Homework 1 #3. v 10. Student Name/ID: Integrated Mathematics II / AIR Int Math II (Robertson) 1. Simplify.

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1 Homework #3 Integrated Mathematics II / AIR Int Math II (Robertson) Student Name/ID:. Simplify. v 0 Assume that the variable represents a positive real number. H om ew or k #3 Page / 0

2 2. For each experiment, determine whether events A and B are independent or dependent. Experiment Events Independent Dependent Kala randomly selects one of her sports trading cards. She then returns the card to the deck and mixes the deck. She then makes another random selection. 6 A number cube with sides labeled through is rolled twice. At the beginning of each of two football games, a coin is tossed, and the winner of the coin toss is determined. 2 A bin contains marbles numbered through. A marble is randomly selected from the bin and set aside. Then another random selection is made from the remaining marbles. A box contains pens. Some pens have ink and some do not. A teacher randomly selects a pen and sets it aside. Then another random selection is made from the remaining pens. Event A: The first selection is a soccer player. Event B: The second selection is a baseball player. Event A: The first roll is an even number. Event B: Both rolls are even numbers. Event A: In the first game, the home team loses the coin toss. Event B: In the second game, the home team wins the coin toss. Event A: The first selection is an odd numbered marble. Event B: The second selection is an even numbered marble. Event A: The first selection is a pen with no ink. Event B: The second selection is a pen with ink. H om ew or k #3 Page 2 / 0

3 3. Graph the line. y 2x y x x 2 7x Find all complex solutions of.. Draw the image of the following triangle after a dilation centered at the origin with a scale factor of. 2 8 y x C 8 6. The circle below with center is divided into equal slices. H om ew or k #3 Page 3 / 0

ACB AB Central angle intercepts, forming the shaded sector. A C B Complete the statements below. Give your answers as exact values, not decimal approximations.

4 ACB AB Central angle intercepts, forming the shaded sector. A C B Complete the statements below. Give your answers as exact values, not decimal approximations. (a) Find the ratio of the area of the sector to the area of the circle. Area of sector Area of circle (b) From the figure we see that ACB The measure of is [ equal to / twice / half ] the measure of. m AB So,. This gives the following equation. m AC B. AB m AB 360 (c) Choose the equation that is true. Area of sector Area of circle Area of sector Area of circle Area of sector Area of circle Area of sector Area of circle 360 m AB m AB 360 m AB 8 m AB 360 πr 2 (d) Using for the area of the circle, choose the equation that gives a formula for the area of the sector. Area of sector m AB 360 8π r 2 H om ew or k #3 Page / 0

5 Area of sector Area of sector Area of sector 360 πr 2 m AB m AB 360 π r 2 m AB πr 2 7. For the triangles below, use the tools to move the solid triangle exactly onto the dashed one. Then answer the parts below. 8 C D Y 2 27 X W E (a) Complete the congruence statements below. W ~ (Choose one) X ~ (Choose one) Y ~ (Choose one) (b) Find the following ratios. Write your answers as fractions in simplest form. CE WX ED XY CD WY (c) Select the true statement. WXY WXY and and CED CED are similar. are not similar. H om ew or k #3 Page / 0

8. For each figure below, determine (by using the markings) if there is a pair of congruent triangles. If there is, name the congruence and give the property justifying the congruence.

6 8. For each figure below, determine (by using the markings) if there is a pair of congruent triangles. If there is, name the congruence and give the property justifying the congruence. Note that the pairs of triangles are drawn as congruent, but you should not rely on how they are drawn in determining your answers. (a) N Q M O R P Not Necessarily Congruent Congruent : MNO ~ by the (SAS SSS AAS ASA) Congruence Property (b) G L H K I J Not Necessarily Congruent Congruent : GHI ~ by the (SAS SSS AAS ASA) Congruence Property (c) U Z V Y W X Not Necessarily Congruent Congruent : UVW ~ by the (SAS SSS AAS ASA) Congruence Property H om ew or k #3 Page 6 / 0

7 6 9. A number cube with faces labeled from to will be rolled once. The number rolled will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling a number greater than. If there is more than one element in the set, separate them with commas. Sample space: Event of rolling a number greater than : H om ew or k #3 Page 7 / 0

