Geometry Questions

Let G be a connected graph with k 0 vertices of odd degree i Show that the minimum number of trails that together include every edge of G and that have no edges in common is k 2 ii How many continuous pen strokes are needed to draw the diagram in Fig 6 8 without repeating any line

Find the midpoint of each line segment 1 5 2 3 154 43 AY M x x yfy 2 2 M 1 S 2 M 62 2 1 20 M 3 1 2 3 4 2 2 4 AY AY Y

Find the midpoint of the line segment with the given endpoints 5 6 1 2 5 6 4 3 1 6 7 5 4 6 3 9 11 10 3 9 8 4 3 5 5 10 8 2 9 8

2 The diagram is a straightedge and compass construction Lines m and n are the perpendicular bisectors of the sides of triangle ABC Select all the true statements A E A Point E is closer to point A than it is to point C B Point L is closer to point B than it is to point A C Point D is closer to point B than it is to point C D Point J is closer to point A than it is to point B or point C E Point K is closer to point C than it is to point A or point B F Point L is closer to point C than it is to point A or point B OF

the figure below O is between Mand P and N is the midpoint of MO If NO 6 and NP 8 find MP

On a reality show contestants had to spin two wheels of fate Spinning the first wheel determined the remote location where contestants would reside for the duration of the season Spinning the second wheel determined which bonus survival tool they would be allowed to bring along with a few other necessary items A tent Matches A rope Desert Rainforest 3 7 9 4 4 3 What is the probability that a randomly selected participant spun the second wheel and landed on matches or a tent Simplify any fractions

61 66 Right triangle relationships Draw a right triangle to simplify the given expressions Assume x Q 62 cos sin x 3 61 cos sin x 63 sin cos x 2 64 sin cos e for 0 0 2 65 sin 2 cos x Hint Use sin 20 2 sin 0 cos 0 cos 0 sin 0 66 cos 2 sin x Hint Use cos 20

Determine the volume of a right trapezoidal cylinder whose bases are B 16 m and b 9 m height is h 3 m and length is 1 17 m b B 1 1

the scalar equation of the plane containing the following 3 points P 2 1 3 Q 1 1 1 R 1 2 3

1 12 points A particle traveling in 3D space has the following position r t t t 1 1 at time t Consider the vector 2 3 0 a At what time s t is the particle traveling in a direction parallel to b At what time s t is the particle traveling in a direction perpendicular to u

2 12 points i and u are vectors in 3D space satisyfing 5 6 7 15 a Find the angle between u and b If u and 7 lie in the plane x y z 0 find a vector that is either ux v or v x u

8 Name all pairs of congruent segments in KLMN Use the congruence symbol to write your answer 9 M 4 8 is the midpoint of DE D has coordinates 6 1 Find the coordinates of E KM KL NL M2 For Exercises 10 and 11 use a ruler to draw each figure Label the figure and mark the congruent parts 10 AB and CD with M as the midpoint of both AB and CD AB 6 4 cm and CD 4 0 cm A B and C are not collinear 12 Sketch six points A B C D E and F no three of which are collinear Name the lines defined by these points How many lines are there E 11 AB and CD C is the midpoint of AB with AC 1 5 cm D not on AB is the midpoint of AE with AD 2BC B 13 In the figure below B C H E is a set of four coplanar points Name two other sets of four coplanar points How many sets of four coplanar points are there F 8 cm H 8 cm Cube M

Your answer is incorrect In the figure below mz WXZ 113 and m2 2 is 7 more than mz 1 Find mz 1 W X 2 m 21 X

Quadratic Functions 1 Here are 4 equations of quadratic functions and 4 sketches of the graphs of quadratic functions A y x 6x 8 B y x 6 x 8 C y x 6 8 D y x 8xx 6 a a x 2 Match the equation to its graph and explain your decision Equation A matches Graph because Equation B matches Graph Equation C matches Graph Equation D matches Graph because because 3 because 4 b Write the co ordinates of the points P Q R 2 The graph of a quadratic function has a y intercept at 0 5 and a minimum at 3 4 Write the equation of its curve function S S

the figure below mz WXZ 113 and mz2 is 7 more than mz 1 Find mz 1 W X 2 Y mz1 0

3x 4 3 Find the area of the composite figure 2X x 1

Q3 Sharon is remodeling the floor her studio apartment and needs to know how many square total area is for this apartment The figure below shows the layout of the floor Polynomial lox 3x 4 2x x3 3x 4 x 1 3x 4 x 2x 5 4x 6 c If x 6 then what is the total square footage of the studio apartment 510 d If flooring will cost 35 per square foot then how much will she have to pay Q

