Record and Practice Journal Answer Ke Chapter Fair Game Review......... F. floors......... $. groups. Activit. Triangle. a. The sum of the angle measures of a triangle is. Answer should include, but is not limited to: The sum of the angle measures of each triangle should be. Some might be a little off due to rounding.. a. = ; = = ; =. = ; =. d... = ; =.. Sample answer: If ou notice a pattern, ou can use inductive reasoning to write a rule. Then ou can test our rule using several eamples. You can use the rule to write an equation that can be used to solve a problem.. Practice. =. w =.. =. k =. z = n =. =. h =. p =.. p. =.; p = $.. c = Angle A Angle B Angle C A B C a. d.. Activit. a. n = ; n = ;,, = ; = ; ( ) ( ),, q = ; q = ;,, m m = ; m =.; d. ( ).,,. = ; = ; e. ( ),, t. t = ; t =.; f. ( ),,. f = ; k = ; m = ; n = ; p = ; s = ; t = ; w = ; = ; = indigo:,, violet:,, orange:,, ellow:,, blue:,, green:,,. a d.. Sample answer: To solve a multi-step equation, use inverse operations. To check the reasonableness of a solution, make sure the solution makes sense and substitute the solution back into the equation.. Practice Monda Tuesda Wednesda Degrees Percent % % % People Thursda Frida Degrees Percent % % People. =. b =.. z =. w =. a =. q =. w = cm. m = months Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. Activit. a. = ; = ; ft; ft = ; = ; ft; ft = ; = ;. ft;. ft d. = ; = ; ft; ft e. = ; = ; ft; ft = ; = ; ft; ft f. ( ) g. = ; = ; ft; ft. a. = ; = ; in. ; in. = ; = ; in. ; in.. smaller triangle:,, ; larger triangle:,,. Collect the variable terms on one side and the constant terms on the other side. Sample answer: ( ). Practice = = = = = =. =. =. p =. =. = or =. = or =. no solution. = or =. = or =. = or = Graph. Graph. Graph. Graph. Graph. Graph. Graph. Graph. Graph. Graph. Graph.. g =. n =.. w =. = ; =.. Etension. = or = Graph. Graph.. = or = Graph. Graph.. = or =. =.. Activit. a. Graph. Graph. P P = w ; w = ; w = in. A A = bh; h = ; h = in. b C C = πr; r = ; r = cm π Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke A d. A = h( b B) ; h ; h in. = b B = e. A = bh; h = A ; h = m b. a. V = Bh; h = V ; h = in. B V V = Bh; B = ; B = ft h V V = Bh; B = ; B = π cm h V d. V = Bh; h = ; h = m B. Activit. a. Sample answer: Sample answer: (, ), (, ) Sample answer: Solution Points =. Sample answer: You can solve a given formula for a different variable to form a new formula that can be used to solve for the variable.. Practice. =.. =.. r = f.. h. a. Chapter A h = h = in. b Fair Game Review = V w = h S π r = π r......... $.. (, ). (, ). Point F. Point G Choose,. d. Sample answer: ( ) =? = ( ) = e. es; Because the line is the graph of the equation, all points on the line are solution points. f. Sample answer: Solution Points =. Point B, Point H. Point C, Point E. (, ) (, ) (, ) (, ) (, ) Each point lies on the line. g. es; The graph of the equation is the set of all solutions to the equation. So, each of these solutions falls on the line. h. The graph of an equation of this form is a line. Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. d. In the ond graph, it is easier to see where the line crosses the -ais and the -ais.. A linear equation is of the form = a. Its graph is a line and can be drawn b finding solution points to an equation and drawing a line through them. Sample answer: = (linear) = (not linear) a. es; no; You can see that the graph crosses the -ais between and. You cannot see where the graph crosses the -ais. Sample answer: You can choose a lower minimum -value.. Activit. a. ; ; es; It appears that the slope between an two points on a line is the same. ; ; es; It appears that the slope between an two points on a line is the same. ; ; es; It appears that the slope between an two points on a line is the same.. a. d. ; ; es; It appears that the slope between an two points on a line is the same. O. Sample answer: You should use a graphing calculator because if ou graph it b hand ou will have to scale our aes b tenths.. Practice.. (, ) (, ) =. =. (, ) = O O (, ). a. $. (, ) = (, ) O = (, ) O (, ) = = (, ) O (, ). The two lines are parallel. The two lines are parallel. O O The two lines form a right angle. The product of the slopes of the two lines is.. The slope can tell ou whether the line rises or falls from left to right and how steep the line is.. Two different nonvertical lines in the same plane that have the same slope are parallel. Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke.. Practice.... undefined.. staircase ; The slope of staircase is greater than the slope of staircase,.. Etension Two lines in the same plane whose slopes have a product of are perpendicular. which is. line B and line G ; The both have a slope of.. line B and line R; The both have a slope of.. es; Both lines are vertical and have undefined slopes.. no; The line = has an undefined slope and the line = has a slope of.. es; Because opposite sides have the same slope, the are parallel. Because opposite sides are parallel, the quadrilateral is a parallelogram.. line B and line R; Line B has a slope of. Line R has a slope of. The product of their slopes is ( ) =. O. line R and line G; Line R has a slope of. Line G has a slope of. The product of their slopes is =.. es; The line = is vertical. The line = is horizontal. A vertical line is perpendicular to a horizontal line.. no; Both lines are horizontal and have a slope of.. es; Because the products of the slopes of interting sides are equal to, the parallelogram is a rectangle.. Activit. a.. ;, ( ) ; (, ) d. ;, ; (, ) ( ) ;, line; ( ). =. line; ; (, ) line; ; (, ). =. = line; ;, ( ) = line; ; (, ) = Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke.. = line; ; (, ) line; ; (, ).. = = =. -intercept:. -intercept:. a. = (, ) (, ) = O (, ) (, ) (, ) (, ) O = line; ;, ( ) line; ; (, ). =. line; ; (, ) line; ; (, ). A line with slope m that crosses the -ais at (, b ). a. It affects the steepness of the line and whether it rises or falls from left to right. It affects where the graph crosses the -ais. Works for an equation.. Because m is the slope and b is