0. Use the given information to complete the proof of the following theorem. If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

8 0. Use the given information to complete the proof of the following theorem. If a line divides two sides of a triangle proportionally, then it is parallel to the third side. I K H L J Given: JL LH IK KH Prove: JI LK Statement Reason Line(s) Used J L L H I K KH Given J L I K L H KH J L L H 3 + L H L H I K KH + KH KH Fraction Algebra 2 + J L L H L H I K + KH KH Fraction Algebra 3 6 J H J L + I H I K + Segment Addition Property Segment Addition Property J H 7 L H H 8 ~ I H KH H 9 H I J ~ H J I 0 ~ H L K SAS Similarity Property 7 8 J I H om ew or k #3 Page 8 / 0

9 . Find each length below. (a) In the figure below, two secants are drawn to a circle from exterior point. EW 68 EZ 2. EX 3 XY Suppose that,, and. Find. E E Z X Y W (b) In the figure below, two chords intersect inside the circle at point. UJ 3 UK 39 UN 9. UM Suppose that,, and. Find. U M K J U N 2. The three right triangles below are similar. J P X 27.6 The acute angles,, and are all approximately measured to be. The side lengths for each triangle are as follows. Note that the triangles are not drawn to scale cm 27.6 J 7.8 cm L 9. cm K H om ew or k #3 Page 9 / 0

10 R cm 36.6 cm P cm Q Z 8.38 cm.9 cm X cm Y (a) For each triangle, find the ratio of the length of the side adjacent to Note that "side adjacent" cannot also refer to the hypotenuse. Round your answers to the nearest hundredth. JK JL PQ PR XY XZ 27.6 sin 27.6 cos 27.6 tan 27.6 (b) Use the ALEKS Calculator to find,, and. Round your answers to the nearest hundredth. sin27.6 cos27.6 tan27.6 to the length of the hypotenuse. (c) Which trigonometric function gives each ratio of sides in part (a)? sine cosine tangent none of these H om ew or k #3 Page 0 / 0

11 3. Use the graph to determine the behavior of the function between the indicated points. A B y C D E x Points Behavior of the function increasing A and B constant decreasing increasing B and C constant decreasing increasing C and D constant decreasing increasing D and E constant decreasing 8m 2 m 3. Factor. H om ew or k #3 Page / 0

12 . The entire graph of the function is shown in the figure below. Write the domain and range of using interval notation. f f y 3 2 x H om ew or k #3 Page 2 / 0

l k m 69 m 0 6. In the figure below, lines and are parallel. Suppose that and. 2 l 3 k m n Complete the statements below. By the angle addition property,. We are given that and, so.

13 l k m 69 m 0 6. In the figure below, lines and are parallel. Suppose that and. 2 l 3 k m n Complete the statements below. By the angle addition property,. We are given that and, so. We see that and are. And since lines and are parallel, and are. So,. We see that and are. And since lines and are parallel, and are. So,. m 2 + m + m m 69 m 0 m 2 l k m 3 l k 3 m 3 m + m 2 + m 3 Therefore,. 2 3 The relationship between,, and is an example of the following rule. The sum of the interior angle measures of a triangle is. H om ew or k #3 Page 3 / 0

7. Use the given information to complete the proof of the following theorem. If opposite sides of a quadrilateral are congruent, then it is a parallelogram.

14 7. Use the given information to complete the proof of the following theorem. If opposite sides of a quadrilateral are congruent, then it is a parallelogram. By definition, a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. Use this definition in your proof. R S 2 Q 3 T Given: QR QT ~ ~ QRST ST RS Prove: is a parallelogram Statement Q R ~ S T Given 2 Q T ~ R S Given Reason Line(s) Used 3 ~ Reflexive Property ~ ~ 2 6 ~ CPCTC Property CPCTC Property 7 Q R 8 Q T 9 Q R S T is a parallelogram H om ew or k #3 Page / 0

