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d. How many out-of-school youth a year before 2008? If 2008 is year 1, 2009 is year 2, 2010 is year 3 and so on, what be the y-intercept of the graph? Exercises 2. A. Co Answer: If the number of out-of-school youth is increased by 7 yearly from 2008, conversely from 2012 the number of out-of-school youth would be decreased by 7. Thus, the number of out-of-school youth before 2008 is 30 - 7 = 23. The solution suggest that the corresponding number of out-of-school youth in 2007 is 23. The preceding pair of (2008, 30) would be (2007, 23). If 2008 is year 1, so the pair would be (1, 30). Thus the pair of values describing the year before 2008 is (0, 23). Henceforth, the y-intercept is 23. e. What is the equation that would best describe the situation? Answer: Base from the answers in questions c and d, using slope-intercept form y = mx +b would be y = 7x + 23. B. Exercises 1. Read and answer what is asked. Find the slope of this given graphical representation. 1 . 2. 3 4 . week 5 page 4Exercises 2. Read and answer what is asked. A. Complete the table of values given the equations. 1. f (x) = 2x - 3 X -2 -1 0 1 2 2. g(x) = 3x - 10 X -4 -3 -2 -1 0 V 3. h(x) = =+ 5 X -4 -2 0 2 4 y B. Solve the following problems. Show your solutions and graphs. 1. A pay phone service charges Php 5 for the first three minutes and Php 1 for every minute additional or a fraction thereof. How much does the caller have to pay if his call lasts for 8 minutes? 2. A motorist drives at a constant rate of 60 kph. If his destination is 240 kilometers away from his starting point, how many hours will it take him to reach the destination? C. Assessment/ Application/Outputs (Please refer to DepEd Order No. 31, s. 2020) Direction. Read and analyse each item carefully. Show your solution. 1. It has been observed that a particular plant's growth is directly proportional to time. It measured 2 cm when it arrived at the nursery and 2.5 cm exactly one week later. If the plant continues to grow at this rate, determine the function that represents the plant's growth and graph it. 2. A car rental charge is 100 per day plus 0.30 per mile travelled. Determine the equation of the line that represents the daily cost by the number of miles travelled and graph it. If a total of 300 miles was travelled in one day, how much is the rental company going to receive as a payment? 3. A city parking garage charges a flat rate of $3.00 for parking 2 hours or less, and $0.50 per hour for each additional hour. Write a linear model that gives the total charge in terms of additional hours parked. week 5 page 54. Six 2 foot tall pine trees were planted during the school's observation of Earth Awareness Week in 1990. The trees have grown at an average rate of 34 foot per year. Write a linear model that gives the height of the trees in terms of the number of years since they were planted. Suggested Enrichment/Reinforcement Activity/ies 1. The pollution level in the center of a city at 6 am is 30 parts per million and it grows in linear fashion by 25 parts per million every hour. If y is pollution and t is time elapsed after 6 am, determine: a. The equation that relates y with t. b. The pollution level at 4 o'clock in the afternoon. 2. A town's population has been growing linearly. In 2004 the population was 6,200. By 2009 the population had grown to 8,100. Assume this trend continues. a. Predict the population in 2013. b. Identify the year in which the population will reach 15,000. References: week 5 page 6Readings Discussions A simple flow of rowing from the if-clause to the then-clause is called simple implication. There are some conditional materments not written in this form but you can Turtle them using the if-then for. Example- 1. Opposite sides of a rectangle are parallel. If then form: If a quadrilateral is a rectangle, thenincognitorides At prints, 1. A triangle Is a polygon with three sides. It-then form: If a polygon is a triangle, then it hat three sides Exercises I Convert each statement in if then farm. 1 Cigarette smoking is dangerous to your health. If-then form: 2. Angles in a linear pair are supplementary. if-then form: 3. A quadrilateral has four sides. It-then form: 4. The sum of the measures of complementary angles is 40". if-then form: 5. Two intersecting lines lie in one plane. If then form: Exercise 2 Transform/rewrite the conditional statements using the -then form and Identify the weatheris and the conclusion. Cigarette smoking is dangerous to your health. If-then form Hypothesis Conclusion It is more fun in the Philippines. If-then form week 6 page 1Tustratio compin: 1.) If you get good grades, then you wil get into a good college. The part offor the If you get good grades - is called a hypothesi and the part after the "then" - you will get into a good cologe - is called a conclusion. 