Alg1 Qtr1 Sy16-17 Rev8 FINAL 14Jun16
Algebra 1Quarter 1 The Prelude Functions Linear Functionsx4 “x to the34 “3 to thefourth power” means“4 factors of x”fourth power” means“4 factors of 3”y-intercept:x-intercept: 3 3 3 3 81In the picture below, a 5 x 5 square is surroundedby a checkerboard pattern. How many colored tiles are in thecheckerboard pattern? Use an efficientstrategy (i.e., do not simply count up the tilesone at a time) and explain your method. Create an algebraic expression to representthe number of colored tiles needed for anyn x n square center.Solving Equations: find the numberthat will make the statement true.25x 800 130025x 800 1300– 800– 80025x 50025x 50025251x 20Therefore, x 20.Check: does x 20 make the originalequation a true statement?25x 800 130025(20) 800500 8001300
31 10 41thesamesigns:ExampleB:–9 (–4) mpleH:7 9 63ExampleI:–7 –8 56ExampleJ:–7 –7 49ExampleK:64 8 8ExampleL:–72 –8 9ExampleC:–413–200 è ��200 è Sincetheyhavethesamesigns,weaddthem.–413–200 –613ExampleD:50–(–40) è –(–40) sitive4050–(–40) 50 40 pleE:31–45 è 31–45 DIFFERENTè Thinkaboutthisaspositive31andnegative45signs:è SincethenumbershaveDIFFERENT signs,weSUBTRACT.è .31–45 –14ExampleF:–123 100 è –123 100è heyhaveDIFFERENT signs,weSUBTRACT.è .–123 100 –23ExampleG:–12–(–19) è –12–(–19)è –(–19) 2andpositive19–12 19 7è sincetheyhaveDIFFERENT signs,weSUBTRACT.è .ExampleM:–6 9 –54ExampleN:6 –8 –48ExampleO:–42 6 –7ExampleP:36 –6 –6
Table of ContentsAlgebra 1The PreludePageP.1P.2P.3P.4P.5P.6P.7Order of Operations; Equations and their SolutionsBuilding and Solving EquationsTranslating pictures and words into algebraic expressionsEquations with more than 1 VariableHomework – Coordinate Plane PreviewEquations that have 2 different variablesPatterns15913171921Module 1: -4.3F-4.4F-4.5Introduction to FunctionsIntroduction to Function NotationHomeworkTables and GraphsWhen is it NOT a function?The m&m GameHomework -- ReviewStations Activity – Function Tables and GraphsHomeworkReviewDifferent Ways to Represent the Same FunctionHomework – A Refresher on Linear FunctionsConnecting the Different Ways to Represent a FunctionHomeworkConnecting Symbolic and Graphical RepresentationsCheckerboard BordersHomework – Perimeter and Area of Rectangles RefresherWhich Representation is Better?Function 7798387899397Module 2: Linear FunctionsLessonQuarter 5L-5.6Tables and Graphs of Linear FunctionsTables and Graphs of Linear Functions RevisitedHomeworkFunctions of the form f(x) mxFunctions of the form f(x) mx bA more formal definition of slopeHomeworkWarm-upLinear Functions in ContextStations Activity -- Profit and CostHomeworkWarm-upBuilding the Equation of a Line -- Slope-Intercept FormPoint-Slope Form for the Equation of a LineHomeworkWarm-upBuilding and Interpreting a Linear EquationDetermine the Equation of Line with 2 Known PointsHomeworkBuilding and Interpreting 135139143145148153159161165Vocabulary Section171Appendix
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Algebra 1 – The PreludeP.1: Order of Operations; Equations and their SolutionsNamePd DatePart I: Use the Order of Operations to determine the value of each expression.A. –30 (2 8 – 8) B. –8 (2 – 4) 32 C. 44 (–5 – 6) [–5 – (–6)] D. (-15 13) * (5 - 13) E.7 * 3 [(–15 – (–12)] F.G.(11 – 12 – 13)*( –1)2 H. (–7 – 7) * (–7 7) I.25 15 5 15J.32 23 2 *3K.(10 1) *(10 1) *(0 1) L.–4 * [12 – (–13)] 4(10) 2(20) 3(30) 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.1
Algebra 1 – The PreludeP.1: Order of Operations; Equations and their SolutionsNamePd DateM.5 ( 6) 6 ( 7)N. –6 [–12 – (–13)] 6 O.(0 5) 2 (1 7) 2 P. 9 11 (2 3) 2R.2 ( 3) *( 4) Q. 15 ( 1 1) 4 Part II: Reading an equation as a questionAn equation that contains a variable is essentially asking you a question. For example: The equation 5x 13 43 is asking you to answer the question,“What number, when I multiply it by 5 and then add 13 is equal to 43?”Translate each of the following equations into a complete sentence/question. (Do NOT solve theequations; just translate them into words.)S.x 7 23T. 100 2(x 5)U. x 2 1 50V.45 5pW. r s 10 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.2
