Geometry Questions

Bianca calculated the height of the equilateral triangle with side lengths of 10 tan 30 h 8 7 h A 30 Then she used the formula for area of a triangle to approximate its area as shown below bh 10 8 7 43 5 units2 5 Calculate the area of the equilateral triangle using the formula for area of a regular polygon and compare it to Bianca s answer The apothem rounded to the nearest tenth is units The perimeter of the equilateral triangle is Therefore the area of the equilateral triangle is or approximately 43 5 units V The calculated areas are units

Manuel wants to buy a window shade to cover the window and frame shown The window is in the shape of a regular octagon The radius of the window including the frame is 2 ft and the measure of each edge of the octagonal frame is 1 52 ft Window 1 52 ft What is the approximate area of the window that nee to be covered including the frame O2 ft O 7 ft O 11 2 ft O22 5 ft

A community pool that is shaped like a regular pentagon needs a new cover for the winter months The radius of the pool is 20 10 ft The pool is 23 62 ft on each side To the nearest square foot what is the area of the pool that needs to be covered O192 ft O 960 ft O 1 921 ft 3 842

A regular pentagon has an apothem measuring 3 cm and a perimeter of 21 8 cm 3 cm What is the area of the pentagon rounded to the nearest tenth O 13 8 cm O 17 3 cm O 32 7 cm O 69 0 cm

A hexagon has a radius measuring 23 cm What is the approximate area of the hexagon O 686 6 square cm O 793 5 square cm O 1374 4 square cm O 1587 0 square cm

A regular pentagon has a perimeter of 60 cm B A D What is the measure of angle CBD What is the length of segment CD cm Which trigonometric ratio can be used to compare Bo to CD using angle CBD What is the approximate length of BC cm What is the approximate length of BD GM

Probability and Counting 6 A fair die is rolled once Let A be the event of rolling a number less than 4 Let B be the event of rolling an even number A 4 1 Draw a Venn diagram 2 What is the probability of event A P A 3 What is the probability of event B P B 4 What is the probability of A and B P AnB 5 What is the probability of A or B P AUB

The floor of a gazebo is in the shape of a regular octagon The perimeter of the floor is 72 feet The distance from the center of the octagon to one of the vertices is 11 8 feet What is the approximate length of the apothem 3 feet What is the approximate area of the floor of the gazebo square feet 3

The pentagon below has an area of 8 3 square centimeters 2 2 cm What is the approximate length of the apothem O 0 4 cm O 0 8 cm O 1 5 cm O 1 9 cm

The radius of a regular decagon a 10 sided figure is 15 units The length of one side of the polygon measures about 9 3 units What is the approximate area of the regular decagon rounded to the nearest tenth O273 6 square units 0547 3 square units 663 1 square units 1069 9 square units

The area of the octagon below is 10 391 9 square millimeters 56 mm What is the approximate perimeter of the octagon Round to the nearest whole number mm What is the approximate length of one side of the octagon Round to the nearest whole number mm

The polygon below is a regular hexagon 18 cm 18 cm What is the approximate length of the apothem Rou to the nearest tenth O9 0 cm O 15 6 cm 20 1 cm 25 5 cm 0

A regular pentagon has an apothem measuring 20 cm and a perimeter of 145 3 cm 20 cm What is the area of the pentagon square centimeters

The sum of all but one interior angle of a heptagon is 776 What is the measure of the final interior angle O 42 O 56 O 124 304

What is the sum of the measures of the interior angles of a 12 gon O 1620 O 1800 O 1980 O 2160

77 66 59 62 12x What is the value of x O 6 O 8 O 10 O 12

Use circle J 5x 15 K 120 L J What is the value of x

2 Find an equation for the plane that contains the line in the ry plane y 2r 1 and the point 3 2 2

Consider the plane that contains the three points p 2 3 8 q 6 8 4 r 9 4 3 using p as your reference point write the equation of the plane in the form ax by cz d and state the value of d

In the circle below suppose m GHE 122 and m ZHGF 68 Find the following a m2GHE b mZHEF 0 X

6 5 4 3 2 6 5 4 3 2 1 2 3 4 6 The graph above is a transformation of the function x Write an equation for the function graphed above

10 5 4 3 2 6 5 4 3 2 1 2 3 5 1 2 3 4 5 2 The graph above is a transformation of the function Write an equation for the function graphed above

merry go round is rotating at the constant angular speed of 4 3 RPM counterclockwise The platform of this ride is a circular disc of radius 26 feet You jump onto the ride at the location picture elow Impose coordinates as pictured with units in feet a If 31 then what are your xy coordinates after 3 minutes Round your answers to three decimal places x y rotating 4 3 RPM b If 15 then what are your xy coordinates after 15 minutes Round your answers to three decimal places x y c If e x y jump on here X 11 then what are your xy coordinates after 8 seconds Round your answers to three decimal places

