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3 ) b: (0, 7) Lesson PDF

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Lesson a: The shape would be stretched verticall. In other words, there would be a larger distance between the lowest and highest points of each ccle. b: Each ccle would be longer horizontall.
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Lesson a: The shape would be stretched verticall. In other words, there would be a larger distance between the lowest and highest points of each ccle. b: Each ccle would be longer horizontall. Fewer ccles would fit on a page of the same length See graph at right. domain:, range: 0, asmptotes at = and = 0 f!1 () = a: 7.04 feet b: cm c: 8.94 meters º - 60º:! 1,! ; 45º - 45º:! 1,! 1 or, 7-7. = 6! 7-8. = 5, does not check a: = ( + 5 ) + 4, verte (! 5, 4 ) b: (0, 7) c: ( 5, 7); See graph at right No -intercepts, -intercept: (0, 88) (!1) + = 0 ; See graph at right. center: (1, 0), intercepts: (± 0 + 1, 0) and (0, ± 9) 01 CPM Educational Program. All rights reserved. Lesson 7.1. (Da 1) a: 0 60: hpotenuse:, leg: ; isosceles: hpotenuse:, leg: 1 b: See diagram at right =,! 5, = a: 0 b: c: 4 d: : ; 4; 5; undefined; 7; 8 a: See graph at right. It is linear. The data does not all connect because f (1) is undefined. b: = + 5, f (0.9) = 5.9, f (1.1) = 6.1, no asmptote. c: The complete graph is the line = +5 with a hole at (1, 6) a: An eponential function b: = (0.9) t 7-1. If he drives down the center of the road, the height of the tunnel at the edge of the house is onl approimatel.56 feet. The house will not fit. 7-. a:.75 b: = 18, = 1, z = 9 01 CPM Educational Program. All rights reserved. Core Connections Algebra Lesson 7.1. (Da ) 7-4.! # º or 19.5º 7-6. She should have subtracted!16 = 48 to account for the factor of three. The verte is (4, 7) See graph above right a: b: c: d: 7-0. = or! 1 4, = W -1 () 7-1. a: See graph at right. 1 b: No; when the points are interchanged, the input = 0 has two outputs R + B + G = 40,!R = B + 5,!R = G ; 18 red, 1 blue and 9 green Selected Answers 01 CPM Educational Program. All rights reserved. Lesson See graph at right (a): Above ground just past the highest point. (b): Just below ground. (c): Back to the starting point. See diagram at right feet B A C 1 (a) -1 (c) (c) (c) (c) (b) (b) 7-9. a: log 6 = log + log! b: log15 = log + log 5! c: log 9 = log! d: log 50 = log 5 + log! =!± 6, = = ( +1)! ; See graph at right No real solution C + W + P = 40, W = C! 5, C = P ; 18 from California, 1 from Washington, and 9 from Pennslvania 4 01 CPM Educational Program. All rights reserved. Core Connections Algebra Lesson (Da 1) ( 4, 1 4 ) 15 or (! 4, 1 4 ) P: (cos 50º, sin 50º ) or (~0.64, ~0.766); Q: (cos110º, sin110º ) or (~ 0.4, ~0.940) ( ) a: 00 b: 1,! c: 1,!! a: 0 b: 60 c: 67 d: = a: downward parabola, verte (, ), see graph above right. b: cubic, point of inflection (1, ), see graph below right Solving graphicall: a: = 5d m and = 0.0() m!1 b: R vs. T: $55 vs. $15.6, $60 vs. $15,78.64, $100 vs. ~ $1.901! All of these problems could be solved using the same sstem of equations. Selected Answers 01 CPM Educational Program. All rights reserved. 5 Lesson (Da ) º, 1º, 8º, or 0º 7-6. a: An angle in the 4 th quadrant. b: 70 or 90 c: An angle in the rd quadrant. d: Approimatel 160 e: No, an angle with sine equal to 0.9 has cosine equal to ±0.459, so the point (0.8, 0.9) is not on the unit circle a: (0.40, 0.997) b: (cos70, sin70 ) c: (cos 70 ) + (sin 70 ) = = Graph is sine, while graph 1 is cosine. Answers will var a: All es. b: Answers will var. c: = (! n) for all integers n intercept: (0, 17), -intercepts: (! + 1, 0) and (!! 