Coordinate system Questions and Answers

11 If the following triangles are similar find x All drawings are not to scale 20 30 X The units are in inches X

A 6 0 8 D 2 2 32 6 1 b 6 2 C 2 2 B 6 0 00 6 8 10 X

Two reflections over intersecting lines is the same as a single B i U Font Family Y 130 50 AAAF equal to two times the If an object was first reflected over the line segment OA and then reflected over the line OB explain what single transformations would this be equivalent to A between the lines of reflection

5 Determine if the following is a reflection a rotation or a translation O Reflection about the y axis O Rotation O Translation O Reflection about the x axis

on coordinates of the image after you ve applied the following translation vector 3 y 2 A 6 0 D 2 2 4 C 2 2 B 6 0 10 X

Find the distance between each pair of points Round your answer to the nearest tenth if necessary 1 2 3

In Exercises 1 to 10 classify each statement as true or false 1 AB is the longest side of AABC A Exercises 1 2 70 2 AB BC 3 DB AB A 65 A 32 110 100 100 5 45 50 B Exercises 3 4 4 Because mA m ABC it follows that DA DC 5 m A m B m C B C

not satisfied Show all work pos f x 3x 4 x 2 3x 10

In Exercises 21 to 26 AABC is a right triangle Use the given to find the length of the third side of the triangle information 3 2 21 a 4 and b 22 a 3 12 and b 5 23 a 15 and c 17 24 b 6 and c 10 A a B

29 Which of the following can you not conclude from this diagram K A B C D X 15 G 5 ALKG AMLG AKGLAMGL AKGL ALGM LG LG M

Instructions Your job is to add each of the four bases to the simulated spill to determine exactly how much of each is required to neutralize the acid Remember that neutralizing means to make the pH 7 This process of determining the amount of a chemical needed for a certain reaction is called a titration Chemical Magnesium Hydroxide Mg OH 2 Laboratory Acid Base Neutralizaton keachokd Reactions The Perfect Storm Spill Drill Sodium Hydroxide NaOH Sodium Carbonate Na CO Calcium Hydroxide Ca OH 1 Shovels required to neutralize acid Amount required to neutralize the acid 500 kg per shovel kg 500 kg cost per 1000kg 3085 Cost per 1000 kg kg 330 308 88 88 Total Cost I

1 In the diagram below ZDEF has been reflected in line t by reflecting points D E and F a As in class draw in segments DD EE and FF Mark the intersections of the segments with the line t b What is true about the points that you marked in part a Verify using an appropriate tool c What is true about the angles that the segments make with line t Mark these on your diagram D D E E tractor that the two angles are equal F

If sin a 0 444 and sin 0 774 with both angles terminal rays in Quadrant l find the values of cos a 3 sin a 3 Your answers should be accurate to 4 decimal pla

Given right triangle ABC shown below do the following a Measure the three side lengths to the nearest millimeter AB BC sin A b Based on your measurements in a state the value of each of the following in decimal form Round to the nearest thousandth cos A AC c Given the partial table of trigonometric values shown below which angle in the table is closest to the m A Verify using your protractor tan A Angle 37 38 39 40 41 A sine 0 6018 0 6157 0 6293 0 6428 0 6561 cosine 0 7986 0 7880 0 7772 0 7660 0 7547 B tangent 0 7536 0 7813 0 8098 0 8391 0 8693 0 0001

4 Although it may seem obvious from the diagram of rectangle ABCD pictured ADMC is isosceles Explain why this must be true M

Given quadrilateral EFGH with vertices at E 4 8 F 8 4 G 5 5 and H 7 1 prove using coordinate geometry that EFGH is a rectangle Note that there are a few different methods that work y

10 Consider the definitions of the sine and cosine ratios Why can their values never be greater than 1 Use the triangle below as reference to help you answer C

4 Square ABCD has vertices at A 8 1 B 3 6 and D 3 10 What are the coordinates of point C TL

4 Given that RSTU is a parallelogram and ST TU explain why RSTU must also be a rhombus R

Weights in grams of apples are normally distributed with a mean weight of 110 and a standard deviation of 5 5 grams An apple is selected at random Which has the greatest probability Select one a The apple weighs less than 75 grams b The apple weights between 95 and 100 grams c The apple weighs between 115 and 120 grams d The apple weights greater than 150 grams

Graph the circle x2 y2 2x 8y 19 0 Ty Select one a 5 Ob 10 10 10 10 x

Given a 61 43 4k and b 3i xj 9k find x when a b 2

The figure below shows quadrilateral ABCD and a line of reflection A B C R 9 x y 8 7 6 5 4 3 2 B x y C 4 5 6 7 Determine the coordinates of A B C and D using only reasoning that is without folding x y 1 2 3 D 1000 00 8 T 9