15 8. Four different linear functions are represented below. Function Function 2 0 y x x y Function 3 Function y x + The slope is 2 y and the -intercept is. Answer the following questions. Which function has the graph with a -intercept closest to? Function Function 2 Function 3 Function Which functions have graphs with slopes less than? (Check all that apply.) Function Function 2 Function 3 Function Which function has the graph with the greatest -intercept? Function Function 2 Function 3 Function y 0 y H om ew or k #3 Page / 0

16 9. Each of sixty-four students in grade 7 or 8 was asked, "What is your favorite sport?" Here are the results. students in seventh grade and 7 8 students in seventh grade and 2 2 students in seventh grade and Construct a two-way frequency table for the data. students in eighth grade chose "Basketball". students in eighth grade chose "Hockey". students in eighth grade chose "Swimming". Seventh grade Eighth grade Basketball Hockey Swimming ABC DEF 20. Consider and shown below. D A C B F E Answer the following questions. ABC m A 30 m B 7 DEF m D 30 m E 7 (a) In, and. In, and. Use this information to find the following angle measures. m C m F (b) Use the ruler to find all side lengths for each triangle. Assume all lengths are whole numbers. H om ew or k #3 Page 6 / 0

17 AB DE BC EF CA FD (c) Find the following ratios. Write your answers in simplest form. AB DE BC EF (d) Three pairs of statements are shown below. For each pair, select the true statement. ABC ABC The angles in have the same measures as the angles in. The angles in do not have the same measures as the angles in. The ratios of corresponding side lengths are all equal to each other. The ratios of corresponding side lengths are not all equal to each other. The triangles are similar. The triangles are not similar. CA FD DEF DEF 2. For each sum or product, determine whether the result is a rational number or an irrational number. Then choose the appropriate reason for each. A: The sum of two rationals is always rational. B: The sum of a rational and an irrational is always irrational. C: The sum of two irrationals is sometimes rational, sometimes irrational. D: The product of two rationals is always rational. E: The product of a nonzero rational and an irrational is always irrational. F: The product of two irrationals is sometimes rational, sometimes irrational π Result is Reason { rational, irrational } { A, B, C, D, E, F } { rational, irrational } { A, B, C, D, E, F } { rational, irrational } { A, B, C, D, E, F } { rational, irrational } { A, B, C, D, E, F } H om ew or k #3 Page 7 / 0

y 22. Solve for. 6y 2 + 30y 0 23. Below are three circles. The circumference and diameter of each circle have been approximately measured. Circle : Circumference: Diameter: 9 units 28.

18 y 22. Solve for. 6y y Below are three circles. The circumference and diameter of each circle have been approximately measured. Circle : Circumference: Diameter: 9 units units Circle 2: Circumference: Diameter: 8 units 2.26 units Circle 3: Circumference: Diameter: units units (a) Use the measurements above and the calculator to fill in the blanks. Write each answer as a single decimal. Do not round. Circle : Circle 2: Circle 3: Circumference Diameter Circumference Diameter Circumference Diameter (b) Let represent the circumference of any circle and represent the diameter. C d π 3. π C d C d d π C d π C π Using the fact that is approximately, which formula seems reasonable? (c) Write a formula that relates the circumference,, of a circle to its diameter,. C C d H om ew or k #3 Page 8 / 0

19 2. Solve. y + y (If there is more than one solution, separate them with commas.) 2. Look at the graphs and their equations below. Then fill in the information about the leading coefficients A, B, C, D and. y y x x y A x 2 y B x 2 y y x x y C x 2 y D x 2 A B C D (a) For each coefficient, choose whether it is positive or negative - Positive - Negative - Positive - Negative - Positive - Negative - Positive - Negative (b) Choose the coefficient closest to 0 (c) Choose the coefficient with the greatest value H om ew or k #3 Page 9 / 0

20 26. Find the equation of the quadratic function f whose graph is shown below. 0 y x , 3 -, H om ew or k #3 Page 20 / 0

21 27. The figure below is a right triangle with side lengths,, and. m X m Y Suppose that does not equal. X x y z z y Y x Z Complete the following. XYZ X Y Part : In, and are - supplementary. - complementary. - neither complementary nor supplementary. x y z Part 2: Use,, and to fill in the blanks. Make sure to use the appropriate upper-case or lower-case letters. sinx siny cosx cosy Part 3: Select all of the true statements. cosx cosy sinx siny sinx cosy cosx siny None of the above is true. Part : Fill in the blank. cos 67 sin H om ew or k #3 Page 2 / 0