Algebra 1 – The PreludeP.1: Order of Operations; Equations and their SolutionsNamePd DatePart III: Verifying SolutionsA solution is a value that makes an equation a true statement (i.e., when you substitute the solution inplace of the variable, the value on one side of the equal sign is the same as the value on the other side).For example, let’s verify that x 6 is a solution for the equation 4x 11 3(2x – 1):4x 114(6) 1124 1133 3(2x – 1)3(2*6 – 1)3(12 – 1)3(11)33 è since BOTH sides of the equation result in thesame value (33), then x 6 is a solution to theequation.Lance solved each of the following equations; his solutions are stated below. Determine if Lance’ssolutions are correct. Justify your answer.V. 3n – 14 26 è Lance’s solution: n 4Is Lance’s solution correct? Yes or NoW. 25 – 2x 7x - 20 è Lance’s solution: x 5Is Lance’s solution correct? Yes or NoX.1(c – 13) 19 – c è Lance’s solution: c 25 Is Lance’s solution correct? Yes or No2Y. 100 4v - 20 è Lance’s solution: v 30Is Lance’s solution correct? Yes or NoPart IV: Reflect and Summarize (follow your teacher’s instructions). 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.3
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Algebra 1 -- The PreludeP.2: Building and Solving EquationsNamePd DatePart I: Reviewing the Algebraic Properties of EqualityAddition Property of EqualitySubtraction Property of EqualityIf a b, then .If a b, then .In other words, this property allows us toIn other words, this property allows us toand still have equality.and still have equality.For example, givenIf we add 5 to both sides:4(3) 2(6)4(3) 5 2(6) 5We end up with:17 17 For example, given6(3) 2(9)If we subtract 5 from both sides:We end up with:Multiplication Property of EqualityDivision Property of EqualityIf a b, then .If a b, then .In other words, this property allows us toIn other words, this property allows us toand still have equality.and still have equality.For example, given6 1 2 5For example, givenIf we multiply both sides by 3:If we divide both sides by 2:We end up with:We end up with:5 9 11 3Part II: Using Algebraic Properties of Equality to Build EquationsEach chart below shows a series of equations that were created by applying one of the Properties ofEquality. first, simply analyze the steps and try to identify what was done to each side of equation to getfrom one step to the next; then, complete the chart by stating the Property of Equality that justifies each step; finally, verify that the given solution makes the final equation a true statement.1.2.Equationx 2JustificationGivenEquationc –93x 6c 4 –53x 7 132(c 4) –10Check:JustificationGivenCheck: 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.5
Algebra 1 -- The PreludeP.2: Building and Solving Equations3.NamePd Date4.Equationx 16x 82x 5 32JustificationGivenEquationy –7– 2y 145 – 2y 19Check:Check:5.6.Equationm –8m 245m 1045m 3 134JustificationGivenEquationr 1JustificationGiven–25r –25–25r 13 –12 25r 13 34Check:Check:7.8.Complete the chart below by writing theequation that would result from applyingthe description of the next step to theequation in the previous step.Equationn 5JustificationGivenDescription of Next StepGivenBuild your own equation: starting with theequation that is given (t 3), show 3 stepsusing any Algebraic Properties of Equality tobuild an equation.Equationt 3Description of Next StepGivenMultiply both sides by 3Subtract both sides by 7Multiply both sides by –10Check:Check: 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.6
Algebra 1 -- The PreludeP.2: Building and Solving EquationsNamePd DatePart III: Solving EquationsRecall: Fill in each blank with 1 word to complete each sentence.A. An equation is simply asking you a .B. A solution to an equation is the value that makes the equation a statement.For each equation below, first, write in words the question that the equation is asking you; then, solve the equation to find the value that makes the equation a true statement. Show yoursteps to justify your solution.x 2059.10x 20 3010.14 11.3(x 2) 912.12 7c 5413.1x 50214.5(3 2a) 75 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.7
