Geometry Questions

7 6 A 10 9 8 7 6 5 4 3 fy 2 3 4 5 6 7 8 9 10 B 2 3 4 5 6 30 8 Position points A and B so they both lie on the graph of f g x

F C Q A 10 y 8 6 4 4 2 0 2 2 6 8 10 2 B E 4 D X 6 Move the points so that they all lie on the graph of f x x 4 x 3 x 5 x 1 x 2 and do not coincide

6 4 C 10 A 8 6 4 1 2 0 2 4 6 8 10 y 2 B 4 D 946 X Move the points so that they all lie on the graph of f x x 4 x 3 x 5 60 and do not coincide

A 10 y 9 8 7 6 5 4 3 fr 3 J5 5 6 7 8 9 10 23 5 6 8 Position points A and B so they both lie on the graph of f g x

3 3 6 7 9 8 7 65 9 4 3 2 1 2 3 4 5 6 7 8 Y 1 2 3 4 4 2 5 3 6 Move the points so they do not coincide and both lie on the graph of fog f x x 1 g x x 2

8 The graph of a function h is shown Graph the inverse of h on the blank coordinate grid 10 5 0 5 0

quadratic function f x 4x 48x 128 Give the a vertex b axis and d range ex is dered pair

K For the given equation and graph of the quadratic function do each of the following Complete parts a through e f x 2 x 8 2 a Give the domain and range The domain is 00 00 Type your answer in interval notation The range is 0 2 Type your answer in interval notation b Give the coordinates of the vertex The vertex is 0 Type an ordered pair 986 10 2 4 6 x 4

Sore 23 Penalty back to zero Question Watch Video In the diagram below of triangle RST U is the midpoint of RT and V is the midpoint of ST If m TRS 33 5r and m LTUV 39 Se what is the measure of TUV Show Examples w UMAN S ay as and F PANG Toan ayam amare d Viruses found And

Draw AMGT Use the triangle to answer the questions below 1 What angle is included between GM MT and ZT 2 Which sides include 3 What angle is included between GT MG and

Given ARST with a point U inside such that ZRST ZRTS 42 and ZRSU ZSRU 18 Find ZUTS S U R

26 Given APOR ASTU m P 5x 30j mLQ 7x 35 mLT 4x 12y mzU 8y 2 Find MLP MLQ m R y MLS MLT mLU SHOW WORK You might want to draw a picture to help you get started but you don t have to

25 mm 60 60 These figures are congruent What is men 50 mm 30

Find the point on the curve h x x2 8 that is closest to the point 18 8 Enter your answer as an order pair

Using the prototype oblique triangle shown below and the information given find the measure of the remaining sides and angles in the triangle b a 7 C a If b 9 68542 y 124 and a 3 50173 then B

A right circular cone has a radius of 2x 4 and a height 5 units less than its radius Express the volume of the cone as a polynomial function The volume of a cone is Vr h for radius r and height h Enter as pi help formulas V x

A rectangle has a length of 12 units and a width of 6 units Squares of x by x units are cut out of each corner and then the sides are folded up to create an open box Express the volume of the box as a polynomial function in terms of x f x help formulas

Population standard deviation 23 N 49 X 14 a Set up a 98 C I E for population Mean b Set up a 95 C I E for population Proportion c Between what two values around the mean 99 of observations fall d Between what two values around the mean 98 of observations fall e Above what value only 2 of observations fall f If s 23 do parts a and b

The angle bisectors of AXYZ are XG YG and ZG They meet at a single point G In other words G is the incenter of AXYZ Suppose FG 17 YG 18 mz DXF 92 and m2 EYG 24 Find the following measures Note that the figure is not drawn to scale X D Y F E m LEYD DG 0 0 m LEZG 0 00 X UIU

4 Find all points on the curve r 2 2 cos 0 where the tangent line is vertical List the points in polar form

1 8 Write a polar equation of a conic with the focus at the origin and the given data 1 Ellipse eccentricity 12 directrix x 4 2 Parabola directrix x 3 3 Hyperbola eccentricity 1 5 directrix y 2

Point Q is the midpoint of PR and PR 21 75 yards What is the length in yards of QR

The following graph shows a proportional relationship What is the constant of proportionality between y and in the graph 54 6 5 8 ON 1 29 3 4 12 5 Constant of proportionality 6 x

Find the exact value of each expression it it is defined If an answer is undefined enter UNDEFINED a tan 0 b tan sqrt 3 c tan sqrt 3 3

29 C 1 sino A r 3 sing intersection ts 12 n

Part B Draw DE parallel to BC You can draw DE any length and place it anywhere on the coordinate plane but not on top of AABC Find and record the ratio n of the length of DE to the length of BC Then multiply the lengths of AB and CA by n and record the resulting lengths

In Exercises 7 and 8 sketch a diagram of the description 7 RS bisecting KL at point R In Exercises 9 14 use the diagram to determine whether you can assume the statement 9 Planes A and B intersect at EF 10 Points C and D are collinear 11 HJ and ID are perpendicular 12 GD is a bisector of EF at point D 8 AB in plane U intersecting CD at point E and point C not on plane U 13 IHHG 14 ZHJD and ZHDJ are complementary angles C IG D B

6 A reservoir R supplies two towns Alton and Barnsville with water The pipelines from R to each town are being replaced to cope with increased demand The towns are connected by a straight road through them and the reservoir is 7 km from this road 4 km R 7 km 11 km B a Find the distances AR and BR to the nearest metre b Find the total cost of the new pipelines given that each 100 m will cost 2550

