Geometry Questions

empt in Progress For the pair of compounds below determine whether they are identical compounds constitutional isomers or stereoisomers O stereoisomers O constitutional isomers O identical compounds

9 Using Figure 9 13 below a Draw isobars at 4 mb intervals e g 1004 mb 1008 mb 1012 mb 11 b Label the low pressure center with an L c Draw the warm and cold fronts L49 38 124 31 O 41126 33 O 128 34 22 36 124 28 38 110 41103 30 L48 4 40 088 42 109 36 20 48 126 38 38 448 026 50 52 128 45 096 43 4569 R 40 66 59 d Label a maritime tropical mT and continental polar air mass CP e Outline the area where cloud cover exceeds 75 f Shade the areas receiving precipitation 61 075 57 60 040 48 63 153 61 Figure 9 13 45 114 66 24 60 ras 57 39 084 39 024 61044 57029 54 66 53 70 40 591 39 154 39 4332 41 46 124 43 54 097 43 45 099 66 111 55 71 72 69171 64 61 60 9 149 45 163 8 4 1 11

Given a parallelogram ABCD with D lying inside the outer circle ABC Point E is the point of intersection of the outer circle ABC with line BD where E B Point F is the point of intersection of the outer circle AABC with line CD where F C It is known that AEC 55 and EAF 30 2 DAE is A 35 B 40 F E B C 45 D 50

1 By using the midpoint formula show that the axis of symmetry of the parabola b 2a y ax bx c is x uloz 1091 vnom woH 21500 d

Graph the equations b y 4 3 x 2 7

11 Are the two shaded triangles below similar If so then what is the scale factor If not why are they not similar 5 8 cm 4 5cm 6 7 3 48 cm 27cm 4 02 cm

What mass of reactants are used during the reaction Hydrogen Bromine Hydrogen Bromide 16 25 g g Give your answer to the correct number of significant figures g Hydrogen Bromide

The use of the set of axes below is optional 24 16 Line n is represented by the equation 3x 4y 20 Determine and state the equation of line p the image of line n after a dilation of scale factor 3 centered at the point 4 2 Explain your answer The use of the set of axes below is optional

Triangle sum theorem The sum of the interior angle measures of a triangle is 180 A D 1 Proof B 1 DE 2 Given AABC with DE AC Prove ml m 2 m 3 180 2 21 DBA 3 C F 3 m1 m DB 1 Civer Oiver

HW8 3 Centroid of a Composite Area Consider the composite area shown below all dimensions in mm Determine the coordinates of the centroid relative to the x y axes shown 18 10 0 9 0 9 74 11 0 7 31636207570 10 0 11 0 8 0 mm X 0

72 Consider the following experiment You are one of 100 people enlisted to take part in a study to determine percentage of nurses in America with an R N registered nurse degree You ask nurses if they have an R N degree The nurses answer yes or no You then calculate the percentage of nurses with an R N degree You give that percentage to your supervisor a What part of the experiment will yield discrete data b What part of the experiment will yield continuous data

8 When asked to state the nature of the roots for you are a Finding the location of the x intercepts b Finding the location of the axis of symmetry Determining the number of x intercepts d Determining the direction of opening

Refer to the given diagram with FB DE Which figure has the greatest measure Om ACE O Arc BD O m FBE D 78 F 50 E

Solve the right triangle with a 4 and c 10 State exact answers as discussed in the notes Remember use sin or cos to find the exact angles b Do not round until the final answer Exact only Do not round until the final answer Exact only B Do not round until the final answer Exact only

a Starting with the graph of f x 2 write a function that results from shifting f x down 4 units and reflecting f x about the y axis f x P b Graph function found in Part a Drag the two blue points on graph to the correct points that f x passes through Then use the remaining red point to drag the horizontal asymptote to the correct line Note that all three points are adjusted in increments of 1 4 Y

The graph of f x 5 0 15 is given below click on graph to enlarge

b C 3 9 D 5 4 Find the midpoins of set of orderd pairs

Follow the steps for graphing a rational function to graph the function F x UL Ine domain is the set of all real numbers Write F x in lowest terms Select the correct choice below and if necessary fill in the answer box within your choice A F x Simplify your answer B F x is already in lowest terms x 17x 18 X 6 Find the intercepts of the graph Select the correct choice below and if necessary fill in the answer box es within your choice OA The graph has y intercept and x intercept s Simplify your answers Type integers or fractions Use a comma to separate answers as needed Type each answer only once OB The graph has y intercept and no x intercept Simplify your answer Type an integer or a fraction OC The graph has x intercept s and no y intercept Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once OD The graph has neither x intercepts nor y intercepts

2 Tell whether the transformation appears to be an isometry Explain your answer

9 Determine the number of lines of symmetry for each figure a b c

1 Name the transformation that maps the lighter turtle preimage to the darker turtle image a b c 2 Tell whether the transformation appears to be an isometry Explain your answer t

Steps for graphing a rational function to graph the function P x 1 The graph has y intercept and no x intercept 6 Simplify your answer Type an integer or a fraction OD The graph has neither x intercepts nor y intercepts 6 36 X Determine the behavior of the graph of P at any x intercepts Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The graph will cross the x axis at x and touch but not cross the x axis at x Type integers or simplified fractions Use a comma to separate answers as needed Type each answer only once OB The graph will touch but not cross the x axis at x Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once OC The graph will cross the x axis at x Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once OD There is no x intercept

7 Use your compass to construct two circles with the same radius intersecting at two points Label the centers P and Q Label the points of intersection of the two circles A and B Construct quadrilateral PAQB What type of quadrilateral is it