2 ) li a polypon is a rectangle, then its opposite sides are parallel. Hypothesis; A polygon is a rectangle. Conclusion: is oppos to sides are parallel 3.) Congruent segments have equal longthe. Hypothesis: Congruent soorents Conclusion: Equal lengths. H. Exercises 1 Given the conditional statements below underthe the hypothesis once and the conclusion twigs, 1. If two coplanar Ines are porpond cutir to the same Inn, them they are parallel 2 If you are Filipino then you are God-Scaring people. 3 if the polygon is a triangle then it has three sides. Exorose 2 Directions: Identify the hypothesis and conclusion of the following conditional statements not in it-then form. 1. Chopto contains calcium. Hypothesis: Condusion, 2. The massure of an souto angle is between O and 90. Hypothoils Conclusion 3. Equilateral bangles aro equaangular. Hypothesis; Conclusiont week 6 page24. Two distinct points determine a line. If-then form 5. Collinear points lie on the same line. If-then form Suggested Enrichment/Reinforcement Activity/ies There are things in life which involve decision-making. Find out how valid decision making affects our life. The given article below deals with the effect of having or giving misguided conclusion. Read the excerpts on the article from Bombo Radio Philippines entitled, "Judge wak ng SC due to wrong decisions" then answer the follow-up questions below. Judge sinibak ng SC due to wrong decisions Revoked of license by the Supreme Court (SC) is a judge in Cotabato City because of the issuance of a decision in the case of annulment of marriage without conducting a hearing. In the per curiam decision of the supreme court en banc discharge on May 15 2012, proven guilty of gross misconduct and dishonesty is Judge Cader Indar Al Haj, presiding judge of the Regional Trial Court (RTC), branch 15, Sharifi Aguak, Maguindanao. Along with its disbarment Indar was removed from the service and also the benefits that he should get from his retirement except leave credits Also stated in the decision was indar can't work in any office of the government owned including any government owned and controlled corporations. According to the court, Indar violated the Canons 1 and 7, as well as rule 1.01 of the Code of Professional Responsibility, thus, also removing his name on the roll of attorneys. The penalty of Indar stemmed from a report sent by the LCR of Manila and Quezon City to the Office of Court Administration (OCA) in relation to the decisions resolutions and orders in the marriage annulment issued by the same judge. Answer the question below in an if-then form. 1. Comment on the article. 2. Site a situation where important decision making is needed. 3. Suggest a procedure on how to make a wise decision. week 6 page 3SELF-LEARNING BONET ALTHATE Writ T Competing, Code WILL al Self-Operating Napain The cation ippopeniston at the right 3 M. connected to each other, that when something Is done to the Inst, it rove, and same thing will happen is too noud object whin the preceding opec h mond. The process is dascribed below the picture. Soup spoon (A] h rased to mouin, poling string (Bj and thereby Hring jadia IC), which macker [D) past patrol (E). Parrot Jumps offer cracker and perch (F) this, updating sandy (d) "H) Extra weight in pail pulls gord (To which opens and ignites ligtick (). coding Racket (10), which causes sickle (L) to cut string (M) whoare pending ain arechad parkin to Tick and forth, thereby wiping chin walls of soothes can ba written in if-thes form, Ing actsites at a time. The and toolpic cone for you If the soup spoon is raned to the morn, then it puts Desiring IN the wring is pulled, than it jerks the Ladle. the wiring is out, then the pandulum swings. If the pendulum swings, then the naper swings haul boat, thereby wiping the chin writing converse of a conditional statement. "pool waterant is written in f-men for, where the /-photo is the hypothesis and the tank the conduson. week 7 page1WENOISES Comemeet Il's man doesrol spout il of others, then he reaparts train, 3. FM Is the midpani of AB. then AM - Ma. Comena FAME MD, Den Misen AB. A and cf are Incarpur, then al + 28 - 180 Converse : If of and of and supplementary then toy wolrear par. 1 7hop Ing heneed and form a nghi ange, then they we perpendicular. Canveria: if two Ions are perpendicular. then Pery ke'm a right ampla Lingerie the happy face look * the imma Is correctly walod, the sad face iron I'll it art I'mep Has interact, Foon ther itemstion is s port a person in truthd, Ben he is hosted by other Itverse : If'n person least truthhut, then held at quited by other Fo parninio gram in a equaro, than the a homies Iwere : If a phralulagiam is not a square, then it is not a rhombus a, ha tringale, I the angle is opbouto the longout ado