22 28. For the figure below, do a dilation centered at the origin with a scale factor of. Then answer the questions. 20 y Dilation x (a) Find the following. Shortest side length of the original figure: units Shortest side length of the final figure: units (b) Fill in the blank to make a true statement. Shortest side length of the final figure (c) True or False? Shortest side length of the original figure The original figure and the final figure are similar. True False H om ew or k #3 Page 22 / 0

29. An automobile manufacturing plant produced vehicles today: were sedans, were vans, and were trucks. Plant managers are going to choose two of these vehicles for thorough inspection.

23 29. An automobile manufacturing plant produced vehicles today: were sedans, were vans, and were trucks. Plant managers are going to choose two of these vehicles for thorough inspection. The first vehicle will be chosen at random, and then the second vehicle will be chosen at random from the remaining vehicles. What is the probability that two vans will be selected? Report your answer as an exact fraction Find the volume of this rectangular pyramid. Be sure to include the correct unit in your answer. 6 ft 9 ft ft 3. Simplify the expressions below as much as possible. Leave no negative numbers under radicals and no radicals in denominators Determine whether a triangle with the given vertices is a right triangle. Right triangle Not a right triangle Cannot be determined T 6,, R 8,, I 3, D, 0, E, 0, F 9, A 3, 3, B, 6, C, 0 H om ew or k #3 Page 23 / 0 2

24 x y x 2 + x Find the -intercept(s) and the coordinates of the vertex for the parabola. If there is more x than one -intercept, separate them with commas. 3. Complete the proof below by writing the correct "Reason" and, if applicable, giving the statements upon which the reason was based. C D E F Given: Prove: CD EF CE DF Statement Reason CD EF.. CE CD + DE DF DE + EF DF DE + CD.. CE DF.. 3. Simplify. 7v 2 2v + v + 6 g x 36. Find the average rate of change of from to. Simplify your answer as much as possible. 2x 2 9x x 2 x 6 H om ew or k #3 Page 2 / 0

25 f x 3 x g x x Compare the functions and by completing parts (a) and (b). x 3 (a) Fill in the table below. Note that the table is already filled in for. x f x 3 x g x x x f x g x (b) For, the table suggests that is [always / sometimes / never] greater than. 38. For the following right triangle, find the side length. x 2 6 x H om ew or k #3 Page 2 / 0

26 , 7 8, In the figure below, the solid circle has center and radius. The dashed circle has center and radius. Use the transformation tools given to move the solid circle exactly onto the dashed circle. Then answer the parts below. 3 y x (a) Fill in the blanks to describe the transformations necessary to move the solid circle exactly onto the dashed circle. Translate the solid circle {to the left,to the right} by unit(s) and {up,down} by unit(s). Dilate the solid circle by a scale factor of. (b) Are the original solid circle and the dashed circle similar? Yes No H om ew or k #3 Page 26 / 0

27 0. The Venn diagram below shows the students in Ms. Jones's class. The diagram shows the memberships for the Basketball Club and the Math Club. Note that "Leila" is outside the circles since she is not a member of either club. One student from the class is randomly selected. Let Let A B denote the event "the student is in the Basketball Club." denote the event "the student is in the Math Club." 9 Basketball Math Elsa Debra Goran Salma Amanda Mai Reuben John Leila (a) Find the probabilities of the events below. Write each answer as a single fraction in simplest form. P A P B P A andb P A orb P A + P B P A and B P A + P B P A and B (b) Select the probability that is equal to. P A and B P A or B P B P A H om ew or k #3 Page 27 / 0

28 x. Solve for. x 20 y 2. The Sugar Sweet Company is going to transport its sugar to market. It will cost to rent trucks, and it will cost an additional C $0 for each ton of sugar transported. S C S 8 $00 Let represent the total cost (in dollars), and let represent the amount of sugar (in tons) transported. Write an equation relating to. Then use this equation to find the total cost to transport tons of sugar. 3. P S Q R Given: Prove: QR RS PQ SP PQ ~ RS H om ew or k #3 Page 28 / 0