Algebra 1 -- The PreludeP.2: Building and Solving Equations15.1 50 m3NamePd Date16.2(3w 4) 5Part IV: Reflect and Summarize (follow your teacher’s instructions). 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.8
Algebra 1 -- The PreludeP.3: Translating Pictures and Words into Algebraic ExpressionsNamePd DateWarm-up: Follow your teacher’s instructions. 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.9
Algebra 1 -- The PreludeP.3: Translating pictures and words into algebraic expressionsNamePd DatePart I: Algebra tiles can help us to visualize algebraic expressions. Consider the tiles below:xx1111This rectangular-shaped tile has a length of x unitsand a width of 1 unit.1.This square-shaped tile has a length of 1 unitand a width of 1 unit. Area (length)(width),o A (x)(1)o The area of the rectangle is x. Area (length)(width),o A (1)(1)o The area of the square is 1. Therefore, this tile represents a value of x. Therefore, this tile represents a value of 1.Write an algebraic expression that is represented by each set of tiles shown.A.B.Part II: Translate the following statements into an algebraic expression. Use a variable of your choice torepresent an unknown quantity in the statement.2. Chris had some money in his piggy bank and then he put 65 more into it.Write an expression to represent the total amount in Chris’s piggy bank now.3. Maile had 8 boxes of cookies and each box had the same number of cookies.Write an expression to represent the total number of cookies Maile had.4. Ray is much taller than Drew. Write an expression to represent the differencebetween Ray’s height and Drew’s height.5. The Imua Gym charges a one-time membership fee of 45 plus a monthly feeof 21. Represent the total cost for being a member for several months.6. Tickets to watch a college volleyball game cost 13 for adults and 8 for children.Represent the total cost of purchasing some adult tickets and some children tickets. 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.10
Algebra 1 -- The PreludeP.3: Translating pictures and words into algebraic expressionsNamePd DatePart III:7.At the high school swimming state championship meet Matt, Kurt, Elijah and Ryan swam in the4 x 100 freestyle relay race for their school (each person swam 4 lengths of the pool). Thefollowing variables represent the time it took each person to swim their 4 lengths of the pool in therelay race: M Matt’s time (in seconds) K Kurt’s time (in seconds) E Elijah’s time (in seconds) R Ryan’s time (in seconds)Use the variables above to interpret the expressions below:8.a.M K representsb.M K E R representsc.M K E R represents4d.E – R representsA movie theater charges a different price for tickets for people of different ages: c the cost for a children’s ticket (for ages 4 – 12 years old) g the cost for a general admission ticket (for ages 13 – 65) s the cost for a senior citizen ticket (for ages 65 and older)Use the information above to interpret the expressions below:a.c g s representsb.3g 2c representsc.4(c s) representsd.4c s representse.g – s representsf.Write an expression that represents the total cost of 3 children, 1 adult and 2 seniors: 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.11
Algebra 1 -- The PreludeP.3: Translating pictures and words into algebraic expressionsNamePd DatePart IV: Below are 4 equations that look quite similar, but are actually very different (and havedifferent solutions). 9.First, simply examine each equation and make some mental notes about how they differ fromeach other.Then, translate each equation into a complete sentence/question (do NOT solve the equations;just translate them into words). Fill in the blanks with the appropriate phrases to complete thesentence/question that the equation is asking3x 4 11510.“What number, when“What number, whenthenthenthenthenis equal to ?”11.3(x 4) 115is equal to ?”!x 3# 4 & 11"5 %12.“What number, when3x 4 115“What number, whenthenthenthenthenis equal to ?”is equal to ?”Part V: Solve the following equations. Show how you arrived at your solution.13.2 ( m 5) 714.7 5 2k 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.15.r 5 7212