then hit the biggest engle heoreo : In a triangle. if me angie is not oppoilis the longest gift then Hit the smallest angle. you are 18 years old, Pen you cin vote. livere : If you are not 18 years old, than you cannot vote White the contrapositive of each converse shaleant. Be polygon has three sides. Init is a trungle. Comverse: If a polygon in a thangio, then I has mris udos, Contrapositme: the oil price increases, then prices of commodilen site incosin Converse: H prices of commodiles nexusto, then of price increases Contrapositive In person shown symptoms of the disease, then he will be quarandned Converse : if a person will be quarantined, then he shows carpsome of the datain. week 7 page27. Given, "If I have a Siberian Husky, then I have a dog." Identify the converse. A. If I do not have a Siberian Husky, then I do not have a dog. B. If I do not have a dog, then I do not have a Siberian Husky. C. If I do not have a Siberian Husky, then I have a dog. D. If I have a dog, then I have a Siberian Husky. Given, "If angles are congruent, then the measures of the angles are equal." Identify the converse. A. If the measures of the angles are equal, then the angles are congruent. B. If the angles are not congruent, then the measure of the angles are equal. C. If angles are not congruent, then the measures of the angles are not equal." D. If the measures of the angles are not equal, then the angles are not congruent. To write the converse , (a) you negate the hypothesis (b.) you negate the conclusion A. a only B. b only C. both a and b D. neither Conditional: If it does not rain today, then we will have practice. What is this statement called: If it rains today, then we will not have practice. A. Converse B. Inverse C. Contrapositive D. Negation Conditional: If Maria gets married, then the reception will be at the country club. What is this statement: If the reception is at the country club, then Maria will be getting married. A. Converse B. Inverse C. Contrapositive D. Negation . Original statement : If Jenny buys a guitar, then she will not buy a keyboard. What form of the statement is this? If Jenny does buy a keyboard, then she will not buy a guitar. A. Converse B. Inverse C. Contrapositive D. Negation Siva the other three forms of the given statement. Given : Inverse : If the measure of the angle is not 90 degrees, then it is not right. 13. Conditional : 14. Converse : 5 Contrapositive: L .]gested Enrichment/Reinforcement Activity/ies cose one picture and write an if-then statement in four forms. Sepak Takraw Cebu Province Is Bohol Finals Picture is taken by screenshot from laura by https://www.y hill: Ridao outube.com/ unsp watch?v=Ojk 29TRSsT4&a week 7 page4READINGW/DISCUSSION us review your skill in rewriting conditionals to its other tons Conditional: If two angles are bath right angles, then they are congruent you construct the cormerge? two is the inverse : If two angles are not both right angles, then they are not congruent you constrict the commapositive ? Studying the meaning of each statement, do you agree to each of them? Let us leam how to know whether they are true or false in the next section of the activity, Conditional : I two angles are both right angles, then they are congruent. Is the slatement bug ? YES, because if both angles are right. each measures 90 degrees, so the wo have same measure, so they are congruent, Converse : If two angles are congruent. then they are both right angles. the statement true? Are all congruent angles always right angles? Do the converse is not true or simply FALSE Let's say cM = 43 and AN- 43" , they have the same measures yet, are they right angles? No. Inverse: If two angles are not both right angles, then they are not congruent Is the statement true? the two angles are not both right, could they be congruent? is it possible that A = 38 , and _B = 34", so they are both not right, but are they not congnian! ? Go we could say that the inaroo is FALSE week 8 page 1Contrapotties; If the angles are not congruent than they are not both right angles. call were be We andispatch am not congruent thon they are boo nent? 190, so the whereni is TRUE Let us have another example to figure it out some more. FALSE Conditional: If the ground is wet, then It rains. It is possible for the ground to got wet even if there is no rain. TRUE Conversa: If It rains, then the ground is wet. Can you hide the ground from the nin? @ verse: If the ground Is not wet, then it does not rain TRUE e pound is not unit, how could there be mint Contrapositive: If It does not rain, then the ground is not wet. FALSE Apain there can be another reason for the ground to get wet, even if there is no rin, 50, which forms have the same truth value? The conditional is true, the contrepositive is also true. If the conditional in When, then if' conpolite