29 b a Given:: a b Prove: ~ 8. What are the leading coefficient and degree of the polynomial? 3u + u 8 23u Leading coefficient: Degree: i 6. Write in terms of. Simplify your answer as much as possible. 3 H om ew or k #3 Page 29 / 0

30 7. For each set of probabilities, determine whether the events and are independent or dependent. A B Probabilities Independent Dependent P A P B 2 P A B ; ; and 0 P A P A P A 9 P B 9 ; ; P B 3 ; ; P B 7 ; ; P B A P A B P A B 2 8. For each set of probabilities, determine whether the events and are independent or dependent. A B Probabilities Independent Dependent P A P B 3 P A B ; ; and 2 P A P A P A 8 8 P B ; ; P B ; ; P B 9 ; ; P A B P B A P A B 3 9. Write the following as a radical expression. 3 H om ew or k #3 Page 30 / 0

31 0. Translate this sentence into an equation. The difference of Gail's height and Use the variable g to represent Gail's height is H om ew or k #3 Page 3 / 0

32 Homework #3 Answers for class AIR Int Math II. v 2. For each experiment, determine whether events A and B are independent or dependent. Experiment Events Independent Dependent Kala randomly selects one of her sports trading cards. She then returns the card to the deck and mixes the deck. She then makes another random selection. 6 A number cube with sides labeled through is rolled twice. At the beginning of each of two football games, a coin is tossed, and the winner of the coin toss is determined. 2 A bin contains marbles numbered through. A marble is randomly selected from the bin and set aside. Then another random selection is made from the remaining marbles. A box contains pens. Some pens have ink and some do not. A teacher randomly selects a pen and sets it aside. Then another random selection is made from the remaining pens. Event A: The first selection is a soccer player. Event B: The second selection is a baseball player. Event A: The first roll is an even number. Event B: Both rolls are even numbers. Event A: In the first game, the home team loses the coin toss. Event B: In the second game, the home team wins the coin toss. Event A: The first selection is an odd numbered marble. Event B: The second selection is an even numbered marble. Event A: The first selection is a pen with no ink. Event B: The second selection is a pen with ink. H om ew or k #3 Page 32 / 0

33 3. y x (2, -) (, -3) - (0, -) x +, 2 i 2 3 i. 8 y x H om ew or k #3 Page 33 / 0

34 6. (a) Find the ratio of the area of the sector to the area of the circle. Area of sector Area of circle 8 (b) From the figure we see that ACB The measure of is [ equal to ] the measure of. m AB So,. This gives the following equation. m AC B. AB m AB (c) Choose the equation that is true. Area of sector Area of circle Area of sector Area of circle Area of sector Area of circle Area of sector Area of circle 360 m AB m AB 360 m AB 8 m AB 360 πr 2 (d) Using for the area of the circle, choose the equation that gives a formula for the area of the sector. Area of sector Area of sector Area of sector Area of sector m AB 360 8π r πr 2 m AB m AB 360 π r 2 m AB πr 2 H om ew or k #3 Page 3 / 0

35 7. D 8 C Y 2 27 X W E (a) Complete the congruence statements below. W ~ C X ~ E Y ~ D (b) Find the following ratios. Write your answers as fractions in simplest form. CE WX 3 2 ED XY 3 2 CD WY 3 2 (c) Select the true statement. WXY WXY and and CED CED are similar. are not similar. H om ew or k #3 Page 3 / 0

8. (a) N Q M O Not Necessarily Congruent Congruent : R P MNO ~ PQR by the (ASA) Congruence Property (b) G L H K I Not Necessarily Congruent Congruent : GHI ~ J by the ( ) Congruence Property

36 8. (a) N Q M O Not Necessarily Congruent Congruent : R P MNO ~ PQR by the (ASA) Congruence Property (b) G L H K I Not Necessarily Congruent Congruent : GHI ~ J by the ( ) Congruence Property (c) U Z V Y W X Not Necessarily Congruent Congruent : UVW ~ XYZ by the (AAS) Congruence Property 9. Sample space:, 2, 3,,, 6 6 Event of rolling a number greater than : H om ew or k #3 Page 36 / 0