Algebra 1 – The PreludeP.4: Equations with More than 1 VariableNamePd DatePart I: Review of what it means to “combine like terms”Consider the following algebraic expression: 2x 8 3x 6Often it is helpful to rewrite an algebraic expression so that it has the fewest number of terms possible.Thus, when we can, we want to “combine like terms” to create a new expression that is equivalent to theexpression we started with.LIKE TERMS have the same variable and the same exponent on that variable.To write an equivalent expression for 2x 8 3x 6 , identify the like terms and combine them.2x 8 3x – 65x 2Therefore, 2x 8 3x 6 5x 2Let’s verify that these expressions are indeed equivalent. Evaluate each expression using any value for x. Let’s use x 10:2x 8 3x 6 5x 22(10) 8 3(10) 6 5(10) 220 8 30 650 25252 1.Combine like terms to create an equivalent expression for each of the following.A. 6x 20 19x 25B.14 7r 6r 6C.4g 5h 7 g 7 hD. 3(4c 5) d 22cE.2(9m 7) 6(5 3m)F.3k 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.1(10 8k ) 6213
Algebra 1 – The PreludeP.4: Equations with More than 1 VariableNamePd DatePart II: Solving equations that require you to combine like terms.Example J: 2x 8 3x 6 37Example K: 3(2x 5) 5(x 6) 12. Solve each equation. Then, substitute your solution into the original equation to verify that yoursolution is correct.A.7x 10 5x 20 18B.24 3(2 p 7) pC. 5 ( 4k 2 ) 7 ( 4 3k ) 17 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.14
Algebra 1 – The PreludeP.4: Equations with More than 1 VariableNamePd DatePart III: Solving equations with variables on BOTH sides of the equation.Example L: 2x 8 3x 6Example M: 3 ( 2x 6 ) 4 ( x 3)3. Solve each equation. Then, substitute your solution into the original equation to verify that yoursolution is correct.A.9x 4 6x 11B. 5 ( x 2 ) 4xC.1(10x 2) 3(2x 4)2Part IV: Reflect and SummarizeLook back at the work you did to solve the four equations (examples J, K, L and M) in Parts III and IV.Example J: 2x 8 3x 6 37Example L: 2x 8 3x 6Example K: 3(2x 5) 5(x 6) 1Example M: 3 ( 2x 6 ) 4 ( x 3)Working with a partner, compare the equations AND how you solved them and write down a few ideasyou discussed regarding how are they similar and how are they different. 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.15
Algebra 1 – The PreludeP.4: Equations with More than 1 VariableNamePd DatePart V: Mixed practice.Solve each equation to find the value that makes the equation a true statement. Show your steps tojustify your solution. (HINT: before writing down any steps, first ask yourself, “Are all the variables onone side of the equation, or are there variables on both sides of the equation?”)A.5x 7 x 91B.5x 7 xC.40 10x 5x 30D.2(3x 4) x 1E.50 5x 2 6x 3F.15(2x 5) (18x 40)2 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.16
Algebra 1 – The PreludeP.5: Homework – Coordinate Plane ReviewNamePd DatePart I: Use the coordinate plane shown below to answer the following questions.1.Identify the x-axis by labeling it “x” and identify the y-axis by labeling it “y”.2.The point labeled O is a special point on the coordinate plane:a. Which one of the following is the name for this special point (circle the correct name):CenterOriginBlack HoleDeath Starb. State the coordinates of this special point, O:4.State the coordinates of the following points:RPBC5.Mark the location of point K which has coordinates (-5, -8).6.Kalena stated that point J has coordinates (-3, 5). Write a brief statement to explain why thosecoordinates are NOT correct and then state the correct coordinates for point J.PBRCOJ 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.17
