225 The center of the ellipse is 0 0 Type an ordered pair ww The vertices of the ellipse are Use a comma to separate answers as needed Type an ordered pair using integers or fractions

Graph the ellipse Identify the center vertices endpoints of the minor axis and foci 36 y 1 The center is 0 0 Simplify your answer Type an ordered pair www The vertices are Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as r

A water main is to be constructed with a 25 grade in the north direction and a 10 grade in the east direction Determine the angle 8 required in the water main for the tum from north to east 0 radians Type your answer in radians Round to the nearest hundredth as needed JELEN Points 0 of 2 North East not drawn to scale

g x Identify the transformations of the graph of f x x that produce the graph of the given functio Then graph on the same coordinate plane as the graph of g x by applying the transformations to the reference points 1 1 0 0 and 1 1 g x x 3 Reference Points 1 1 0 0 1 1 First Transformation Second Transformation 4 2 4 2 0 2 4 2 4

Graph the following ellipse Give the domain range center vertices endpoints of the minor axis and foci 9x y 324 The center of the ellipse is Type an ordered pair

Write an equation for the ellipse with x intercepts 7 0 and y intercepts 0 6 D An equation for the ellipse is Simplify your answer Use integers or fractions for any numbers in the equation Type your answer in standard form

9 This design began from the construction of a regular hexagon Describe a rigid motion that will take the figure onto itself F A G B C

Find the missing values by solving the parallelogram shown in the figure The lengths of the diagonals are given by c and d Round your answers to two decimal place b 27 C 54 d 40 O L G

find the missing angle with a question mark 30 40 50 20

3 1289 X y

10 cm Find the area 18 cm 17 cm 21 cm A cm A b h

5 N X y Z W 64 yo x q wo

In 1 8 Find the value of all variables 1 110 X y 2 10 x y

6 133 X y Z to Z 20

3x 5 2x 8x 20

3y 18 9x 54 y 12

4 x y Z to 55

9 X 2x 2X 6

4 Almost everyone has played the rock paper scissors game at some point Two players face each other and at the count of 3 make a fist rock an extended hand palm down paper or a V with the index and middle fingers scissors The winner is determined by these rules rock smashes scissors paper covers rock and scissors cut paper If both players choose the same object then the game is a tie Suppose that Player 1 and Player 2 are both equally likely to choose rock paper or scissors a Give the probability model for this chance process b Find the probability that Player 1 wins the game on the first throw 5 Canada has two official languages English and French Choose a Canadian at random and ask What is your mother tongue Here is the distribution of responses combining many separate languages from the broad Asia Pacific region Language English French Asian Pacific Probability 0 63 0 22 0 06 a What probability should replace in the table Why Other b Find the probability that this Canadian s mother tongue is not English c What s the probability that a randomly chosen Canadian s mother tongue is Asian Pacific or Other

Step 1 Given Information Two official languages in Canada are English and French When a Canadian is chosen randomly and asked about their mother tongue the distribution of responses combining the majority of separate languages from the broad Asia Pacific region is as follows Probability of English is P E 0 63 Probability of French is P F Probability of Other languages from Asia Pacific region is P A p 0 06 Step 2 Probability Distribution In a probability distribution The probabilities must be non negative The sum of probabilities of all events should add up to 1 Using the second condition we can calculate the probability of Other languages from Asia Pacific region as P Other 1 P E P F P A p 10 91 0 09 0 22 Therefore the probability that should replace is 0 09 0 37 Step 3 Probability of not English The probability that a Canadian s mother tongue is not English can be calculated by using the complementary probability formula P notEnglish 1 P English 1 0 63 Therefore the probability that a Canadian s mother tongue is not English is 0 37 0 15 Step 4 Probability of Other languages The probability that a Canadian s mother tongue is a language other than English or French can be calculated by adding the probabilities of Other languages from Asia Pacific region and languages other than Official Languages i e P Asian Pacificor Other P Asian Pacific P Other 0 06 0 09 Therefore the probability that a Canadian s mother tongue is a language other than English or French is 0 15