37 0. Statement Reason Line(s) Used J L L H I K KH Given J L I K L H KH Addition and Subtraction Properties J L L H 3 + L H L H I K KH + KH KH Fraction Algebra 2 + J L L H L H I K + KH KH Fraction Algebra 3 J H J L + L H Segment Addition Property 6 I H I K + K H Segment Addition Property J H 7 L H I H KH Substitution Property (Using 3 lines) 6 8 H ~ H Reflexive Property 9 H I J ~ H K L SAS Similarity Property H J I ~ H L K Corr. s of similar triangles are ~ 9 J I L K If corr. s ~, then lines 0 H om ew or k #3 Page 37 / 0

38 . (a) In the figure below, two secants are drawn to a circle from exterior point. EW 68 EZ 2. EX 3 XY Suppose that,, and. Find. E E Z X X Y 7 Y W U UJ 3 UK 39 UN 9. UM (b) In the figure below, two chords intersect inside the circle at point. Suppose that,, and. Find. M K J U U M 26 N H om ew or k #3 Page 38 / 0

39 2. (a) For each triangle, find the ratio of the length of the side adjacent to Note that "side adjacent" cannot also refer to the hypotenuse. Round your answers to the nearest hundredth. JK 0.89 JL PQ 0.89 PR XY 0.89 XZ 27.6 sin 27.6 cos 27.6 tan 27.6 (b) Use the ALEKS Calculator to find,, and. Round your answers to the nearest hundredth. sin cos tan to the length of the hypotenuse. (c) Which trigonometric function gives each ratio of sides in part (a)? sine cosine tangent none of these H om ew or k #3 Page 39 / 0

40 3. Points Behavior of the function increasing A and B constant decreasing increasing B and C constant decreasing increasing C and D constant decreasing increasing D and E constant decreasing. m 2 8 m. domain range 6. 3, 3, By the angle addition property,. We are given that and, so. We see that and are alternate interior angles. And since lines and are parallel, and are congruent. So,. We see that and are corresponding angles. And since lines and are parallel, and are congruent. So,. m 2 + m + m 80 m 69 m 0 m 2 6 l k m 69 3 l k 3 m 3 0 m + m 2 + m 3 80 Therefore,. 2 3 The relationship between,, and is an example of the following rule. 80 The sum of the interior angle measures of a triangle is. H om ew or k #3 Page 0 / 0

41 7. Statement Reason Line(s) Used Q R ~ S T Given 2 Q T ~ R S Given 3 ~ R T R T Reflexive Property Q R T ~ S T R SSS Congruence Property 2 3 ~ CPCTC Property 6 2 ~ 3 CPCTC Property 7 Q R S T If alt. int. s ~, then lines 8 Q T R S If alt. int. s ~, then lines 6 9 Q R S T is a parallelogram Definition of a Parallelogram Which function has the graph with a -intercept closest to? Function Function 2 Function 3 Function Which functions have graphs with slopes less than? (Check all that apply.) Function Function 2 Function 3 Function Which function has the graph with the greatest -intercept? Function Function 2 Function 3 Function y 0 y H om ew or k #3 Page / 0

42 9. Basketball Hockey Swimming Seventh grade Eighth grade Answer the following questions. ABC m A 30 m B 7 DEF m D 30 m E 7 (a) In, and. In, and. Use this information to find the following angle measures. m C 7 m F 7 (b) Use the ruler to find all side lengths for each triangle. Assume all lengths are whole numbers. AB BC 2 CA DE 2 EF 6 FD 2 (c) Find the following ratios. Write your answers in simplest form. AB DE 3 BC EF 3 CA FD 3 (d) Three pairs of statements are shown below. For each pair, select the true statement. ABC ABC The angles in have the same measures as the angles in. The angles in do not have the same measures as the angles in. The ratios of corresponding side lengths are all equal to each other. The ratios of corresponding side lengths are not all equal to each other. The triangles are similar. The triangles are not similar. DEF DEF H om ew or k #3 Page 2 / 0