Algebra 1 – The PreludeP.5: Homework – Coordinate Plane ReviewNamePd DatePart II: Graph the equation y 2x 1 using the following steps: Step 1: Complete a table of values for the equation y 2x 1 . Step 2: State the order pairs that result from your table of values. Step 3: Plot the points each of the ordered pairs in the coordinate plane. Step 4: Draw the line that goes through all of points you plotted.Step 1: Table of ValuesStep 2: Order Pairsx2x 1y-22(-2) 1-3Steps 3 & 4: plot the points aand draw the line(-2, -3)-10121x 3 is graphed in the coordinate plane below. Circle all of the ordered21pairs that represent points that lie on the graph of y x 3 .2Part III: The equation y (-2, 2)(4, -1)(-4, -5)(-1, 4)(-3, 0)(0, 6)(-2, 4)(6, 0)(2, 2)(0, -3) 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.18
Algebra 1 – The PreludeP.6: Equations that have 2 Different VariablesNamePd DatePart I: Equations that have 2 different variables.Recall: to solve an equation means to find the value that makes the equation a true statement.Consider the equation y 3x 5 . Since there are 2 different variables, the solution to this equation will be the PAIR of values thatmake the equation a true statement. Therefore, the solution will be written as a coordinate pair: (x, y).If a coordinate pair is a solution to an equation, then substituting the values for x and y into the equation will result in a true statement; and, the coordinate pair will be a point that lies on the graph of the equation.First, let’s determine if a coordinate pair is a solution using substitution.Is (1, –5) a solution to the equation y -3x 5 ?Is (2, –1) a solution to the equation y -3x 5 ?Now let’s take a look at the graph of the equation.The equation y 3x 5 is graphed in the coordinate plane tothe right.Discuss with your partner the following: Just by looking at the graph, determine if (1, –5) is asolution to the equation y 3x 5 ? How do you know? Just by looking at the graph, determine if (2, –1) is asolution to the equation y 3x 5 ? How do you know? Identify one other coordinate pair that must be a solutionto the equation y 3x 5 . How do you know? 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.19
Algebra 1 – The PreludeP.6: Equations that have 2 Different VariablesNamePd DatePart II: Solutions to equations that have 2 different variables1.Without graphing, determine if the coordinate pair is a solution to the equation y -3x 2? Showyour work to justify your conclusions.a. (1, 5)2.b. (0, 2)c. (2, 0)Below is the graph of y 2x – 7. Just by looking at the graph, determine if each of the followingcoordinate pairs are solutions to the equation y 2x – 7? Circle YES or NO.a. (-7, 0)YESNOb. (0, -7)YESNOc. (2, -2)YESNOd. (2, -3)YESNOe. (6, 5)YESNOf. (5, 4)YESNOg. (4, 0)YESNOh. (4, 1)YESNOy 2x - 73.Solve the following equations. Show your work.a.5x – 11 13 – x 14b.5x – 11 13 – x 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.c.8 x 9720
Algebra 1 – The PreludeP.7: PatternsNamePd DateLearning math helps us to develop important skills for identifying and generalizing patterns (i.e.,creating an algebraic expression to represent a pattern).Part I: Visual PatternsLook at the following figures.Figure 1Figure 2Figure 31. What do you notice? Turn to a partner and talk about what you see.2. Describe the similarities and differences from one figure to the next in this sequence. What changesand what stays the same?3. Use the space below to describe or sketch what Figure 4 and Figure 5 would look like if the patterncontinued. 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.21
Algebra 1 – The PreludeP.7: PatternsNamePd DatePart II: Patterns in a Table of ValuesLook at the sequence of figures on the previous page and fill in this table of values to record theinformation you observed.Figure NumberNumber of Squares4. How does the number of squares change as you move down the table?5. How can you relate this change to the sequence of figures? Where do you see it in the diagrams?6. Work with your partner to determine how many squares will be in Figure 20 (assuming the patterncontinued). What is your answer and how did you find it?7. Let’s use 𝑆 4𝑓 1. Each variable and number in this equation represents something about thesequence of figures and the table of values you created above. Talk to your partner about how theequation might relate to the sequence of figures and to the table of values.8. After talking with your partner, interpret the meaning of each variable and number in the context ofthe given situation (i.e., the sequence of figures).a. S representsb. 4 representsc. f representsd. 1 represents9. Use the equation to determine how many squares will be in Figure 20. Is your answer the same asyou got earlier without the equation?10. Use the equation to determine which Figure (number) will have 45 squares. 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.22