2x 3 2 Find the area of the composite figure X 4x4 X 4

7 The endpoints of line segment AB are located at 5 2 and 3 10 What is the equation of the line that is perpendicular to AB and passes through the midpoint of AB A y 4 2 1 B y 4 x 1 C y 6 x 4 D y 2 2 3

Calculator A cosine function has a period of 5 a maximum value of 20 and a minimum value of 0 The function is not a reflection of its parent function over the x axis Which function could be the function described f x 10 cos 5x 10 O f x 10 cos 5x 10 f x 10 cos 2x 10 O O f x 10 cos x 10 1 2 3 4 5 Next

8 Get Fit Power House and Fitness Frenzy are competing gyms that are trying to recruit new members They all have new deals to attract customers Get Fit 35 one time registration fee and 5 for every time you visit Power House 40 one time registration fee and 4 for every time you visit Fitness Frenzy No sign up fee Pay 15 a month Consider the graphs that represent the cost of attending a gym for the first month if you visit times for each gym a Which gym s graph if any would represent a horizontal line Explain b Which gyms graphs if any would represent perpendicular lines Explain c Come up with a pricing scheme for a new gym Run Around the Clock so that the graph of monthly cost of attending the gym a times is parallel to that of Power House

5 Which of the following equations does NOT represent the line shown in the graph A 3x 5y 15 3 B y 3 x I Y 5 3 1 D y x 5 3 6 5 4 3 2 2 1 0 2 6 7 8 9 10

Calculator Which equation represents the function on the graph f x sin x f x cos x f x sin 2x f x cos 2x O O 3 K24 2 AA 2 3 KIN 74

Consider the function f x y x y Which of the following graphs is the graph of a level curve of f x y Select all that apply 04 x y 0 Oy x 1 x y 1 O z x 1 O z y 1

Solve AABC a 3 2 cm c 2 6 cm and ZA 46 Begin by sketching and labellin a diagram Account for all possible solutions Express each angle to the nearest degree and each length to the nearest tenth of a unit

Select the graph of the function and its parent function g x x 4 O 4 2 y 24x y 11 Describe the transformation The graph of g is a translation unit s of the parent function

Tree height feet Tree Growth 6 4 2 0 0 6 2 4 Age years X Use the graph to write an equation of the line y Interpret the slope A The height increases 2 3 feet each year B The height increases 1 5 feet each year C The height increases 1 foot every 1 5

Find a vector parametrization of the line through P 1 1 1 in the direction v 6 3 4 r t t i 9 it j

a Find a parametric equation for the line through the point 1 4 6 and in the direction of ai bj ck F t b Find conditions on a b c so that the line you found in part a goes through the origin Be sure you can give a reason for your answer Then use your work to give two distinct triples a b c tham result in the line passing through the origin Choice 1 a b Choice 2 a b 1 c

The function r t traces a circle Determine the radius center and plane containing the circle r t 4i 12 cos t j 12 sin t k Plane x 4 Circle s Center Radius 9

Callie is sending her nephew a soccer ball for his birthday She packs the ball in a cubic box that has the same side length as the diameter of the ball She needs to determine how much space needs to be filled with packing material Use 3 14 or the button on your calculator Round all results to the nearest hundredth box If the sides of the box are 24 cm soccer ball a What is the volume of the box 13 824 b What is the volume of the ball of cm cm c What is the remaining volume of the box that needs to be filled with packing material Enter an integer or decimal number imo

Look at the diagram and evaluate Which of the statements below is TRUE I J K L 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Answer IK JL IJ JK IL JK I is the midpoint of IK Submit Answer

Find the value of x Hint The sum of the angle measures of a quadrilateral is 360 X Simplify your answer 2x 30 4x

5 North C 104 33 135 Points A B and C are at sea level A is 104 m from C on a bearing of 064 Bis 135 m from C on a bearing of 122 a Calculate AB b Calculate the bearing of A from B c A boat T travels in a straight line from C to B Calculate the shortest distance of T from A during this journey d C is a point at the base of a vertical cliff D is the point on the top of the cliff vertically above C The angle of depression of B from D is 27 B

4 State whether the following graphs are even odd or neither Determine their symmetry x axis y axis origin or none Select all of the following graphs which are one to one functions 03 a d 2375 3432 b e C f

