Coordinate system Questions and Answers

1 Use the parallelogram to answer each of the following questions a Find the height 5

2 A man who is 6 feet tall stands in front of a flagpole His shadow is 10 feet long and the distance from the flagpole to the tip of his shadow is 85 ft How tall is the flagpole 6 ft ft

6 5x2 4 H

7 In the circle above ABCD is a quadrilateral and mA 8x 15 mzB y 10 mzC x 75 and m2D y 10 Which angle is greatest in measure in the quadrilateral A acib odal E lo esimenom od B

Which of the following is equivalent to S a 330 b 45 c 225 d 150 ii Which of the following is equivalent to 270 a b C d ENEINGIN 2 3 2

sosceles trapezoid ABCD has base angles that measure 82x 14 and 142 16 Find the indicated measurement below x

Which word below completes this antonym analogy intimidating pleasant sedentary A sluggish B active C immobile

6 Which of the following points lies on the circumference of the circle x 3 y 12 29 a 15 7 b 8 12 c 2 14 d 9 3 9 10

14 The equation of Circle A is x y 8y 4x 4 Determine the center and radius then graph and label the circle on the coordinate plane

3x 13 12 and 2 Suppose cos 2x and tan 2x no decimals csc x x 2t Find the exact values of sin 2x and

1 Find the closets point on the parabola y r 4 to the point 16 2

5 Which triangles are congruent in the figure FAABC AEBD G AABE ACBD HAAEB ACBD A B X LU

Calculator A rectangular lawn is 65 m long and 34 m wide Over time people have walked along a diagonal as a shortcut and have created a straight path What is the length of the path to the nearest tenth of a meter Enter your answer as a deicmal in the box 65 m 34 m

Calculator BC is parallel to DE What is AC Enter your answer in the box units 10 D 8 B A C 15 E

Triangle ABC is similar totriangle DEF The length of AC is 12 cm The length of EF is 15 cm The length of DF is 9 cm What is the length of BC Enter your answer in the box 20 cm

Flagpole a and flagpole c are both casting a shadow that ends at point s The distance x between the flagpoles is 12 m The distance y from flagpole c to point s is 10 m The height of flagpole a is 4 4 m What is the height of flagpole c

8 In the circle below ABCD is a quadrilateral and m A 8x 15 mzB y 10 mzC x 75 and m2D y 10 a Which student set up the correct equation to solve for x Why Student A 8x 15 x 75 Student B 8x 15 x 75 180 b Solve for the measure of ABC D B

Rewrite the following equation in terms of base e Express the answer in terms of a natural logarithm then round to three decimal places y 3 2 0 7 Rewrite the equation in terms of base e Express the answer in terms of a natural logarithm

Find the measure of minor arc JN L 41 K 47 M N J Write your answer as a whole number or a

Find parametric equations for the line through the point 0 2 3 that is perpendicular to the line x 1 t y 2 t z 4t and intersects this line Use the paramete x e e z t

2 What is the value of x if AABC is equilateral H A 18 6x 3 10x 5C

Describe a sequence of transformations that take trapezoid ABCD to TSCU You may use the draw tool to help illustrate your thinking but MUST describe the sequence of transformations in the text box B O Size Undo Clear All A D U C T

What is the area of the shaded sector created by central angle DOE 0 2 T 0 277 7 r 3 t 4 8 1 4 257 D 0 37 4 75 5 r 3 15 E units

When the measure of the sector is found by multiplying these two factors The ratio of the central angle over The area of the Area of a sector Ag nr 0 7 7 7 8 2 1 1 70 4 units is given in radians the area of a 2 2 Z Y 8

For central angles and inscribed angles that intercept the same arc W W M 1 the measure of the inscribed angle is the measure of the W angle when the intercepted arc is a semicircle a right triangle is created when the chords of the inscribed angle are congruent a For central angles and circumscribed angles that intercept the same arc created the central angle and the circumscribed angle are the angles form a kite angles is

on the Circle the Equation Given the center and a Point Find the equation of the circle with a center at 1 5 that passes through the point 3 8 1 Use the d x x y y Let x y 1 5 and xz 3 8 formula to determine the radius T 13 3 1 8 5 4 8 5 V449 Substitute the known values into the standard form x h y k r x 1 y 5 13 x 1 y 5

The General Form of an Equation of a Circle The To convert an equation in general form to standard form square form of an equation of a circle is x y Cx Dy E 0 Complete the square for the x and y terms Group together the x terms x 4x y Determine what value needs to be added to both sides of the equation to complete the square x 4x 4 y 8y 16 10 4 16 10 Factor the polynomials x y 4x 8y 10 0 1 T 10 h k 2 10 2 41 the 2 4 2 2 20 y

34 m 2 x 71 60 A 7 C 12 2 B 11 D 10

The graph of y f x is shown as a red dashed curve with the points A B C and D highlighted Draw the graph of y f x by dragging the blue movable points to the transformed locations of A B C and D Provide your answer below 10 5 10 5 0 5 1 1 1 VA 5 B D 10

C H B A 9 rotation 90 counterclockwise about the origin H 421 H G

What is the center of Clue 18 Input your answer as a coordinate point x y with no spaces A Identify the center of the circle with the equation shown below x 6x y 4y 7

equal siope intercept form do not include any spaces in the equation Write the equation of a line perpendicular to 2x 5y 10 that passes through 10 3