Step 1 Given information Player 1 and Player 2 are both equally likely to choose rock paper or scissors in a rock paper scissor game Step 2 a Let a b represent the outcome of the game where a and b are the choices of player 1 and player 2 respectively Let R represent the rock S represents the scissor and P represent the paper The total of 9 possible outcomes of the game will be PossibleA outcomes R R R P R S P R P P P S S R S P S S Each outcome is equally likely to happen with a probability of The probability model will be a b P a b Step 3 b From the above table there are only 3 outcomes player 1 is winning that are R S P R and S P The probability that Player 1 wins the game on the first throw will be computed as Winning outcomes Total outcomes R R 1 9 P Player 1 R P 1 9 R S 19 P R 1 9 P P 1 9 3 0 33 So the probability that Player 1 wins the game on the first throw is 0 33 P S 9 S R 1 9 S P 19 S S 10 9

Provide a trigonometric equation Considering only the space between x 0 and 2 pie the equation must only have solutions at x 1 and x 2 explain your thought process and the work you did to create the equation You may round decimal values to 3 places

Create a single BPMN diagram using the Camunda Modeler of the below process narrative Feature appropriate pools and lanes to represent the different entities participants and the message flows between these entities participants Please label all flows sequences messages Do not use sub processes Canvas is a leading provider of LMS Learning Management Software software Canvas is used by many colleges as a teaching course portal

n 6 S 1 1 n 2 S 13 80 e Refer to the diagram for question 12 22 Plot a graph of the values of energy y axis against the square of the number of the level i e n on the x axis C

The distance D between a point Q and a line in space is given by PQ x u D X where u is a direction vector for the line and P is a point on the line a Find the shortest distance between the point Q 9 0 0 and the line passing through the points P 0 0 8 and P 0 1 9 b Find the shortest distance between the point Q 9 0 0 and the line segment from P 0 0 8 to P 0 1 9

7 Use the universal substitution to find the general solution of the equation 2 cos 3x sin 3x 2

4 PB X P 9 C Y 15 B Z

For 6 and 7 find the coordinates of the circumcenter of the triangle with the given vertices 6 A 2 6 B 8 6 C 8 10 7 D 7 1 E 1 1 F 7 9 D

For 6 and 2 6 B 8 t EX 3x 16 FX 11 K H 3x 1 E For 14 16 explain which segments would need to be perpendicular in order for a segment to bisect the angle 14 16 15 B

Fays or segments intersect in the same point they are called rays or segments For 2 5 the perpendicular bisectors of the triangle intersect at a point and are shown in bold Find the indicated measure 2 BG X A 4 PB B G C 15 N 3 GA 5 HP 17 D 11 X X 15 nter of the triangle with the given vertices

12 P is the circumcenter of AXYZ Use the given information to find PY PX 4x 3 P PZ 6x 11 X D CY E Z

3x 16 M 18 H 19 G N E FX 11 For 17 19 classify the triangle by its SIDES 17 G For 14 16 explain which segments would need to be perpendicular in order for a segment to bisect the angle 14 F 15 16 3x 1 H H 8 D 21 22 F For 20 22 classify the triangle by its ANGLES 20 55 65 M E 80 A 45 25 40 20 120

NG NHZx 3 ed angle A N H

For 8 11 N is the incenter of AABC Use the given inform 8 ND 6x 2 NE 3x 7 NF 10 NK 2x 2 NL x 10 NM M ING 143 NH 2x 3 D 12 P is the circumcenter of AXYZ Use the given information to find PY P PX 4x 3 PZ 6x 11 Z 11 NQ 2x NR 3x 2 G NJ N BJ NM H N SC

Find the cosecant secant and cotangent of angle A given that a 17 3 and b 13 2 Although it is best to leave the ratios as reduced fractions for the purposes of this question round to 4 decimal places Diagram is for reference only and is not drawn to scale CSC A sec A cot A A C 000 B

Midpoint 14 A 2 1 B 10 7 Midpoint AB AB

Write a function based on the given parent function and transformations in the given order Parent function y H 1 Shift 2 5 units to the right 2 Shrink horizontally by a factor of 3 Reflect across the y axis The function based on the given parent function and transformations in the given order is y 23

For 5 9 if point P lies on the perpendicular bisector of LM explain which segments are congruent and which segmen are perpendicular 5 L M 201 211 N 6 L 211 211 M 7 P M 211 N 211 T 8 L N 211 211 P M

Amplitude 9 3 Period 8 7 6 5 4 Show Transcribed Text 1 24 4 Based on the graph above determine the amplitude midline and period of the function Close 4