the -intercept. Sample answer:. Practice. slope: ; -intercept:. = slope: ; -intercept:. slope: ; -intercept: = (, ) Slope = = O Big Ideas Math Algebra = The slope is. So, the length of each game is minutes. The -intercept is. So, there are games in the tournament.. Activit. a. = The points form a line. d. es; Solve the equation from part (a) for.. a. = = Number of Adult Tickets, Number of Child Tickets, =. Sample answer: It is a line with a slope of c -intercept of. b a b and Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. Activit uses a table. Activit uses the slope-intercept form. Sample answer: The slope-intercept form ma be considered easier because ou can use the slope and -intercept to graph the equation.. Sample answer: You sold $ worth of lemonade. You sell large cups for $ and small cups for $.. When the equation is in standard form, ou can see that when =, =, and when =, =. You can graph the equation through its -intercept and its -intercept.. Practice. =.. =... a. = = (, ) O = The -intercept is. So, ou can bu shirts if ou don t bu an jeans. The -intercept is. So, ou can bu jeans if ou don t bu an shirts.. Activit (, ) (,) (, ) O = (, ) O = (, ). a. top line: slope: ; -intercept: ; = middle line: slope: ; -intercept: ; = bottom line: slope: ; -intercept: ; = The lines are parallel. right line: slope: ; -intercept: ; = middle line: slope: ; -intercept: ; = left line: slope: ; -intercept: ; = The lines are parallel. line passing through (, ): slope: ; -intercept: ; = line passing through (, ): slope: ; -intercept: ; = line passing through (, ): slope: ; -intercept: ; = The lines have the same -intercept. d. line passing through (, ): slope: ; -intercept: ; = line passing through (, ): slope: ; -intercept: ; = line passing through (, ): slope: ; -intercept: ; = The lines have the same -intercept.. a. square units; = ; = ; = ; = The opposite sides have the same slope. square units; = ; = ; = ; = The opposite sides have the same slope.. a. mi mi h hours d. mi. Let the slope be m and the -intercept be Then the equation of the line is = m Sample answer: What is the equation of a line with a slope of and -intercept of? = Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. Practice d.. =. =. =. =. =. =. =. =. Activit. a. -intercept: = O -intercept: = O -intercept: = -intercept: =. a Sample answer:. d. Sample answer: The rise is the change in, or difference in the -coordinates. The run is the change in, or difference in the -coordinates. e. m = f. m( ) = = This result represents ; the equation of a line with slope m that passes,. Balance (dollars) O O (, ) through the point ( ) A A = t Run (, ) Savings Account Rise t Time (months). The results are the same. The formula from Activit can be used to write the equations in slope-intercept form. Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. It is the formula that can be used to write the equation of a line given a point on the line and the slope of the line. The slope and the coordinates of the point are substituted into the formula to get the equation. It is important because it allows ou to write the equation of a line given a point and a slope.. Plot the given point and use the slope to plot additional points to find the -intercept. Then use the slope m and -intercept b to write the equation = m Sample answer: What is the equation of the line,? with a slope of that passes through ( ) =. Practice. =.. =. = =. a. = $; the -intercept. Etension. =. =. =. =. =. =. =. =. =.. O =. = =. =. =. =. =. Activit. Answer should include, but is not limited to: Make sure students interpret the slope, -intercept, and -intercept from the stor. Make sure the table values are possible in this situation.. a. Sample answer: A hot air balloon is feet above the ground. After onds, it has descended all the wa to the ground. Elevation (feet) Sample answer: You withdraw $ per month from our savings account. After months, ou have no mone left in the account. Mone left in account (dollars). Sample answer: You can represent as a unit and as a unit and then its slope as a rate. miles per gallon; dollars per ear; cost per unit. Practice Time (onds) Time (months). Sample answer: the depth of a pond Depth (feet) Time (ears) Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. Sample answer: reccling paper Pages remaining Time (minutes). Activit. a. t ; e.;. a. ; all values of greater than or equal to > ; all values of greater than ; all values of less than or equal to d. < ; all values of less than. a. -intercept: You can bu at most shortsleeved shirts if ou bu no long-sleeved shirts. -intercept: You can bu at most long-sleeved shirts if ou bu no short-sleeved shirts.. = Chapter Fair Game Review. >. =. <. <. >. <. our friend;. ft is about ft and in.......... S M > L a. es; > no; < no; =. You can use inequalities to describe real-life statements where a value has a limit, but also has man possible values. Sample answer: The number of students in a class is no less than. Each item is allowed at most timeouts.. Practice. p. n. solution. not a solution. solution. not a solution... ;. Activit. (b), (d), (g), and (h) are true; (b) is true because if there are no incomplete passes, then C N = A, but there are times where there are incomplete passes, so C N A. (d) is true because a completed pass is either a touchdown or not a touchdown, so T C. (g) is true because attempts minus completed passes is equal to the sum of incomplete and intercepted passes, so A C M. (h) is true because an attempt can be either completed, intercepted, or incomplete, so A = C N M.. A, C...... Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. Sample answers are given. a. A =, C =, Y =, T =, N = ; all values of P less than A =, C =, Y =, T =, N = ; all values of P greater than or equal to A =, C =, Y =, T =, N = ; all values of P greater than d. A =, C =, Y =, T =, N = ; all values of P greater than or equal to e. A =, C =, Y =, T =, N = ; all values of P greater than. Add or subtract the same number from each side of the inequalit to get the variable alone on one side. a. P < P P > d. P e. P >. You can use addition or subtraction to solve an inequalit just like ou solve an equation, b adding or subtracting the same number from each side.. You subtract from each side to solve both. However, the solution to the inequalit is a set of numbers, and the solution to the equation is one number.. a. ;. Activit. a.. a.? T T T T F F F T T T F F F F >? < >? F F F F F F T. Practice. < >. p. <. z.. < ; <. > ; >...? T T T T T T F T T T F F F F? Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke d. F F F F T T T > If ou divide each side of an inequalit b the same positive number, the inequalit remains true. If ou divide each side of an inequalit b the same negative number, ou must reverse the direction of the inequalit smbol for the inequalit to remain true.. a. > < > > > >. a. <?? > F F F T T T T <? F F F F T T T? F F F F F T T d. < < < If ou multipl each side of an inequalit b the same positive number, the inequalit remains true. If ou multipl each side of an inequalit b the same negative number, ou must reverse the direction of the inequalit smbol for the inequalit to remain true. > < < ( ) ( ) T T T T F F F >? T F F F F F F? < < < F F F F T T T ( ) ( ) Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. If ou multipl or divide each side of an inequalit b the same positive number, the inequalit remains true. If ou multipl or divide each side of an inequalit b the same negative number, the direction of the inequalit smbol must be reversed for the inequalit to remain true.. Practice. n <. a. >. The width can be greater than feet but less than feet.. Sample answer: You can bound the area or perimeter b a number and then find what the possibilities are for the missing side. Sample answer: Area < ft. ft ft. t <. q.. p >. m.. r. t <.. q.. ;. Activit.................... a. > and < > and < > and d. > and e. w > f. w > g. > π and < h. > and < <. Practice. >. d. n >. z < ft > ft. all real numbers. no solution. das. Etension. < q <. r <. s < Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. t or t <. < or. <. < a <. <. b > or b. < or >. c and c. no solution..; The least weight of the coin that the countr s mint will allow to be released into circulation is. grams. The greatest weight of the coin that the countr s mint will allow to be released into circulation is. grams.. Activit. a. = (, ) (, ) (, ) O Sample answer: (, ); > (, ); > (, ); > None of the points result in true statements. d. above e. Sample answer: (, ); > no; When =, the statement > is not true because it states is greater than, not greater than or equal to. f. To include the points that lie on the graph of =, use the greater than or equal to sign ( ) instead of the greater than sign ( > ) in the inequalit.. a. = The solutions of the inequalit are all ordered, such that is less than. pairs ( ) < ; < ; The line is dashed so it does not. a. include the points on the line. > Sample answer: (, ); > (, ); > ( ), ; > All of the points result in true statements. Big Ideas Math Algebra (, ) (, ) O = (, ). You can use a coordinate plane to solve problems involving linear inequalities b representing the solutions of the inequalit as a shaded region separated from the points that do not satisf the inequalit b a dashed or solid line depending on whether the points on the line make the inequalit true (solid line) or do not make the inequalit true (dashed line). Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. Practice. es. no. es. no.. O. a. Let be pounds of tomatoes and be pounds of red peppers.. Two possible solutions are (, ) and (, ). So, ou can bu pounds of tomatoes and pounds of red peppers, or pounds of tomatoes and pounds of red peppers. Chapter Fair Game Review O. =. a =. k =. a. es; ( ) ( ) =. Activit. a. C = R = C =. a. R = nights. a O C R C R. m =. t =. h =. calculators.. O O (, ); nights; This is the same breakeven point that was determined in Activit... O O. Use a table to determine when the equations have the same value, or graph both equations and find the point of intertion. Check our solution b substituting it into each equation and making sure both are satisfied. Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. Sample answers: a. (.,. ); Used a graphing calculator because of the decimals ( ) = =, ; Used a table because of the equation = (.,.) = (.,.). Activit. a. (, ) (, ) (, ) d. (, ) e. (, ) f. (, ) Method : Substitute the epression for into the ond equation and solve for. Then substitute the value of into one of the equations and solve for. Method : Substitute the epression for into the ond equation and solve for. Then substitute the value of into one of the equations and solve for. The solutions are the same using both methods.. Sample answer: a. (, ) = = Partner s sstem: = = Solution: (, ). Give me a place to stand, and I will move the Earth. (.,. ); Sketched a graph to estimate the point of intertion. Practice. ; = C R.. (, ) (, ). (, ). (, ). bos, girls O. Solve for a variable in one equation. Substitute the epression for that variable into the other equation and solve the equation. Substitute the variable value that ou know into one of the equations to find the value of the other variable.. Practice. (, ).,. a. = =. (, ). (, ) Regular: gal; Premium: gal. Activit. a. (, ) (, ) (, ) Method : Once ou have subtracted the equations and eliminated a variable, ou can solve for the remaining variable, then substitute its value into one of the equations and solve for the other variable. Method : Once ou have added the equations and eliminated a variable, ou can proceed as above to solve for both variables. The solutions are the same using both methods. Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. a. Yes, but ou have to multipl one of the equations b a constant first so that a variable is eliminated when ou add or subtract. Multipl the equation b. Multipl the equation b. d. The solution for both is (, ). e.. Activit. a. = t = t. Hpatia. Add or subtract the two equations so that one variable cancels out. You ma have to multipl one or both equations b a constant first. After eliminating a variable, solve for the remaining variable, then substitute its value into one of the equations and solve for the other variable.. You can add equations if the coefficient of one of the variables in one equation is the negative of that variable s coefficient in the other equation. Eample: = = You can subtract equations when one variable has the same coefficient in both equations. Eample: = = You have to multipl first if neither of the above is true. Eample: = =. The Multiplication Propert of Equalit states that multipling both sides of an equation b the same constant produces an equivalent equation.. Practice. (, ). (, ). (, ). (, ). a. = = females; males. a.. a. ; difference between ou and our cousin s age no; You and our cousin will never be the same age at the same time. Your compan will never break even. You need to sell each backpack for more than $ to make up the $ ou invested for equipment. es; The intert at ever point because the are the same line. An point on the line =. d. C R C R = t = e. es f. There are man solutions. The solution of the sstem is all points on the line =. Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. A sstem of linear equations can have no solution if the two lines are parallel because parallel lines do not intert. A sstem of linear equations can have man solutions if the equations are the same when written in slope-intercept form. Sample answer: The sstem of equations consisting of = and = has no solution because the lines are parallel, as ou can see from the graph. = The sstem of equations consisting of = and = has man solutions because the are the same line, as ou can see from the graph.. Practice. no solution. infinitel man solutions. infinitel man solutions. no solution = = =. no; You have a page head start and ou both read at the same pace.. min. a. = ears. Activit. a. Inequalit Inequalit. When ou graph both inequalities in the same coordinate plane, ou get a coordinate plane divided into four regions. The pink region represents points that satisf Inequalit but not Inequalit. The blue region represents points that satisf Inequalit but not Inequalit. The purple region represents points that satisf both Inequalities. The unshaded region represents points that satisf neither Inequalit.. () () () (). Woming, Colorado; The state must have straight edges and be shaped such that a line between an two points inside the state doesn t cross the state boundar.. Graph each inequalit in the same coordinate plane and shade in the solution of each. The solution to the sstem is the region where the shading overlaps.. The region where the solutions of each inequalit overlap is the solution to the sstem. No, not all sstems have a solution. If the lines in the graphs of the two inequalities are parallel, their solutions could never overlap.. Practice.. O O. You both bu the same number of songs.. Etension. =. =.. O O. =. =. es; You earn the same amount each da if =. Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. a. O. Input Output no; If = and =, is not satisfied. Chapter Fair Game Review. As the input increases b, the output increases b.. As the input increases b, the output increases b.. As the input increases b, the output increases b.. As the input increases b, the output decreases b.. As the hours increase b, the customers increase b.. Input Output. Input As the input increases As the input increases b, the output b, the output increases b. increases b.. Input Output. Input.. As the input increases As the input increases b, the output b, the output decreases b.. increases b. Output Output. Activit. a. =,,,, ; = is not in the domain because the output becomes negative, and ou cannot sell a negative amount of child tickets. = is not in the domain because ou cannot sell half of an adult ticket.. a.,,,, d. (, ), (, ), (, ), (, ), (, ) d. domain:,,,, range:,,,,.. domain:,,,, range:,.,,., domain:,,,, range:,,,, domain:,,,, range:,,,,. The domain is the set of all possible input values. The range is the set of all possible output values. Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. a. women: men: b and women: = =. (Domain). The domain is,,, and. The range is,,, and.. a. =, men:. Practice. The domain is,, and. The range is,, and.. The domain is,,,, and. The range is,, and.. (Range).... (Domain) The domain is,,, and. The range is,,, and. (Range).... (Domain) (Range)... (Domain) (Range)..... (Domain) (Domain) (Range).... (Range)...,,,,, The domain is,,,, and. The range is,,,,,,,, and,.. Etension. not a function. function. function. not a function. not a function. function. function. not a function. a. es; Each input has eactl one output. no; Some inputs will have multiple outputs. For eample, input has outputs,,, and.. Activit Input, Output, Input, Output,. a. = Total hotel cost Hotel Reservations Number of rooms domain:,,,,,, range:,,,,,, The domain is discrete. Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke = Total weight of luggage domain: and range: and The domain is continuous.. A discrete domain is a set of input values that consists of onl certain numbers in an interval. A continuous domain is a set of input values that consists of all numbers in an interval. Sample answer: discrete domain: The total cost of families attending a football game. continuous domain: The height of a building.. Practice.. The domain is continuous. Luggage Weight Pounds per piece O The domain is discrete.. Activit. a. = = = d. O O =. The domain is continuous.. a. Yes, because ou can bu cards. Yes, because ou can bu cards for $.. a. = π ; is the radius; is the circumference π π π π π = ; is the width of the rectangle; is the perimeter Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke = ; is the length of one of the bases; is the area d. = ; is the width of the prism; is the surface area. Sample answer: A linear function helps ou to see the relationship between and. The slope shows the rate at which is changing for each increase of in.. Sample answer: After plotting the points, ou can find the slope between the points. Then, ou can draw a line through the points to find the -intercept