4 Find m A C 8 cm B 105 32 cm 14 A

7 2 PQRS is a parallelogram S ST and P 120 O DO

Type the inverse of the matrix Use decimals If no inverse exists type none 1 32 5 5

d If 8 2 1 rad then what are your xy coordinates after 2 hours and 6 seconds Round your answers to three decimal places x y Draw an accurate picture of the situation end start end start end start

A 101 1 10 101 101 110 110 b 2 2 4 12 5 2 SOXXB The general least squares solutions of Ax b for the given matrix A and vector b are all vectors of the form x Simplify your answers x with x

1 Given the two functions f x x 4x 1 and g t 1 t a Find and simplify f g 4 b Find and simplify g f x c Find and simplify f x g x

4 a Draw the area 9x y 9z 18x 4y 18z 32 0 b In a spherical coordinate system draw the area p sin2 cos 20 2 cos

4 Consider the matrix equation Ax b where a b A 1 1 1 where a b 0 a When is A strictly diagonally dominant and what does this tell us about the Gaus Seidel method for Ax b 1 marks b Find the iteration matrix for the Gauss Seidel method applied to Ax b 5 marks c Using your previous answers for what values of a and b does the Gauss Seidel metho 4 marks converge

1 Draw an SVAJ diagram 2 Find the coordinates of Q at q p 2 p and 3p 2 However Rb 1m W S 0 0 1 2 YA Rb base circle sin 20 S 0 2 2 0 1 2 sin 20 Efl m

BC bi ects LABD B a x 3x 3 C Note Figure not necessarily drawn to scale 5x 1 D Enter a list of integer or decimal numbers more degrees b LABC d LABD c ZCBD degrees degrees

e If 02 1 rad then what are your xy coordinates after 7 seconds Round your answers to three decimal places x y Draw an accurate picture of the situation start end end start start end start end X

8 0 625 10 0 938 3 0 25 Write a rational function that goes through the dashes on the graph When you finish press Graph and submit response E Graph and submit response

If log34 1 2619 evaluate log30 25 Give your answer to four decimal places Enter

cone hemisphere frustum rectangular pyramid rectangular prism triangular prism cylinder prism with octogonal base

Write an equation for a line that passes through the origin and is perpendicular to y 5x 2

The table shows the lengths of cables needed to connect computers to create a network Find the minimum length of cable using the greedy and edge picking algorithm AB C D E C A 10 22 9 15 8 B C 10 22 12 12 14 16 5 14 9 16 D E 9 15 14 16 14 9 7 7 15 13 F 8 5 16 15 13

Simplify 3 0 X Enter the answer that belongs in the green box for the numerator of the exponent Enter

3 Line 2 x 2 1 y 1 3A z 5 1 x 7 11 z and Located in a plane The B plane passes through the points A 2 1 0 B 1 0 3 and C 3 1 1 Determine the point distance P 2 4 1 to the intersection of the a and planes 3

Complete the missing statements or reasons for the proof Given 21 22 23 44 Prove n Statements PROOF 1 21 22 and 23 24 1 2 2 3 214 4 2 3 4 l Reasons m n If two lines intersect the vertical Zs are 3 4 If two lines are cut by a transversal so that alternate exterior Zs are the lines are

3 Line 2 x 2 1 y 1 3A z 5 1 3 x 7 11 z and Located in a plane The B plane passes through the points A 2 1 0 B 1 0 3 and C 3 1 1 Determine the point distance P 2 4 1 to the intersection of the a and planes

Enter the letter for the function graphed below a y x 2 b y x 2 c y x 2 2 d y x 2 2 e y x 2 Enter

The points C 2 8 D 7 6 E 5 1 and F 0 3 form quadrilateral CDEF Plot the points then click the Graph Quadrilateral button Click on the graph to plot a point Click a point to delete it 10 9 8 7 6 slope of CD slope of DE D slope of EF slope of FC E 5 4 3 C 2 1 10 9 8 7 6 5 1 9 10 F 1 2 3 Find the desired slopes and lengths then fill in the words that BEST identifies the type of quadrilateral 4 5 6 length of CD length of DE length of EF length of FC 7 8 9 10 Quadrilateral CDEF can BEST be described as Submit Answer

Can you explain by detail how to find modulo inverse by using euclidean algorithm Find the value of 3 mod 43

3 Line 2 y 7 3 x 3 11 z x 2 y 1 32 z 5 1 and Located in a plane The plane passes through the points A 2 1 0 B 1 0 3 and C 3 1 1 Determine the point distance P 2 4 1 to the intersection of the a and planes

KL is tangent to the unit circle at point T A tanx K D cosecx X m TOL x Accordingly ITLI is equivalent to which of the following T B secx E cotx C sinx

Which sequence of rigid motions will definitely work to take triangle STU onto triangle GHJ S 111 H Rotate STU clockwise 90 degrees around point T Translate S T U to the left 1 unit Translate STU to the right 8 units Reflect S T U over HJ Reflect STU over ST Rotate ST U clockwise 180 degrees around point I 1p

2 Find FD 4 Find US 6 Find MN at appear to be tangent are C 15 F 3x 5 U 3x 1 T 8 12 8 E R 42 D x 11 30 2x 7 S N M