10 The diagram shows two circular discs with centres A respectively They lie and B of radii 11 cm and 7 cm on a straight line MPQN and touch each other at R such that ARB is a straight line M 11 cm 18 R B 7 cm P 17 5 Q i Show that ZPAB is approximately 77 2 ii Hence find the area of the shaded region N

Exercise 6 two phase method Solve the following linear programming problem using the two phase simplex method minimize x x2 x3 subject to X1 X2 x3 3 x 2x2 7x3 4 X1 X2 X3 0 Start by adding slack variables and note that the problem was to minimize rather than maximize In Phase 1 set up an auxiliary LP problem that either proves the original problem is infeasible or provides a basic feasible solution to the original problem If Phase 1 yields a basic feasible solution then proceed to Phase 2 solve the original LP problem starting from this basic feasible solution

Find the points of intersection of the following pair of curves y x 5x 5 y x 7x 9 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The intersections are Type an ordered pair Use a comma to separate answers as needed OB There are infinitely many solutions of the form x x where x represents all real numbe OC There are no points of intersection

2 Translate the following statements into coordinate points a f 1 1 c g 1 1 b h 2 7 12 d k 3 9 9

Let ro xo yo zo be a fixed point r x y z be a variable point and a b c be a vector V If r ro tv is a vector equation for the line through ro co yo zo in the direction of v a b c then we can conclude that Select all that apply robus x xo a AXIN x x0 at y yo bt z 20 ct are parametric equations for the line y Yo b CAPANS If r x y z is on the line then the displacement vector r ro x xo y yo z zo is parallel to the vector v 2 20 C HAVYNS Masin The equation v r ro 0 that is a x xo b y yo c z zo 0 is an equation for the plane containing the line a b c are symmetric equations for the line

Let ro co yo zo be a fixed point r x y z be a variable point and v a b c be a vector If r ro tv is a vector equation for the line through ro xo Yo zo in the direction of v a b c then we can conclude that Select all that apply 0 x x at y yo bt z 20 ct are parametric equations for the line If r x y z is on the line then the displacement vector r ro x xo y yo z zo is parallel a b c to the vector v The equation v rro 0 that is a x xo b y yo c z zo 0 is an equation for the plane containing the line x xo y Yo a b z 20 C are symmetric equations for the line

The point P co yo zo is in a plane for which n a b c is a normal vector Which of the following equations must every other point Q x y z in the plane satisfy Select all that apply n PQ 0 nx PQ 0 O ax by cz d where d axo byo czo a b c x xo y yo z zo 0 O a x xo b y yo c z zo 0

Are the given rectangles similar 3 12 91 5 Select one a No O b Can not be determined OC Yes 20 Based on the diagram below we can say that tha 11 91

A parking lot has the shape of a parallelogram see figure The lengths of two adjacent sides are 70 meters and x 120 meters The angle between the two sides is 70 What is the area of the parking lot Round your answer to one decimal place m 70 4411 40 Show Transcribed Text C To determine the distance between two aircraft a tracking station continuously determines the distance to each aircraft and the angle A between them see figure Determine the distance between the planes when A 40 b 35 miles and c 22 miles Round your answer to one decimal place

Determine the angle in the design of the streetlight shown in the figure where x 2 1 Round your answer to one decimal place 0 127 2

Perform a curve discussion of the following function f x x 4x x 2 To do this carry out the following steps and briefly justify the individual results a Maximum definition range b symmetry f x f x oder f x f x c Poles or definition gaps d limits e derivatives f x f x f x f Zeros of the function and the first three derivatives f x 0 f x 0 f x 0 f x 0 g Extreme points high or low points maximum minimum h Turning or saddle points curvature behavior

Show Transcribed Text Construct a certain circle Begin with three independent points Label them A B and C if they are not already labeled that Construct the point D that is the base of the altitude at A Construct the circles B that is centered at B and goes through D Let B intersect AB at P Construct the circle C that is centered at C and goes through D Finally construct the circle that is tangent to B at P and is tangent to C Highlight this last circle by coloring it a unique color

For the following matrix in reduced row echelon form give the set of solutions to the corresponding system of equations Let any free variables be r s or t For example if the solution is 12r 1 22 r you would enter 2 r 1 r 1 0 2 5 013 0 1 0 2 0 5 000 0 16

Q 3 show that there exists a projective transformation r A B C S A2 B2 C A A3 P B3 B C3 C A4 A R B B4 C C4 S

Find the equation for the hyperbola whose graph is shown 30 20 10 30 20 10 10 20 30 F 0 17 10 20 F 0 17 30