1 The shadecloth outside a workplace is 3 m long The building is 2 4 m high How far are the pegs from the base of the building 2 A city park is a square with sides 320 metres long The council decides to build a new walkway from one corner to the opposite corner How long will the walkway be B 3 2 m 14 2 m shadecloth 3 m 2 4 m building Find the length of the truss AB for the roof structure shown

In Exercises 3 6 use the diagram to write an example of the postulate 3 Two Point Postulate Postulate 2 1 4 Line Point Postulate Postulate 2 2 5 Plane Point Postulate Postulate 2 5 6 Plane Intersection Postulate Postulate 2 7 In Exercises 7 and 8 sketch a diagram of the description 7 RS bisecting KL at point R P B A 8 AB in plane U intersecting CD at point E

Given the points below as the vertices of a quadrilateral ABCD determine which sides segments ar parallel to each other and which are perpendicular Hint Draw the shape and name each of the four sides then find the slope of each A 2 5 B 6 3 C 5 1 D 7 2

Given the following figure prove that the m 14 31 degrees 156 20 14 35

The angle of elevation to a nearby tree from a point on the ground is measured to be 74 How tall is the tree if the point on the ground is 54 Feet from the bottom of the tree Round your answer to the nearest tenth of a foot if necessary

For an FCC structure select all reflections that can appear in the XRD pattern O 100 O 110 O 111 O 200 O 210 O 220 O 211 221

What is the maximum atomic scattering factor of Ti 00 O 10 O 22 O 29

Find the measure of the indicated angle Classify the triangle by angles and sides 1 MZA B 46 3 m20 N 7Y 4y 15 M 2 MZR 2x 2 T 4 mLE D 4x 1 3x 1 5x1 E

18 Solve the following inequality for y y 6x 3 Identify the statements which represent the inequality There may be more than one correct answer select all that apply The correct inequality begins with y The graph has a solid line The graph has a dotted line The correct inequality begins with y None of these statements are true

X

Find the exact value of the expression given below 7 12 COS 2 1 3 4 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denomin COS 7 12

Sketch the graph of the function and check the graph with a graphing calculator Before doing so describe how the graph of the function can be obtained from the graph of a basic exponential function x 1 f x 5 Select the correct choice below and fill in the answer box to complete your choice OA Start with the graph of y Shift the graph 1 unit to the left OB X Start with the graph of y Shift the graph 1 unit down OC Start with the graph of y Shift the graph 1 unit up OD Start with the graph of y Shift the graph 1 unit to the right

2 Convert the following equation to its alternate form standard to slope intercept or vice versa 5 x 6 O 18x 30y 25 Ox y 5 O 18x 30y 25 O x y 1 3 Wilbur has sold 87 48 95 and 71 copiers in the last four months respectively How many copiers will he need to sell this month to maintain an average of at least 77 sales per month answer

k

Find the value of the variable and all of the interior angle measures 1 2 W 468 5 vopos H 4 Find the value of the variable Find the measure of the exterior angle de variable F 3x 4 430 Solve for x and find any missing angle measures 03 12711x 74 12x 12x 50 0 37 46 17X XCHOGI OST 134 6 3 7x 4 6x 1 4x 1 126 F G H 5x 17 e Ova xat XP FF 5x 4 4x 9 X 9r 6

X 111 11

X

WA00 Sketch the graph of the function and check the graph with a graphing calculator Before doing so describe how the graph of the function can be obtained from the graph of a basic exponential function X 4 f x 2 1 Describe how the graph of the function can be obtained from the graph of a basic exponential function Start with the graph of y Shift it 4 units and then shift it left up down 1 unit A 27

par and of a in the xy plane are given below Identity the particle s path by finding a Cartesian equation for it Graph the Cartesian equation Indicate the portion of the graph traced by the particle and the direction of motion x 5 sint y 4 cost 0 t The Cartesian equation for the particle is O A Graph the Cartesian equation Draw an arrow at the end of the particle s path showing the direction of motion as t increases Indicate the portion of the graph traced by the particle using a solid curve and the portion not traced by the particle by a dashed curve Choose the correct graph below Ay x y 25 16 O B 1 C Ay O D X

Lesson 2 1 Translations Learning Goal I can develop definitions of translations in terms of angles perpendicular lines parallel lines and line segments Standard G CO A 4 symbolically numerically and graphically A First draw a triangle on lined paper Label the vertices A B and C Then draw a line segment XY An example of what your drawing may look like is shown Using the same piece of tracing paper place A on A and draw a copy of AABC Label the corresponding vertices B and C An example of what your drawing may look like is shown EXPLORE Exploring Translations Read Explore in your textbook Lesson 2 1 and complete the following Show all your work A translation slides all points of a figure the same distance in the same direction You can use tracing paper to model translating a triangle ROIN BUse tracing paper to draw a copy of triangle ABC Then copy XY so that the point X is on top of point A Label the point made from Yas A X L4L Math Resources http Bit ly L4LMath Use a ruler to draw line segments from each vertex of the preimage to the corresponding vertex on the new image

If these patterns are continued how many dots will be in the 100th figure of each sequence 3 Explain Jussends To S06990 08

1 The angle of elevation from the top of a 95 foot tall building to a hot air balloon in the sky s 76 If the horizontal distance between the building and the hot air balloon is 354 feet find the height of the hot air balloon