2D Geometry Questions and Answers

Solve the following formula for b y 3mx 46 b Enter your answer as an expression But be careful to enter an expression like both the numerator and denominator a b 3 m you need to type a b 3 m You need parentheses

Determine the measure of each indicated angle Note the figure is not drawn to scale A C 1069 21 m ACB m CBA m BAC m 1116 8 138 B

A right circular tank lying on its side has bases of radius 5 ft and a horizontal length of 12 5 ft Use the applet below to help in setting up the integral used to solve the following problem Ay X

Consider the function f x y 2 x y Plot it in GeoGebra a Draw level curves of f x y at each value 1 0 1 2 3 4 5 sy J 2 0 2 b Describe in words what the level curves look like and explain why this is t case

For the quadratic function f x x 4x answ a Graph the quadratic function by determining its vertex axis of symmetry y intercept and x i Does the graph of f open up or down

4 Find the dimensions of a rectangular parallelepiped that will maximize the enclosed volume while maintaining a constant surface area of 54 m 31 Figure 1 Parallelepiped 5 Find the interior angles of a rhombus that maximize the area with a maximum height of 12 inches and a perimeter of 64 inches Figure 2 Rhombus

Sketch the graph of f x 2x 10 yolul 10

8 Sketch the surface 1 2 5 x y Describe the boundaries of this surface

4 Find an equation describing the following sinusoidal curve y 3 4 114 5 Find an equation describing the following sinusoidal curve y t 12 7

K Use the graph to find the following a the domain off b the range of f c the x intercepts d the y intercept e intervals on which f is increasing a What is the domain of f Type your answer in Q f intervals on which f is decreasing g intervals on which f is constant h the number at which f has a relative minim i the relative minimum of f j f 6 k The values of x for which f x 3 1 Is feven odd or neither

QUESTION 2 s possible to find the area of a square by first calculating the s hat is the area of this square if the diagonal is 12 cm e the following diagram

MUTHARESE Use the graph to write a polynomial function of least degree f x 260 0 200 400 f x 400 000 200 000 200 000 100 0 200 0 67600

Function Notation Sketch the graph of y x AND y x label ea 5 Stretching and Shrinking Function Notation 10 Sketch the graph ofy x 2 AND ofy x 2 label ea y x 2 Sketch the graph of y x AND y x label e 10 Type of Transformation luvertically 104 galal Change to Coordinate Point Stretched horizontally Shrunk horizon

Use the graph to write the formula for a polynomial functio f x x 2 x 1 6 X 4 2 f x 6 4 2 4

Write the equation for the graphed function y 8 6 4 2 y 8 6 4 N 2 4 2 4

2 Find the area of the shaded region below Give your answer in square feet Note The picture is NOT drawn to scale 15 yd 300 in 150 in 18 yd 120 in 18 ft 30 ft

6 4 2 f x 6 4 2 4 6 4 6

2 Harley is building a rectangular wooden box for storage The box is going to have a base that is 2 feet long and 3 feet wide If the box needs to be able to hold 9 cubic feet of material how tall should it be in feet If the material for the box costs 0 60 per square foot how much will it cost to build the box

Clearly and neatly show all work for answers 1 Convert the following quantities Be sure to include units in your answers Round final answers to 2 decimal places where needed a 2 4 meters to centimeters b 8 cups to quarts c 12 stones to ounces d 12 pounds to grams al 22 kilomotors to vards

Highlight 2 8 Calculator ansit company operates commuter trains to help people get to the city h day Each train travels on a straight route to and from the farthest ion stopping at other stations along the route distance y miles the train is from the station after Commuter Train Distance graph shows the inutes Distance from the Station miles 322595 30 E 20 Torres Bravo 0 10 20 30 40 50 60 70 80 Time minutes Time Remaining 00 33 Question 7 a A Flag for Rea Formula Sheet Calculator Reference Type your answer in the box You may use numbers a decimal point and or a negative sign in your answer Based on the graph what was the average speed in miles per minute of the train during the interval of 30 to 40 minutes

Part 1 of 3 points Points 0 of 1 The median weight of a boy whose age is between 0 and approximated by the function w t 7 04 1 88t where t 0 0015t 2 0 000061t 3 is measured in months and wis measured in poun approximation to find the following for a boy with median w through c