0 This is a vector wit 2 03 magnitude direction

each circle 2 2 1 x 1 y 3 2 2 3 x 1 y 4 2 x 2 y 1 16 2 4 x y 3 25 4 9

2 Diameter of 12 3 Diameter of 22 For problems 4 10 write the equation of the given circle 4 Center 12 7 Radius 4 5 Center 2 14 Radius 5 6 Center 12 10 Radius 7 7 Center 6 4 Radius 8 8 Center 3 13 Diameter 2 9 Center 1 3 Diameter 8

with a diameter of 14 inches 3 A sector that is two thirds the area of a circle with a radius of 10 yards For problems 4 7 find the area of each sector Write your answer as a decimal rounded to the nearest tenth 4 5 6 60 10 in 3 m 150 3x 4 cm

the standard equation of the circle in the graph Center 4 0 4 5 et one a x 4 2 y2 25 0 x y 25 C x 4 2 y2 25 d x y 16 e the standard equation of the circle in the graph 2 1 4 1

Which of the following is the graph of x 2 2 y 1 9 elect one a b C d Lify FRE 2 O

degrees the measure of arc FH is 138 degrees and the measure of arc HB is 20 degrees Find the measure of FPD 3 points P B E 9 In the diagram below the measure of arc SQ is 106 degrees and the measure of arc PR is 120 degrees Find the value of x 3 points

X 6 X 4 12 12 Find the value of x 3 points S x 5 N x 8 M K 4

ow wattage radio station can be heard only within a certain distance from the station On the graph ow the circular region represents that part of the city where the station can be heard and the cen e circle represents the location of the station Which equation represents the boundary for the regic ere the station can be heard ep elect one 4 4 O a x 6 2 y 1 32 b x 6 y 1 32 c x 6 2 y 1 16 Od x 6 2 y 1 16 X

What is the value of sec 0 if the terminal side of angle 0 intersects the unit circle in the first quadrant at x

Find the value of x X Type an integer or a decimal to

K Which arc does ZC intercept ZC intercepts EFC FCE CDE Question 1 12 3 1 EO F Points 0 of 1 C O D E 7 por

Properties are some of the rules of mathematics which allow you to manipulate values and equations Most students are able to use the properties but do not realize their name nor why or how they work Match each property to each situation 3 x 7 3x 21 If a 40 then 3 8 a 15 5 0 0 If y 100 then y 10 90 5 0 5 Choose Zero Product Property Zero Sum Property Subtraction Property of Equality Distributive Property Division Property of Equality Choose Choose Choose

13 LFAC and LCAD are adjacent and AF and AD are opposite rays What can you conclude regarding LFAC and LCAD

For each pair of solids determine whether they are similar If they are give the scale factor of Solid 1 to Solid 2 in simplest form Note The figures are not drawn to scale a The solids are right rectangular prisms Their lengths widths and heights are shown 1 1 15 cm Solid 1 15 cm Solid 1 16 cm 4 cm Solid 1 b The solids are right rectangular pyramids Their lengths widths and heights are shown 20 cm 5 cm 9 cm Solid 2 21 cm n 24 cm Solid 2 28 cm cm c The solids are right cylinders Their heights and base diameters are shown 9 cm 2 cm Solid 2 32 cm 8 cm 18 cm O Similar Scale factor O Not similar O Similar Scale factor Not similar O Similar Scale factor O Not similar

The radius of a cylindrical construction pipe is 2 5 ft If the pipe is 22 ft long what is its volume Use the value 3 14 for and round your answer to the nearest whole number Be sure to include the correct unit in your answer 22 ft 2 5 ft 1

Find an equation for the graph Type the equation of the given graph in the form y Asin Bx or y A cos Bx D otion Ico intogors or fractions for any numbers in the equation Simplify your answer 3 TU 2 JTC 5 3 14 IT

The polar coordinates of a point are given Find the rectangular coordinates of this point 3 3 2 What are the rectangular coordinates of this point Type an ordered pair Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

9 What relationship subset intersect disjoint or equivalent can be used to characterize the two sets shown in the Venn Diagram A a B B A b

The area of the triangle defined by the hyperbola s two focal points and the circle s NORTH point is NOTE b equals two Round your answer to the nearest whole number

Use the dot product to find the magnitude of u u 121 22j u 26

Let P x be a polynomial with real coefficients of the 5 th degree The polynomial P x can have exectly four roots with positive real parts The polynomial P x can have exactly four roots with nonzero imaginary parts The polynomial P x can have all roots with nonzero imaginary and nonzero real parts

Find the coordinates of the circumcenter of ABC with vertices A 4 0 B 8 3 and C 4 3 6 14 5 O 0 1 5 O 2 1 5 O 6 1 1

Use the Root Test to determine the convergence or divergence of the series If you need to use or 00 enter INFINITY or INFINITY respectively 8 1 37 n 1 lim Vla 1 3 81x converges diverges O inconclusive

ne information provided 1 Parallel Line Construction For this part of the assignment you will construct a parallel line through a given line and point First draw a segment AB and point C on your paper Next construct a line through point C that is parallel to AB Label all points and lines used in the construction 2 Perpendicular Line Construction For this part of the assignment you will construct a perpendicular line to a given segment that passes through a given point First draw a segment AB on your paper Draw a point C above that line Construct a perpendicular line through segment AB and point C Label all points and lines used in the

12 10 8 5 4 2 0 0 N 4 6 8 Note It is not necessary to calculate the linear correlation coefficient you simply need to give an accurate educated guess 00 50 00 60 00 75 00 90

9 Given A 1 2 3 4 B 2 4 6 8 and C 1 3 5 7 9 Find a ANB b BUC ANB N BUC