5 occurred to the triangle y K 5 4 3 2 1 1 2 L G 2 3 MathBus com

BB 23 The table shows data from the science fair experiment that studied the number of eggs that hatched at three different temperatures What is the probability that an egg hatched a b What is the probability that an egg hatched or it was kept warm Give an example of two events that are independent of each other hatched not hatched i cool 6 19 room temperature 14 warm 23 2

8A 20 List all possible outcomes for spinning the spinner and rolling a fair die Make a tree diagram table or just a list 8A 21 What is the probability of spinning a Y and rolling a 3 X Z Y

6C 13 Prove that quadrilateral ABCD is a rectangle G B A 1 S D

Find the value of x Write your answer as a decimal 122 X D 41 40 B

Finding the Distance between Two Points in the Coordinate Plane Recall that for any two points x y and x y in the coordinate plane the between them is d x x x y 1 1 x2 1 d 2 1 3 1 3 4 9 16 25 d 5 4 3 2 1 5 4 3 2 1 2 3 4 5 y 45 2 3 4 X

Polygon Exterior Angle Sum Theorem Polygon exterior angle sum theorem The sum of the of the exterior angles of a one ateach vertex is 360 What is the measure of each exterior angle in a regular pentagon Method 1 There are 5 congruentexterior angles 360 Method 2 Use linear pairs 5 Each interior angle has a measure of 108 Using linear pairs we can subtract from 180 180 108 Using the Polygon Exterior Angle Sum Theorem What is the unknown angle measure What is the value of x The sum of the measures of the external angles is 360 90 72 96 82 polygon 360 340 The unknown angle is 20 x 7 20 82 2 linear pair 1 180 3 72 96 5

d Pentagon 3 1 can of paint covers 100 cm Determine the total number of paint cans needed to cover the entire figur below your anst a 12cans b 3 cans C 6 cans d 4 cans 12 6 5

DO NOW 1 Kaliyah and Kennedy were given the task to determine the volume of the figure below Their work is below Analyze their work and determine which student correctly solved for the volume of this figure and identify the other student s error Kaliyah s work 1 V Bh 3 6 15 14 1 3 6 210 V 1 V V 420 ft Kennedy s work 1 V Bh 3 x 1 105X14 14 V 3 1 V 45 14 V 210 ft Which student correctly solve for the volume of this figure What was the other student s error 6 ft 14 ft 15 ft

Consider the graph of a transformed secant shown below 9 8 7 6 y 5 4 y 3 2 1 4 3 2 1 0 1 2 3 4 5 6 7 a What is the period of the corresponding sine graph Show Transcribed Text b What is the amplitude of the corresponding sine graph 2 3 4 5 6 G c What is the midline of the corresponding sine graph d Give a formula for the corresponding sine graph e Give a formula for the cosecant function graphed above

Score 30 an a n 1 d 1 1 For each general term write the first 3 terms of the sequence and identify it as arithmetic geometric or neither 4 marks a an 2n 1 b an 3 c an 8n d an 3n 1 2 The general term is given Find the indicated terms for each sequence an n 3 17 and tis b an n n 2 t11 and 135 4 marks

T6A Describe transformations in the plane 6A 9 Rotate the line on the diagram to the right 90 clockwise about the origin Graph and write the equation of the rotated line LT 6B Translate between the geometric description and the equation of circles and parabolas 68 10 What is the center and radius of the circle with this equation B 2 1 y 4 3 2 NM 2 NM 5 PT

1 Determine whether each scenario represents surface area or volum a Helium in a balloon b Glazing on a donut c The peel to a banana d Water inside a pool e

9 Convert the exponents write in exponential form 33 34 3x2 58 x 53 65 3 2

Consider the diagram shown below Suppose that O 0 0 and A units long a In radians what is the value of 0 equivalently the measure of ZAOB 0 Preview b In radians what is the value of 02 equivalently the measure of ZBOCY Preview c What are the z and y coordinates of point C 02m oy 3 9 0 and B 3 2 2 23 The are between points B and Cis 15 834 Preview Preview B

u V V x y 6 1 u 2 u WebAssign Plot V x In component form we write u V b A vector in a coordinate plane is expressed by using components In Figure II the vector u has initial point x y 3 6 X and v I u 2 u 2 1 Then 2u and terminal point and u v 2 7

Farmer Jones grows oranges The total revenue marginal revenue total cost and marginal cost of producing various quantities of oranges crates in 1000s are presented in the table below Output crates in 1000s 0 2 3 6 Total Revenue 50 150 300 450 600 750 900 Marginal Revenue 150 150 150 150 150 150 Total Cost 0 180 300 360 480 720 1020 Marginal Cost 160 120 60 120 240 300 Suppose the market for oranges is perfectly competitive To maximize protits farmer Jones should produce 4000 thousand crates of oranges Enter a numeric response using an integer At that level of output farmer Jones will earn profit of S

Type the correct answer in each box Assume it 3 14 Round your answer s to the nearest tenth D C 90 30 A The radius of the circle is B In this circle the area of sector COD is 50 24 square units units and mAB is units Reset Next