5 a Draw the vectors a 3 2 b 2 1 and C 7 1 b Show by means of a sketch that there are scalars s and t such that c sa tb c Use the sketch to estimate the values of s and t d Find the exact values of s and t

5 8 Find a vector a with representation given by the directed line segment AB Draw AB and the equivalent representation starting at the origin 5 A 1 1 B 3 2 6 A 4 1 B 1 2

9 12 Find the sum of the given vectors and illustrate geometrically 9 1 4 6 2 10 3 1 1 5

13 16 Find a b 2a 3b a and a b 13 a 5 12 b 3 6

Would you use SSS SAS ASA or AAS to prove the triangles congruent If there is not enough information write There is not enough information Explain your answer E P F R

A chord AB of a circle centre O and radius 21 cm is 36 cm long Express the angle AOB in radians Use your result in a to calculate correct to three significant figures i the length of the arc AB the area of the sector AOB the area of the minor segment cut off by the chord AB Take 3 142 ii iii

Question 12 of 14 12 Assume each outcome in the sample space S provided below is equally likely Find P AB S 0 1 2 3 4 5 6 A 0 1 2 5 B 1 2 4 Round your answer to the nearest hundredths Answer Previous Answer 0 29

The medians of AABC are AE BF and CD They meet at a single point In other words G is the centroid of AABC Suppose BF 27 AG 14 and CG 20 Find the following lengths Note that the figure is not drawn to scale A D F G B E C GD 0 GF AE

11 Find an equation of the sphere that passes through the point 4 3 1 and has center 3 8 1

5 Describe and sketch the surface in R represented by the equation x y 2 hu

5 Describe and sketch the surface in R represented by the equation x y 2

Write a rule to describe each transformation 31 G H H y A

36 reflection across the x axis v 5 1 W 5 3 X 1 3 AY X

4 Write the conditional converse and contrapositive to the following inverse statement If a triangle has 1 right angle then the triangle is a right triangle 40 Conditional Converse Contrapositive 15 Draw a counterexample to the following statement All isosceles triangles are acute triangles 16 A toddler s climbing ramp is designed with the profile of a right triangle The measure of one acute angle is who times the measure of the other acute angle Find the measure of each acute angle Find m2BDC M 28 58 b 84 c 56 d 112 the 5 sides lengths from shortest to longest on the es below 8 7 951 135 B 8 19 A Geometry student was using the following picture to find mzQ Identify the first step if any in which an error occurred R 2x 15 a Yes acute triangle b Yes obtuse triangle c Yes right triangle d No cannot e a triangle X 2 20 Determine if the following measures can be the sides of a triangle 6 14 13 If so classify the triangle by its angles Side 21 Find the value of x Then classify the triangle by its sides angles Angle TO113 22 Find the measure of the smallest angle H 4x 2x 9 W Step 1 Step 2 Step 3 Step 4 10x 3x 8 23 Determine the value of x x x 200 Student Work x 2 2x 15 180 5x 30 180 C mZQ 2 30 15 75 x 150 x 30 3x 28 B 5x 52 2x 10

2x 4 A C B 9 11 BC A A Sy 1 B y 2 C

Question 10 of 14 10 Suppose X is a normal random variable with probability density function defined by 1 16 What is the mean of X f x Answer e 16 Previous Answer 0 Return to overview

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION 2 sin 9 cos 8 1 8

An equation is given Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTI 3 tan 30 1 0 a Find all solutions of the equation Tk TUTU 3 18 8 8 X b Find the solutions in the interval 0 2 T 7T 4 6 X

An equation is given Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION 2 cos 38 1 a Find all solutions of the equation 8 b Find the solutions in the interval 0 2m 8

Given AC L BD and BD bisects AC Prove AABD ACBD Step 1 2 try Statement AC L BD BD bisects AC BD BD Type of Statement Reason Given Reflexive Property A B D C

Given E is the midpoint of BD and AC L BD Prove ABAE ADAE Step 1 try Statement E is the midpoint of BD AC L BD Type of Statement Reason Given A B E D

Given AD AE and AB AC Prove AABE AACD Step 1 try Statement AD AE AB AC Type of Statement Reason Given A D F B

Given D is the midpoint of AC ZAED ZCFD and LEDA LFDC Prove AAED ACFD Step 1 try Statement D is the midpoint of AC LAED LCFD LEDA LFDC Type of Statement Reason Given E B F

Triangle FGH is congruent to triangle QRS Which congruence statements must be true Select ALL that apply FG RS OZGHF LRQS HF SQ OLHGF SQR LCE

Select the correct answer from each drop down menu Consider the figure formed by AAEB and ADCB sharing a common vertex B A The figure E has point symmetry does not have point symmetry D because rotating it 180 about point B maps AAEB onto ADCB The figure because point E is the same distance but in the opposite direction from point B as point C and point A is direction from point B as point D

Complete the proof 1 Given Line AB intersects line DC at point B LAEB and DEC are straight angles Prove LAEC DEB 10 Statements E Reasons 1 1 2 ZAEC is supplementary to CEB 2 3 ZDEB is supplementary to CEB 3 Def of Supplementary Zs 4 4 Supplements Theorem a ZAEB and DEC are straight angles b Substitution c Angle Addition Postulate d Given e Addition Property of Equality f Linear Pair Theorem g ZAEC is congruent to ZDEB B

2 3 pts 1 each For each part below all are separate from each other make up a list of FIVE scores from 0 to 100 inclusive that have the indicated properties If not possible explain WHY not discussing the meanings of all measures of central tendency or spread mentioned in the problem a There are three modes and the mean is 40 b The median is 50 but it changes to 54 if an extra sixth score of 80 is included Make it clear which FIVE scores are your originals n The range is 20 low score is 6 and mean is 15