Algebra 1 – The PreludeP.7: PatternsNamePd DatePart III: More PracticeMalia used square tiles to make the sequence of 4 figures is shown below.Figure 1Figure 2Figure 3Figure 4A.Study the sequence of figures and explain in words how the design changes from one figure to thenext.B.If Malia continued her pattern to create the next 2 figures in the sequence, how many total tiles willthere be in Figure 5 and Figure 6 (try to determine these without drawing the figures).C.Caleb studied Malia’s sequence and created the following equation to generalize the pattern henoticed: T 3r 1. In Caleb’s equation, T represents the total number of tiles in a figure r represents the number of rows that have 3 tiles.Complete the table below using Caleb’s equation.rT(number of rowswith 3 tiles)(total number oftiles in the figure)Figure 1:Figure 2:Figure 3:Figure 4:D.In Caleb’s equation (T 3r 1), explain how the “3” relates to the pattern in the table.E.In Caleb’s equation (T 3r 1), explain what the “3” refers to in the figures and what the “1”refers to in the figures.F.If Malia continued her pattern to make several more figures, use Caleb’s equation to determine thetotal number of tiles in figure 25. 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.23
Algebra 1 – The PreludeP.7: PatternsNamePd DateThe current tuition at a university is 5,000, but the university just announced that starting next yearthey plan to raise tuition by the same amount each year for the next several years. The table belowshows the university’s tuition cost over the next several years.t(time: number of yearsafter this year)In 3 years:0123459In t years:tThis year:Next year:In 2 years:C(Cost of tuition) 5,000 5,700 6,400 7,100A.How does the cost of tuition, C, change each year over the next 3 years?B.If the tuition continues to change in the same way, determine the cost of tuition, C, in 4 years andin 5 years. Write your answers in the table above.C.If the university continued to raise the tuition by the same amount each year for several years, whatwill be the cost of tuition in 9 years? Show your work to justify your answer.D.Chris analyzed the table and created the following equation to generalize the pattern she noticed:C 5,000 700tExplain what each part of Chris’s equation represents in this situation (the university’s tuition).“C” represents“5,000” represents“700” represents“t” represents 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.24
Algebra 1 – The PreludeP.7: PatternsNamePd DatePart IV: Reflect and Summarize (follow your teacher’s instructions). 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.25
2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.26
Algebra 1 -- Module 1: FunctionsF – 1.1: Introduction to FunctionsNamePd DateWarm-up: Follow your teacher’s instructions.Part I:Lilia likes to use her cell phone to listen to music (and check her Instagram). She uses 10 megabytes bythe end of each day. Her data plan starts tracking how much data she uses from the beginning of thefirst day of each month.1. How many megabytes will Lilia use by the end of day on August 5th? (The 5th day of the month)2. Using complete sentences, answer the following questions:a. How much data would Lilia have used by the end of August 7th?b. How much data would Lilia have used by the end of August 9th?c. How much data would Lilia have used by the end of August 11th?d. How much data would Lilia have used by the end of August 20th?e. How much data would Lilia have used by the end of August 25th? 2015 Hawaii Department of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.27