is sho take. on the ciher hand, The convoren is run, the inverge is aso true. If the converse in falso, then the inverse is also false. RISES We arecal inevilusing nach slainment Encircle the latter mat comesporch to your anover is that the converse of the conditional statement 'll & rated last night. than Pre side we's is was Which of the offer it warts has to be false at walt The sidewalk is not wet then it did not rain last night. If a did not rain last right on the sidewalk is not wot. If the sidewalk is wet, then _ rained last right. Ifla rained last night then the sidewalk is wet I ross that the commmy'se statement a figure is a parallelogram, then i is a quadrilateral." is true. tion of me ofar plilaments have to be tus as well? to figure binot a parallelogram then it is not a quadrilateral. If a figure is not a qued fiatoral, then it is not a parallelogram. IN a figure in a parallelogram, thein his a quadrilateral, I'm figure is a quadrilateral, then k is a parallelogram. week 8 page 2I Fran inglot are complementary, Than they are both acuis A ley A Alaina B. monet true C. never tive D. cannot be drkarmined White Wallacer that corresponds to your choice on the space provided, Fheo eratent ingles are scuts, man fery ive complementary Tag sopatent images are complementary, then thay are scuta. Said acute angles are complementary, ben they are agpoem. wo complementary angles are adjacent than they are souls. P is the midport of DR .then OF = PA. ASSESSMENT APPLICATION OUTPUTS (Ploone refer to Duped Order No. 31. s. 2030) ach conditional below, write the convert, Inverse and contrapositive, Then state the truth of each farm. STATEMENTS TRUE or FALSE CONDITIONAL If am angle is obtuse, then its measure is 180 . CONVERSO INVERSE CONTAPOSITIVE STATEMENTS TRUL & FALSE CONDITIONAL It an angle measures 20 , then it is acute. DAIVERSE MERSE ONTAPOSITIVE Vergested Enrichment Reinforcement Activitylien ady the situation below. You may present your solution and explanation in any way that you can markis yoursoll. It may be a diagram form, for a paragraph, or through an example. This pan balance scale was oven until a 10-g weight was removed tom the left pan. Theite are only 1 wrights available: one 5-g, two 3-g, and three 2-g Give at least two possible ways to replace me 10-g weight and explain why your answers work. week 8 page 3Let's solve the using dred proof in tos column form 3. m.4 may J. Tractive property of Equatry 3. ANYZ: AT . FZ Prove mickie ey let's prove the using indirect method in two-column form; weknow ck is congruent to 27 comic'0 - TV. (12 video of a triangle are congruent then the angies cocoons thend sets are congruent ) How contwo-cis me fact that the sun of the measures of mo capital a brungle in 180. Thatelote, the temporary assumption must be lake. So. mick) = 4,Gyan, Mis rol the ridpost of IT. Prove TH - MF (Lafe prove the using indirect method in two-column tum) Stopments 1. Gyen 2. Assumption 3. Ma the mauiport of 21 A. Detrion of Mapoint week 9 page311. Exercise 1 Directions: Write the missing statement and reason. Given: all b with transversal ?' cutting a and 18 2 7 Prove: 42 = 46 3 6 Proof: Reasons Statements 1. m42 + mc? = 180 1. Definitions of supplementary m47 + m46 = 180 angles 2. mc2 + mc7 = mc7 + m26 2. 3. 3. Reflexive property 4. mz2 = m26 4. 5. mc2 = m146 5. Definition of congruent angles Exercise 2 Write a proof using indirect proof in paragraph form. Given: Transversal t cuts lines a and b. a b 2 Prove: m41 # m43 3 IH. Assessment/ Application/Outputs (Please refer to DepEd Order No. 31, s. 2020) Directions: Read the questions carefully. Write the letter that corresponds to your answer on a separate sheet of paper. 1. What property is illustrated in: AB = AB? A. Reflexive Property B. Symmetric Property C. Addition Property D. Transitive Property 2. What property is illustrated in: If a = b, then ac = bc. A. Subtraction Property of Equality B. Addition Property of Equality C. Multiplication Property of Equality D. Division Property of Equality week 9 page43-5. Supply the missing statementreason in the following trust Oicon ed and of an complementary and and of are complementary Stateman LA and IC are complementary Ghan LA and aCare complementary Translive Properly Detrition of Congruent Angos 3. A. Definition of Congruent Angies B. Definition of Complementary Angles G. Anglo Addition Postulate D. Definition of Perpendicular Lines 4. A. LA + CC = L8 B. LA+ LB- 20 C. CA + LL - B + LA 5. A. Addition Property 1. Subtraction Property C. Multiplication Property D. Division Properly B. Write a proof of the folowing 1. Prove this using duect proof in paragraph form. Chron: M is the midpoint of XY Prove: XM - FM 2. Prove this using ind rect picol in two-column form. Gion MP ING Prove &NPM is not a straight angle week 9 