2D Geometry Questions and Answers

In the diagram below FG is parallel to CD If FG is 7 more than DG EG 6 and CD 15 find the length of DG Figures are not necessa drawn to scale State your answer in simplest radical form if necessary

Quadrilateral OPQR is similar to quadrilateral STUV Find the measure of side VS Figures are not drawn to scale 22 4 4 R Q P V U T

Enter segments in the blanks provided that would result in a true equation H K

Find the value of a to the nearest tenth Xx 8 5

Triangle KLM is similar to triangle NOP Find PN Round your answer to the nearest tenth if necessary Figures are not drawn to scale 33 7 14 M

Find the length of the third side If necessary round to the nearest tenth 12

Question Determine if triangle FGH and triangle IJK are or are not similar and if they are state how you know Note that figures are NOT necessari drawn to scale 37 100 135

JK 37 KI 32 JI 42 NL 16 and ML 21 find the perimeter of ALMN Round your answer to the nearest tenth if necessar EP Figures are not necessarily drawn to scale DA

Find the collision probability of 1200 bytes IEEE 802 11 FH packet at 2 Mbps and the Bluetooth Assume dwell period of an 802 11 transmission to be 3 ms and Bluetooth packet duration 0 625 ms What is PER with IEEE 802 11 DS

What is the perimeter of rectangle ABCD A A 30 units B 40 units C 50 units B D C

You approach a hill on top of which there is a tall radio antenna You know from your map that your horizontal distance from the bottom of the radio antenna is 600 feet The angle of elevation to the bottom of the antenna is 10 and the angle of elevation to the top of the antenna is 25 You figure that the height of the hill is feet and the height of the antenna is feet Enter your answers rounded to the nearest foot Hint Draw a picture Figure out the height of the hill Figure out the combined height of the antenna and the hill Compute the difference

Suppose that triangle ABC is a right triangle with a right angle at C and hypotenuse c Also note that a is the length of the side opposite angle A and b is the length of the side opposite angle B Given that b 11 and A 17 determine the values indicated below Round to four decimal places when needed a C B degrees

35 The strength S of a rectangular wooden beam is proportional to its width times the square of its depth Find the dimensions of the strongest beam that can be cut from a 12 in diameter cylindrical log Round answers to the nearest tenth 12 A w 5 9 in d 10 8 in C w 6 9 in d 9 8 in B w 7 9 in d 10 8 in D w 7 9 in d 8 8 in 35

Find the area of the region indicated in blue Area sq units Report answer accurate to 3 decimal places 136 2 2

Find a formula for the trigonometric function graphed below Use a as the independent variable in your formula help formulas 11 Click on graph to enlarge

For what values of x and y are the triangles to the right congruent by HL X A x 1 Ay y 11

A ven AB DC AAED is isosceles Prove AABE ADCE E B C D Statement Reason

5 Given ZM 20 NP bisects MO Prove AMNP AONP N Statement Reason

Find the standard form of the equation of the circle with the given characteristics Center 1 6 point on circle 4 1

Find the standard form of the equation of the parabola with the given graph 2 4 6 5 4 3 9 y 7 5 3 2 1 1 3 5 7 0 0 1 2 X

Find the standard form of the equation of the parabola with the given characteristic s and vertex at the origin 1 1 1 0 Focus

Find the values of x and y X 72 yo 520

Graph the hyperbola Give the domain range center vertices foci and equations of the asy 64x 81y 5184 81 OC y 64 9 OD y gXx The hyperbola 64x 81y 5184 has foci at 145 0 145 0 Simplify your answer Type an exact answer using radicals as needed Use a comma to separate answers as needed Type an ordered pair using integers or fractions Graph the hyperbola Choose the correct graph below OA OB O C O D

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 AUCKEND The vertices are 3 0 3 0 Type ordered pairs Use a comma to separate answers as needed The foci are 3 2 0 3 2 0 Type ordered pairs Type an exact answer using radicals as needed Use a comma to separate answers as needed What are the equations of the asymptotes Choose the correct answer below A y 3x B x y C x 3y D y x Graph the hyperbola x y 9 Choose the correct graph below OA O C 4 OB O D Q

Graph the ellipse Identify the center vertices endpoints of the minor axis and foci 20x 560 7y The center is 0 0 Simplify your answer Type an ordered pair The vertices are 0 4 5 0 4 5 Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as need The endpoints of the minor axis are 2 7 0 2 7 0 Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as neec The foci 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 neec

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

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

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 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

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

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

4 x y Z to 55

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

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

Midpoint 14 A 2 1 B 10 7 Midpoint AB AB

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

8 ATSW APSR ZTSW ZT ZR PR ST SW

Vending machine companies have been receiving customer complaints about their machines not working properly A cup will slide out and be filled with liquid until the cup is nearly full Customers have complained about the cup overflowing If the cup contains too much liquid a customer may get burned from a spill This could be an expensive lawsuit for the company A cup holds 8 oz a Decide a mean and standard deviation you would recommend for the company that minimizes overfill and underfill cup holds 8 oz Mean standard deviation B provide appropriate graphical and numerical representations C Please explain in words why you chose your mean and standard deviation Please explain in words how your mean and standard deviation minimize decrease the chance of overfill and underfill