Algebra 1 -- Module 1: FunctionsF – 1.1: Introduction to FunctionsNamePd DatePart II: A simpler and more efficient way of doing thingsClearly, it gets annoying to have to write the same thing over and over again. Whenever possible,mathematicians love to make things simpler and more efficient.So, instead of writing the sentence, “The data used by the end of ,” over and over again,mathematicians would simply write the situation as D(t) 10t.asd it ”aeRft“D oD(t) 10tD(t) means “The dataused after t days.”The value of D(t) is equalto 10 times the number ofdays (or, 10 per day).If we go back and look at the question 2a (on the previous page), instead of writing that completesentence in words, we could have simply written D(7) 70.Therefore: instead of writing, “At the end of the 8th day she will have used 80 megabytes,” we could simplywrite, ; instead of writing, “At the end of the 15th day she will have used 150 megabytes,” we couldsimply write, ; and, instead of writing, “At the end of the 24th day she will have used 240 megabytes,” we couldsimply write, . instead of writing, “At the end of the 31st day she will have used 310 megabytes,” we couldsimply write, .You try! Write something in function notation for
Apr 06, 2017 · F-2.4 Homework -- Review 55 F-2.5 Stations Activity – Function Tables and Graphs 57 F-2.6 Homework 61 F-2.7 Review 63 F-3.1 Different Ways to Represent the Same Function 67 F-3.2 Homework – A Refresher on Linear Functions 71 F-3.3 Connecting the Different Ways to Represent a Function 73 F-3.4 Homework 77
“white” page in order to maintain manual currency as shown on the List of Effective Pages. TR# Date Page Number Rev8 06/15/09. EMPLOYEE HANDBOOK 00.00 Pg. 6 List of Effective Temporary Revisions Page Intentionally Left Blank Rev8 06/15/09. EMPLOYEE HANDBOOK 00.01 Pg. 1 Table of Contents
uate the quality of grain damaged by rodents with respect to nutritional value, infection by moulds and aflatoxin contamination. 2 Materials and methods 2.1 Study area The study was conducted in Mwarakaya ward (03 49.17́'S; 039 41.498′E) located in Kilifi-south sub-county, in the low landtropical(LLT)zoneofKenya.Thisstudy site wasselect-
TOOLS All options except Online collaboration, Tools on Macro, Templates Spreadsheet 1. Enter the Following data in Excel Sheet REGIONAL SALES PROJECTION State Qtr1 Qtr2 Qtr3 QTR4 Qtr Total Rate Amount Delhi 2020 2400 2100 3000 15 Punjab 1100 1300 1500 1400 20 U.P. 3000 3200 2600 2800 17
13 Dektite Pipe Flashing Sealant (Durasil) Malco Folding Tool (18”) Turbo Shears Malco Hand Seamers Freud Diablo Blade Aviation Snips (By Others) Cordless Driver Drill (By Others) Pancake Fastener HWH Type 17 HiLo Fastener Hex Head Nut Setter (1/4” x 2-9/16”) 12 Large Tab Closure 14 Pro-Lock Vented Closure 15 9” Dekstrip
Aerospace Technology Needs and Trends. Finally an important and well-attended Workshop, co-sponsored by HTD and AIChE, was conducted in conjunction with the International Conference on Energy Sustainability on CO2 Capture and Utilization on the Sunday preceding the meeting. Second, HTD was a major contributor to, and participant in, the IMECE held
detailed picture of the crime scene (Figure 2.3.7) Crime scenes are also usually documented using photography (Figure 2.3.8). Photographs of evidence and the crime scene form a permanent record of often ephemeral and short-lived types of evidence. Photographs of fingerprints, footprints, bodies, injuries, bloodstains, tire marks, and many other
B. Kerrie says the answer is x 2 7 because the exponents should be added. C. Alex says the answer is x 7 12 because the exponents should be multiplied. D. Tracy says the answer is x 1 12 because the exponents should be multiplied. Algebra I - Session I Page 8 orig 2019 b e issori earen o leenar an Seonar aion All rigs resere
Anatomi dan Histologi Ginjal Iguana Hijau (Iguana iguana) Setelah Pemberian Pakan Bayam Merah (Amaranthus tricolor L.). Di bawah bimbingan DWI KESUMA SARI dan FIKA YULIZA PURBA. Bayam merah merupakan tumbuhan yang mengandung beberapa zat gizi antara lain protein, lemak, karbohidrat, kalium, zat besi, dan vitamin. Di sisi lain, bayam merah juga memiliki kandungan oksalat dan purin yang bersifat .