43 2. A: The sum of two rationals is always rational. B: The sum of a rational and an irrational is always irrational. C: The sum of two irrationals is sometimes rational, sometimes irrational. D: The product of two rationals is always rational. E: The product of a nonzero rational and an irrational is always irrational. F: The product of two irrationals is sometimes rational, sometimes irrational π Result is irrational rational rational irrational Reason C C D E 22. y 0, 23. (a) Use the measurements above and the calculator to fill in the blanks. Write each answer as a single decimal. Do not round. Circle : Circle 2: Circle 3: Circumference Circumference Circumference Diameter Diameter Diameter (b) Let represent the circumference of any circle and represent the diameter. C d π 3. π C d C d d π C d π C π Using the fact that is approximately, which formula seems reasonable? (c) Write a formula that relates the circumference,, of a circle to its diameter,. C π d C d y 9 2., H om ew or k #3 Page 3 / 0

44 2. A B C D (a) For each coefficient, choose whether it is positive or negative - Positive - Negative - Positive - Negative - Positive - Negative - Positive - Negative (b) Choose the coefficient closest to 0 (c) Choose the coefficient with the greatest value 26. f x 3 x XYZ X Part : In, and are - complementary. x y z Y Part 2: Use,, and to fill in the blanks. Make sure to use the appropriate upper-case or lower-case letters. sinx cosx x z y z siny cosy y z x z Part 3: Select all of the true statements. cosx cosy sinx siny sinx cosy cosx siny None of the above is true. Part : Fill in the blank. cos 67 sin 23 H om ew or k #3 Page / 0

45 y Dilation x (a) Find the following. Shortest side length of the original figure: Shortest side length of the final figure: (b) Fill in the blank to make a true statement. Shortest side length of the final figure (c) True or False? units units Shortest side length of the original figure The original figure and the final figure are similar. True False ft 3 H om ew or k #3 Page / 0

46 Right triangle Not a right triangle Cannot be determined T 6,, R 8,, I 3, D, 0, E, 0, F 9, A 3, 3, B, 6, C, x-intercept(s): vertex: 2, Statement Reason Line(s) Used CD EF Given 2 CE CD + DE Segment Addition Property 3 DF DE + EF Segment Addition Property DF DE + CD Substitution Property (Using 2 lines) 3 CE DF Substitution Property (Using 2 lines) v 2 3v H om ew or k #3 Page 6 / 0 3

47 37. (a) Fill in the table below. Note that the table is already filled in for. (b) For, the table suggests that is sometimes greater than x f x 3 x g x x x 3 x f x g x H om ew or k #3 Page 7 / 0

48 39. y x (a) Fill in the blanks to describe the transformations necessary to move the solid circle exactly onto the dashed circle. Translate the solid circle {to the left,to the right} by unit(s) and {up,down} by unit(s). Dilate the solid circle by a scale factor of. (b) Are the original solid circle and the dashed circle similar? Yes No H om ew or k #3 Page 8 / 0

49 0. (a) Find the probabilities of the events below. Write each answer as a single fraction in simplest form. P A P B 9 9 P A andb 9 P A orb 8 9 P A + P B P A and B 8 9 (b) Select the probability that is equal to. P A and B P A or B P B P A P A + P B P A and B. x y Equation: Total cost to transport C S 8 $7200 tons of sugar: H om ew or k #3 Page 9 / 0

50 3. Statement Reason Line(s) Used a b Given 2 ~ 8 If lines, then corr. s ~.. Leading coefficient: Degree: i 3 Probabilities Independent Dependent P A P B 2 P A B ; ; and 0 P A P A P A 9 P B 9 ; ; P B 3 ; ; P B 7 ; ; P B A P A B P A B 2 H om ew or k #3 Page 0 / 0

51 8. Probabilities Independent Dependent P A P B 3 P A B ; ; and 2 P A P A P A 8 8 P B ; ; P B ; ; P B 9 ; ; P A B P B A P A B g 9 69

Given that m A = 50 and m B = 100, what is m Z? A. 15 B. 25 C. 30 D. 50

Given that m A = 50 and m B = 100, what is m Z? A. 15 B. 25 C. 30 D. 50 UNIT : SIMILARITY, CONGRUENCE AND PROOFS ) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of. The dilation is centered at ( 4, ). ) Which transformation results in a figure that is similar