and write the linear function.. Practice. =. =. =. =. a. The domain is continuous. = miles. Activit. a. B D A d. C. I evaluated ( ) a. (, ) plotted (, f ( )). (, ) (, ) d. (, ) f at and. a. d. O g( ) is equal to f ( ) shifted up units. g( ) is equal to f ( ) shifted up unit. g( ) is equal to f ( ) shifted down unit. g( ) is equal to f ( ) shifted down units.. You can name a linear function f. The notation f ( ) is another name for. So, the function = becomes f ( ) =. Functions in standard notation and function notation both look the same on the right hand side, but the differ on the left hand side as described above.. The graph of = f ( ) c is the graph of f ( ) = shifted up c units. If c is negative, the function is shifted down.. Practice. =. =. =. O O O = O Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke.. O O. O Translation units left of = Domain: all real numbers Range:. a. $ times. Etension... O O O Domain: all real numbers Range:, > Domain: all real numbers Range: < Domain: all real numbers Range:.. Opens down and is wider than = Domain: all real numbers Range: Translation unit right and units down of = Domain: all real numbers Range:. =. =. Activit. a. P O O P linear. Domain: all real numbers Range: >.., if < =, if O Translation units down of = Domain: all real numbers Range: A A nonlinear Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. a. h linear Height (feet) h nonlinear Height (feet) The bowling ball has an increasing speed.. If the rate of change is constant, the pattern is linear. Sample answer: linear: area of a triangle with a base of and a height of nonlinear: height and age. Practice.. t Time (onds) t Time (onds) The graph is nonlinear. The graph is linear.. Activit. a.. Number of rows, n Number of dots, n -values increase b each time. n -values increase b each time. Number of stars, n Number of sides, n Number of circles, n -values increase b each time. Number of molecules, n Number of atoms,. linear; The graph is a line.. nonlinear; The graph is not a line. The -values increase b each time. There are atoms in molecules.. nonlinear; The area increases b different amounts as the side length increases b one. Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. The values increase b each month. Answer should include, but is not limited to: Students should write a stor that uses the information given in the table. Students should include drawings and graphs. n. Arithmetic sequences show the value for each term of a pattern. Sample answer: You start with $. You save $ each month. An arithmetic sequence to represent our savings is,,,,,.. Practice.,,..,.,......,,.,,.,,. no. es;. a.,,,,, times; After three visits the regular admission has cost ou $ and the season pass is onl $. Chapter Fair Game Review....... ±. s = ft. a = n. a = n n. a = n. a = n n. a. g =.n gal n n n. Activit. a. s = = ft s = = d s = = cm d. s = = mi e. s =. =. in. f. s =. =. m g. s = = ft. a. no; =, but =. no; It is not true in this eample, so it is not true in general. es; = and = =. es; a b = a b ( a b) = = a no; =, but =.. no; It is not true in this eample, so it is not true in general. d. es; es; = and = =. a a a a = = =. b. a. a b = a b a b =. Practice a b b b...... b.. z z. ft Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. Etension Activit : Sum or product Answer Rational or Irrational? Activit : Rational Rational Rational... Rational Rational Rational... Rational Sum or product Answer Rational Rational or Irrational? Irrational Activit : Sum or product Answer Rational or Irrational? Irrational Irrational π π Irrational π π Rational π π Irrational Irrational π π Irrational Rational. no; The product is rational when the rational factor is. Otherwise, the product of a nonzero rational number and an irrational number is irrational.. no; no; The sum two irrational numbers can be rational or irrational. The product of two irrational numbers can be rational or irrational.. es; es; The sum and product of each pair of rational numbers is rational.. The sum is irrational. Activit : Irrational π π Irrational Irrational Sum or product Answer Rational or Irrational? Irrational π π Irrational Irrational Rational. no; = a c. Sample answer: Let and be rational numbers b d where a, b, c, and d are integers and b, d. a c ad bc ad bc For addition, = is b d bd bd rational because the set of integers is closed under addition and multiplication. So, ad, bc, and bd are all integers and the sum ad bc is an integer. a c ac For multiplication, =. Because the b d bd integers are closed under multiplication, ac and bd are integers. So ac is rational. bd. Activit. a. d. e. The product of two powers with the same base is that base raised to the sum of the powers. Big Ideas Math Algebra. a. d. e. The quotient of two powers with the same base is that base raised to the difference of the powers. Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. a. d. e. The power of a power is the base of the powers raised to the product of the powers.. a. ( )( ) ( )( ) ( )( ) d. ( )( a ) e. ( )( ) The power of a product is the product of the factors each raised to the power.. a. d. The power of a quotient is the quotient of the dividend raised to the power and the divisor raised to the power.. If the same pattern holds true for ever eample ou encounter, ou can use inductive reasoning to write a general rule stating that the pattern is alwas true... Practice. m. t.. h a. Activit. a. d. e... p. w e... s = = ft; Check: = a b s = = cm; Check: = s = = in.; Check: = s =. =. m; Check:. =. s = = d; Check: =. a. d. e. C;. because.. A;.. because... B;.. because... E;. because.. D;. because.. f. F;,. because.,.. If is a number, ou can write the nth root of as n. You can evaluate this b finding a number n such that =.. C. mm. Practice......... in.. Activit. a. The graph curves upward with each successive increase in population greater than the last. percent; Earth s population increased b around % during each -ear period. about million d. about. billion; The pattern did not continue. The industrial revolution and improvements in medicine caused the population to increase dramaticall faster than predicted. f. s = = =. mm; Check: = Cube D is the largest because it has the greatest side length,. m. Cubes A and E are the same size because the have the same side lengths, ft = d. Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke.. An eponential function is a function whose output increases or decreases at a constant rate.. a. Year t Population from Activit B.C.. B.C.. B.C.. B.C.. B.C.. B.C.. B.C.. B.C.. B.C.. B.C.. B.C.. A.D.. A.D.. A.D.. = O = () O = (.) O Yes, each of these functions increases at a constant rate. P. Practice..,... Domain: all real. Domain: all real numbers numbers Range: > Range: <. a. Domain: Range: visitors. Etension. =. =. =. no solution. =. =......... no solution... a. on the third da ( = ) O,,,,,. Activit A = = B = =,. a. Conutive points increase b a constant amount,, so the pattern is linear. Conutive points increase b around the same factor,., so the pattern is approimatel eponential. Conutive points neither increase b the same factor or the same amount, so the pattern is neither eponential nor linear. d. Conutive points neither increase b the same factor or the same amount, so the pattern is neither eponential nor linear. Pattern (b) O Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. The pattern is approimate eponential growth with each term increasing b an average factor of.. If the pattern continues, the population will return to, nesting pairs around the ear.. In eponential growth, a quantit increases b a constant factor over time. Other growth patterns increase according to different rules, for eample a linear growth pattern would increase b the same amount over equal time intervals.. a. eponential growth; Ecluding deposits and withdrawals, savings accounts increase b a constant factor, determined b the interest rate. not eponential growth; The speed of the moon doesn t grow b a constant factor, it increases and decreases repeatedl because of its elliptical orbit. not eponential growth; The height of the ball is decreasing, not increasing. It is also not decreasing eponentiall.. Practice. a = ; r = %;.. a = ; r = %;.. a =.; r = %;.. a = ; r =.%;.. = (.) t,,,,,,,,, t. a. = (.) t $.. Activit. a. Conutive points neither decrease b the same factor or the same amount, so the pattern is neither eponential nor linear. Conutive points decrease b a constant amount,, so the pattern is linear. Conutive points decrease b about the same factor,., so the pattern is approimatel eponential. d. Conutive points neither decrease b the same factor or the same amount, so the pattern is neither eponential nor linear. Pattern (c). a. about % P.M.. In eponential deca, a quantit decreases b a constant factor over time. Other deca patterns decrease according to different rules, for eample a linear deca pattern would decrease b the same amount over equal time intervals.. Temperature Time Temperature T........... t Time. about. F Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. Practice. eponential deca. neither. eponential growth. eponential deca. %. %. a. At () = (.) t about. mg. Activit. a. Step Calculator displa The calculator displa doubles for each step. Step Calculator displa The calculator displa is halved for each step. Sample answer:. arithmetic. neither. geometric. a. Multipl b for the net row.,, geometric; You multipl b the same amount each time, so this is the common ratio of a geometric sequence.. Etension.,,,,,. a n,,,,, n. a.. mm. mm. mm d. Sample answer: ;. mm e. Sample answer: es; The paper would be about. millimeters high. This is about. feet, so the paper would be taller than an person.. In the end, the king would have to give the beggar millions of grains of rice. Answer should include, but is not limited to: Students should write a stor about doubling or tripling a small object.. Geometric sequences are used to describe patterns where something is multiplied b the same amount several times. Sample answer: On a game show, for each correct question, the prize mone is double or nothing.. Practice Step Calculator displa...,,. a n n.,, a n n a n n.,,,,, a n O.,,,,, a n a =, a = a. n n a =, a = a. n n a =, a = a. n n n O n Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. a n n =. a =, an = an. a =, an =.an. a = n a =, a =, a = a a ;,,. n n n a =, a =, a = a a ;,,. n n n a =., a =, a = a a ;,,. n n n a =, a =, a = a a ;,,. n n n Chapter Fair Game Review.. h. a. m n. A, H: ; A, B, E, G, I: ; A, D, E, H: ; B, F, H: ; A, F, I: ; E, F, I: ; C, I: ; B, D: ; A B C D E F G H I. d. q.......... cm. Activit. Sample answers: a. Monosllabic; The infant had started speaking but still had a monosllabic vocabular. Biped; Humans are a well-known tpe of biped. Triccle; Our son is too oung to balance on a biccle so we got him a triccle. d. Poldactl; The poldactl cat had si toes on its front paws instead of.. a. ; binomial; it has two terms. ; binomial; it has two terms. d. e. ; monomial; it has one term. ; trinomial; it has three terms. ; binomial; it has two terms. f. ; binomial; it has two terms.. You can use unique figures to represent each of the monomials,,,,,,, then represent a polnomial b displaing a group of figures where the number of a specific figure represents the coefficient of that monomial. The shape and dimension represent the degree of the monomial; degree- terms are large squares, degree- terms are rectangles, and degree- terms are small squares. The color represents the sign of the monomial; ellow, green, and blue are positive and red is negative.. Practice. v ; ; monomial. c c ; ; trinomial. t ; ; binomial m m ; ; binomial.. g ; ; monomial.a a. a; ; trinomial.. no. es; ; trinomial. t ; ft Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. Activit. Step : Step : Step :. a. b d. e. f. g.. Step :. a. Step : Step : Step : h. b d.. You can add polnomials b grouping like terms, then adding the coefficients of the like terms and simplifing.. You can subtract polnomials b grouping like terms, then subtracting the coefficients of the like terms and simplifing.. Practice. d. m m. t t. c c c. s s. w w.... Activit. a. d. z z z. a. d. e. f. g. h. i. j. The product of two numbers with the same sign is positive and the product of two numbers with opposite signs is negative.. a. e. g. d. f. h.. You can multipl two binomials b multipling each term in the first binomial b each term in the ond binomial (four multiplications take place) then simplifing the result.. a.,,. Practice.. g g. w w a a. d d.. n n. a. t t $. Activit. a.. a. a b. a.. a. i. ii. iv. v. iii. vi. a ab b a ab b i. ii. iii. v. iv. vi. z z z. The patterns are: ( a b)( a b) = a b, ( ) a b = a ab b, and ( ) a b = a ab b. Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. Practice. m. p. Practice. b =,. k =,. n =,. s. d. a a. k k.. a. r r. Activit. f f ft ; ft. a. C, D, A, d. B, e. E,. a. ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; d. ; ; ; ; ; e. ; ; ; ; ; f. ; ;,, ; Conjecture: If ( a) form of an equation, then the equation. is a factor in the factored = a is a solution to. a. ; Adding to a number leaves it unchanged; adding to a number increases it b. ; is the onl number ou can multipl a nonzero number b and get. The product of an two numbers that are opposites is. both; is ; is. d. ; Multipling an number b leaves it unchanged. e. ; Multipling an number b results in. f. neither; ; has no opposite.. An equation that is equal to a nonzero number can be made into an equation equal to zero b subtracting the nonzero number from both sides.. Propert b; The Zero-Product Propert is used to solve equations: the equation is written in factored form, then solutions are found b setting each factor equal to zero. It is important because it can be used to solve an equation that can be written in factored form.. v =,. h =. =,. r =,. p =,. ft. Activit. a. ( ) ( ) ( ) d. ( ). a. ( ) ( ) ( ). a. ( ) ( ) ( ). a.,,,,,, ; it is the greatest polnomial that divides both terms.. Find the greatest common factor of the terms, factor it out, then write the polnomial as the GCF multiplied b the sum of the divided factors.. Practice. ( ) nn. t( t t ). a =. r =,. w =,. z =,. =,.. a.. Activit ft p =,. a. ( )( ) ( )( ). a. ( )( ) ( )( ). a. ( ) ( ) ( )( ) d. ( )( ) e. ( )( ) f. ( )( ). You can set each factor equal to zero and solve each of them. Each solution to one of these equations is a solution to the original equation. Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. a. To factor b c, arrange algebra tiles that add up to the terms, b, and c in a rectangular arra that models b c, then label the dimensions of the arra with tiles so that the arra forms a multiplication table with the products of the labels on the outside equal to the corresponding algebra tiles inside the arra. The factors are the sums of the two groups of tiles on the outside of the table. To factor b c without using algebra p and q tiles, find two factors, ( ) ( ) such that ( p q) = b and pq =. a. ( )( ) ( )( ) ( )( ). Practice. ( w )( w ). ( b )( b ). ( )( ). ( h )( h ). ( n )( n ). ( n )( n ). t =,. d =,. ( b )( b ). ( )( ). =,. d =.,. ft b ft. Activit. a. ( )( ). This is a special product studied in Lesson.. ( ). This is a special product studied in Lesson... This is a special product studied in ( ) Lesson.. d. ( )( ). This is a special product studied in Lesson... = ( )( ) ( ) = ( ) =. a. ( ) ( )( ) ( ). a. and meters. Activit. ( )( ). a. ( )( ) ( )( ). a. ( )( ) ( )( ) ( )( ) d. ( )( ) e. ( ) f. ( )( ). To factor a b c, find two factors, ( r p) and ( s q), such that rs a, rq ps = b, and pq =. a. ( ) ( )( ) ( )( ). Practice. ( n )( n ). ( h )( h ). You can tell that a polnomial can be factored a b a b if it can be written in the form ( )( ) a b. You can tell that a polnomial can be factored ( a b) if it can be written in the form a ab b. You can tell that a polnomial can be factored ( a b) a ab b. if it can be written in the form. a. ( ) ( ) ( )( ). Practice. ( b )( b ). ( z )( z ). ( k ). ( f ). =,. r =. ( j )( j ). ( p )( p ). a =,. p =. Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. Etension. a. ft. ( c )( c ). ( k )( k ). ( p )( p ). ( t )( t ). ( a b)( b ). ( )( ). dd ( )( d ). nn ( )( n ). alread factored completel. ww ( ). q =,,. r =,,. a =,,. f =,. a. length: ; width: length: ; width: Chapter Fair Game Review.. O.. O O O. Activit. a... = =. t (, ) (, ) (, ) (, ) (, ) (, ) O (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ).. O......... a. The graphs are a reflection of each other. = = O Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke =. Practice. O = d. O = =. = =.. Both graphs open up, have the same verte, (, ), and have the same ais of smmetr, =. The graph of = is narrower than the graph of =. O Both graphs open up, have the same verte, (, ), and have the same ais of smmetr, =. The graph of = is wider than the graph of =. O O When < a <, the graph of wider than the graph of the graph of of Big Ideas Math Algebra = a is =. When a >, = a is narrower than the graph =. When < a <, the graph of = a is wider than and is a reflection in the -ais the graph of graph of =. When a <, the = a is narrower than and is a reflection in the -ais of the graph of. The graph of =. = a is U-shaped, smmetric about the -ais, and passes through the origin. It has a domain of all real numbers and a range of either or. If a <, the graph is reflected so that the graph is upside down U-shaped. If a >, the graph is narrower than the graph of is wider than the graph of =. If < a <, the graph =.. Both graphs open up, have the same verte, (, ), and have the same ais of smmetr, =. The graph of = is wider than the graph of =. The graphs have the same verte, (, ), and the same ais of smmetr, =, but the graph of = opens down. The graph of = is narrower than and is a reflection in the -ais of the graph of =. Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke.. = The graphs have the same verte, (, ), and the same ais of smmetr, =, but the graph of = opens down. The graph of = is narrower than and is a reflection in the -ais of the graph of =. Incoming angle Beam The outgoing ras are all parallel to the -ais. Bulb Beam Beam. O. Satellite dishes have parabolic shapes so that incoming signals will be reflected to the receiver, located at the parabola s focus. Spotlight reflectors have parabolic shapes so that beams of light emitted from the bulb, located at the focus, will be reflected parallel to the parabola s ais of smmetr. The graphs have the same verte, (, ), and the same ais of smmetr, =, but the graph of = opens down. The graph of = is wider than and is a reflection in the -ais of the graph of =.. Distance: feet; Height: feet. Answer will var.. Practice.. O. Activit. Ra Ra Ra,.., O = Incoming angle (, ), The reflected ras all intert the -ais at (, ). The receiver for the satellite ra is at (, ) because that is where the dish reflects all the incoming signals.. =. =.. = Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke. Activit. a. = =. a. (, ) (, ) O O O O = = = = ± = ± (, ) (, ) O (, ) O (, ) d. = = O d. = ± (, ) (, ) O = = ± Set equal to zero and solve for. The value of c moves the graph up or down b c units. Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. The value of c in of = c translates the graph = up b c unit. ( = will be translated down in c is negative.). Practice. O. Shift the graph units up.. Shift the graph units down.. After. onds. Activit.... Both graphs open up and have the same ais of smmetr, =. The graph of = is a translation units down of the graph of O =. Both graphs open up and have the same ais of smmetr, =. The graph of = is a translation units up of the graph of O =. The graphs have the same ais of smmetr, =. The graph of = opens down. The graph of up of the graph of O = is a translation units =. O The vertices of both graphs have the same -value.. =, O (, ) (, ) The verte is horizontall between and verticall below the -intercepts. Both graphs open up and have the same ais of smmetr, =. The graph of = is wider than and is a translation units down of =. b. =, a b,,, a ( ) = a b b a Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke b b. ; a a. You can find the -coordinate of the verte b finding the two -intercepts then finding the point that is half-wa between or using the equation,. b =. Substitute that -value into the original a equation to find the -coordinate of the verte.. (, ). The graph of ( ) to the left of the graph of. The graph of ( ) = is a translation units =. =. is a translation. units to the right of the graph of. The graph of ( ) =. = is a translation units to the left and units up of the graph of =.. Practice = (, ). a. = (, ). a... Domain: all real numbers Range: Domain: all real numbers Range:. minimum; (, ). maimum; (, ). ft. Etension O. The graph of ( ) to the right of the graph of = is a translation units =.. The graph of ( ) = is a translation units to the right and unit up of the graph of =.. The graph of ( ) = is a translation units to the left and units down of the graph of =.. The graph of ( ) = is narrower than and is a translation unit to the right and units down of the graph of =. = opens down, is. The graph of ( ) narrower than, and is a translation units to the right and units up of the graph of =. = is wider than and is a translation units to the left and units down of the graph of =.. The graph of ( ). g( ) is a horizontal translation units right of f ( ).. g( ) is narrower than and is a vertical translation units up of f ( ).. a. million ears. The graph of ( ) to the left of the graph of = is a translation units =. Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Record and Practice Journal Answer Ke. Activit. Distance (miles) t t = t =.................... The green car has a constant speed because it travels the same distance over each equal time interval. The blue and red cars are both accelerating but the red car is accelerating the most because it makes greater increases in speed as time passes...... = t..... Time (minutes) = = t = t t t The green car has a constant speed. The blue and red cars have increasing speed. The blue car eventuall overtakes the others. After minutes, the blue car travels miles, the red car travels miles, and the green car travels miles.. You can compare growth rate of linear, eponential, and quadratic functions using tables or graphs. Eponential growth eventuall leaves the other in the dust. Even though quadratic growth is the fastest at first, eponential beats it in the long run.. Practice t t = t =.. O = O t a. t t = t = The green car has a constant speed. The blue and red cars have increasing speed. The red car eventuall overtakes the others. After minutes, the red car travels miles, the blue car travels miles, and the green car travels miles. = t eponential quadratic. quadratic. linear. linear; =. eponential; = ( ). a. linear $. Etension Activit a. t... f () t t.. f () t Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Record and Practice Journal Answer Ke The function is increasing when < t <.. d. Practice The function is decreasing when. < t <.. The rate of change is not constant. It is decreasing.. decreasing; The graph shows that the curve begins to flatten as approaches... When the function in increasing, the rate of change is positive. When the function is decreasing, the rate of change is negative.. a. (., ) (, ) (, ) (., ) (., ) (, ) (., ) (, ) (., ) (, ) (, ) t Time interval Average rate of change (ft/) Time interval Average rate of change (ft/) Time interval Average rate of change (ft/) to.. to to.. to to.. to to.. to to.. to t.. f () t decreasing when t d. Time interval Average rate of change (ft/) Rates of change are negative and decreasing. Activit a. es; When =, =. So, each website has videos per hour. Linear Time interval Quadratic Eponential to. Average rate of change (videos/h) Time interval Average rate of change (videos/h) Time interval Average rate of change (videos/h) Time interval Average rate of change (videos/h) Time interval Average rate of change (videos/h). to to.. to to to to to to to to to to to to to to to to (., ) (, ) (, ) (., ) (, ) O... t Time interval Average rate of change (videos/h) to to The average rate of change for the linear function is constant. to Big Ideas Math Algebra Copright Big Ideas Learning, LLC