2 Given AABC determine the measures of all of the sides and angles as well as the perimeter and area of the figure 12 10 00 30 e A B C 10 12

e the graph of the function f in the figure to sketch the graph of the function g Graph segments with closed endpoints only g x f x 5 X

In triangle ABC angle ABC 150 AB 3sqrt 3 and BC 4 The line through A that is perpendicular to AB and the line through C that is perpendicular to BC meet at D Find the area of quadrilateral ABCD

4 4pts Determine the area of the shaded shapes in Figure 4 Show your work 1 unit Figure 4 Nam

Objective Calculate the degree measure of an arc using the arc addition postulate R S 94 O T U Segments RT and SU are diameters of circle O What is the degree measure of arc SRT Hint just give numerical answer do NOT write degrees or use the degree sign

14 6 points Objective Determine the measures of central angles chords and arcs using theorems about angle chord and arc congre P T 4 3 48 66 R S 66 In circle T ZPTQ ZRTS What is the measure of arc PQ 24 33

Objective Solve problems involving angles formed by two intersecting chorc K L 170 125 250 50 55 O A M J 80 In circle O what is the measure of ZMAJ

Objective Apply theorems about inscribed angles and angles formed by a tangent and T 34 V U S Line segment SU is a diameter of circle V What is the measure of arc ST 68 56 112

U 14 D 8 16 C 56 S T 28 Find the missing length The triangles are similar Type your answer

Objective Identify and describe terms related to circles Which circle has a radius that measure 10 units O O 10 10 G H 6 20 F 20

Objective Solve problems involving arc length with central angles measured in degrees Q R 123 P S In circle P diameter QS measures 20 centimeters What is the approximate length of arc QR 10 centimeters 22 centimeters 20 centimeters 43 centimeters

C IL M 72 O 16 8 33 L 24 B The triangles are similar What is the missing length 18

A Ferris wheel has a diameter of 42 feet It rotates 3 times per minute Approximately how far will a passenger travel during a 5 minute ride 3 956 feet 132 feet 659 feet 1 978 feet

Objective Determine segment lengths angle measures and arc measure A 15 C O 8 B 5 D E Angle D is a circumscribed angle of circle O What is the perimeter of kite OBDE 60 units 17 units 27 units 23 units

An airplane takes off and climbs must fly over a 120 foot tower w what is the minimum distance be leaves the ground and the base of Draw and label a diagram for thi

K 54 B 112 C 110 D 108 J L What is the measure of arc KL A 106

A planter shaped like a rectangular prism has a length of 4 meters a width of 4 meters and a height of 3 meters Attached to the side of the planter is a smaller planter with 1 the volume of the larger planter What is the combined volume of both planters 24 cubic meters 34 cubic meters 48 cubic meters 72 cubic meters

Identify the value of x and the length of each secant segment N MY 3 2 5 L O x 12 NL 8 NP 14 Ox 12 NL 14 NP 8 x 10 NL 8 NP 12 Ox 10 NL 12 NP 8 X

Find the value of the indicated angles 8b 1 6b 9

11 M 33 A L 24 B The triangles are similar What is the missing length

18 What is the domain AND range of the function given below Use proper interval notation or Write infinity as inf 8 2 BiUFE EXA

26 Multiply and simplify completely 3x 1 3x 1 6x 6x 1 B 6x 1 9x 1 D 9x Previous 6x 1

What are the solutions to the equation z 9 0 8 11

Write the polynomial as an expression of its simplest fac 7 14a 21a

4y k 7y 9 In the system of equations shown above j and k are Which of the following constants and j is k plus must be true A x is y minus B x is y plus 1 2 C x is y minus D x is y plus 9 2 1 2 3 2 3 2

A circular swimming pool has diameter k meters and depth 4 meters throughout Which of the following expressions give the amount of water it holds in Ocubic meters

116 M C N 2X 8 What is the measure of arc PN 232 degrees 62 degrees 116 degrees 54 degrees

The graph of a function f is illustrated in the figure below a Draw the graph of y f x b Draw the graph of y f x 2 5 A 4 0 2 5 Q Choose the correct graph of y f x below OA OC in q Fin Q OB OD 3 F5 Q O

7 Find the exponential function f x Cb whose graph is given The graph goes 8 points through the points 0 2 and 1 6