page5Supply the missing statement"eaton in the following proof Prove: 21 + 27 are complementary Ronson Gyun FIVE Anglangle Dulinilion od a perpendicular lines Argh Additon Postulate Definition of Complementary week 9 pagedA Readings /Discussions In solving real-Ido word problems, problems gapregard as a verbal description are translated into the language of mathematics Usually, working with mathematical problems involves solutions or answers in terms of numbers. This time, the answers are functions, or more precisely equations defining functions. Below is the slep by stop process on how to solve word problema involving linear functions. Read the problem carefully and write the given information. Identify which variable is independent and dependent variable. Construct a table of values. Identify the slope "m" and y - intercept b and write the equation of the Ine. * Graph on your own the linear equation using your answer in Step 4. Example 1. You own a newly - born German shepherd. Suppose the dog weighs 1kg at birth. You've known from your friend that the monthly average weight gained by the dog is 5 kg. If the rate of increase of the dog's weight every month is constant, determine the equation that will doscribe the dog's weight Predict the dog's weight after five months using mathematical equation and graphical representation. Solutions: Step 1. Read the problom carefully and write the given information. Based from the problem above, it involved the weight of the dog from birth and the average weight of the dog gained morthly 1 bp dog's weight at birth 5 kg average weight gained monthly Step 2. Identify which variable is independent and dependent variab If we analyze, the variables mentioned are the weight and the month for its increasing weight as the dog grows. Therefore. Weight - dependent (yl Month - Independent (x) week 5 page 1Step 3. Construct a table of values. Noticed that at birth the weight (y) of the dog is 1 kg and every month (x) its weight is increased by average of 5 kg. if tabularized, 2 3 months X 11 16 weight y Step 4. Identity the slope "m" and y - intercept "b" and write the equation of the line. There are many forms in determining equation of a line but based on the table constructed, the easiest way is to use the slope- intercept form (y = mx + b), where "m" is the slope and "b" is the y-intercept. If the slope and y -- intercept are determined, then: m = 5 Equation of the Line Y-intercept = 1 y = 5x + 1 Step 5. Graph on your own the linear equation using your answer in Step 4. Recall on how to plot coordinates or table of values. V 18 14 (3, 16) 12 (2, 11) 1, 6 10 1) 2 2.5 3 3.5 X Example 2: Note: (This problem would not require the step by step process discussed but only answer the questions that follow.) A survey of out-of-school youth in your barangay was conducted. From year 2008 to 2012, the number of out-of-school youths was tallied and was observed to increase at a constant rate as shown in the table below. week 5 page 23. A segment has exactly one midpoint. 4. Two If-then for If-then form 5. Colli Hypothesis If-then for Conclusion C Assessment/Application/Outputs (Please refer to DepEd Order No. 31, 3. 2020) . Suggested E 1. Encircle the letter of the chosen correct answer. There are 1. The If-then form of the statement "Parallel lines never intersect," is making affect A. If two lines intersect, then they are parallel. The given Read B. If two lines are parallel, then they never intersect. bak ng C. If two lines are not parallel, then they intersect. D. If two lines intersect, then they are not parallel. 2. Rewrite the statement "A quadrilateral is a figure with four sides." in the if- then form. A. A figure has four sides if and only if it is a quadrilateral. B. If a figure is a quadrilateral, then it has four sides. C. If a figure has four sides, then it is a quadrilateral. D. A figure is a quadrilateral if and only if it has four sides. 3. Which of the following statements is false? A. Any four non-collinear points lie in a distinct plane. B. Any plane contains at least 3 non-collinear points. C. Any two lines intersect at a point. D. Through two given points we can draw three lines. . If garbage are disposed properly then dengue diseases will be prevented. What is the underlined portion called in the conditional statement? A. the conclusion B. the hypothesis C. the argument D. the converse 5.Supply a valid conclusion for the given hypothesis: if ray OM bisects LLON then A. LLOM = ZNOM B. LLOM = LLON C. L MON = ZNOL D. MALON = LLOM + MZMON 11. Underline the hypothesis once and the conclusion twice. Then transform the conditional statement into if-then form. 1. Right angles measure congruent. If-then form 2. Acute angles measure less than 90. If-then form 3. The sum of two even numbers is even. If- then form week 6 page 2