1, 0) a: = 4 b: = ' 5± 57 4 c: no solution d: If a = +, then a + 5 a. Or, solving ields =, but when substituted, gives a zero denominator Tess is correct: A sequence has no more than one output for each input. A sequence is a function with domain limited to positive integers CPM Educational Program. All rights reserved. Core Connections Algebra Lesson a: Same;! and 60 are measures of the same angle. b: 45º, 15º, 405º, etc a: b: a: Set each factor equal to zero to get = 0, 1, or. b: Factor to get ( 1)( + ) = 0. = 0, 1, a:.657 b: 0.96 c: He should have subtracted! 9 4 = 9 to account for the factor of. The verte is (,! 5 ) a: = (! )!1, verte: (, 1), ais of smmetr = b: = (! )! 7, verte: (,! 7 ), ais of smmetr: = 7-8. a: =.511 b: = See graph at right. a: No b: 10 10, c: 00! sq. units f!1 () = (!1) + for 1; See graph at right. Selected Answers 01 CPM Educational Program. All rights reserved. 7 Lesson a: 0.76 b: 7-91.! 6,! 5! ! 4,!,!,!,! 4, 5! 6,!, 7! 6, 5! 4, 4!,!, 5!, 7! 4, 11! 6,! 7-9. See diagram at right. a: A little less than 60 (almost 44 ). b: sin a: 1 b: 1 c: undefined d: ~ 4.7% annual interest sin A cos A = ! a: f!1 () = +1 4 b: g!1 () = a: = 4 or = b: CPM Educational Program. All rights reserved. Core Connections Algebra Lesson a:! ±! n b: See diagram at right. c:, 1, a: 0 b: 0 c: 1 d: 0.5 e: 0 f: undefined Some ma set up a proportion, others ma use! a: 10 b: 00 c:! 4 radians d: 5! 9 radians e: 9! radians f: See graph at right. f() f () = (! 4) + f -1 () a: 5 1 b: a: a + b b: c c: a + b d: a + c a: See graph at right. b: Yes, the pizza will never get below room temperature. temperature time Selected Answers 01 CPM Educational Program. All rights reserved. 9 Lesson a: See graph at right. b: = 1+ sin c: : (0, 1), :!(!!, 0! ),!(,!0 7! ),!(,!0),!... d: Yes, there are infinitel man, at intervals of π a:! b: = sin( +! ) a: This ma go up and down, but the ccles are probabl of differing length. b: This ma or ma not be periodic. c: This is probabl approimatel periodic = 100 sin ( +! )! 50 or = 100 cos! Onl one needs to be a parent, since = sin( + 90 ) is the same as = cos a: =!6 b: =!(0.5) 7-1. a: = ± 5 = ± 15 5 b: = 4, 1 c: = a: b: a =! 15 =! , possible equation: =! 15 (!15) CPM Educational Program. All rights reserved. Core Connections Algebra Lesson a: = sin!! 4 ( ) + ( ) ( ) + or = sin ( + 5! 6 ) + ( )!1 or =!sin ( +! )!1 b: = 1.5 sin +! c: =! sin!! 6 d: = sin!! is the period of = cos!, so shifting it 60 left lines up the ccles perfectl Graphing form: = (!1) + ; verte (1, ); See graph at right a: = (0, 0), 5± (,!0) and = (0, 0) ears a: =! ( ) , = all real numbers, =! 5 8 ; Yes it is a function. b: =!( +1) +15, domain: all real numbers, range:! 15 ; Yes it is a function , unsafe a: 5,000,000 btes b: 1. minutes c: According to the equation, technicall never, but for all practical purposes, after minutes See graph at right. a: The verte of the graph is at (6, 4) with two ras emanating at slopes of ±1. b: See graph at right. Flip all parts of the graph that are below the -ais above the -ais. Selected Answers 01 CPM Educational Program. All rights reserved. 11 Lesson a: Amplitude, period 4π b: See graph at right. c: The differences are the period and amplitude, and therefore some of the -intercepts. The have the same basic shape ,!! = 1 or! (1) =! Colleen s calculator was in radian mode, while Jolleen s calculator was in degree mode. Colleen s calculation is wrong = sin (!1) is correct. To shift the graph one unit to the right, subtract 1 from before multipling b anthing The are both wrong. The equation needs to be set equal to zero before the Zero Product Propert can be applied. + 5! = 4 is equivalent to ( + 7)(!1) = 0. = 1 or =! a: b: 1.5 c: d: a: = 0 ( 1 ) + 5 b: w = a: Answers var, if g() is linear, tangent lines onl. b: An line = b such that b CPM Educational Program. All rights reserved. Core Connections Algebra Lesson a: Yes b: = cos ( +! ) c: = sin ccles, period:! Answers will var a: 180º b: 540º c:! 6 radians d: 45º e: 5! 4 radians f: 70º a:! b: c: 1 d: e: 1 f:! 1 g:! 4 or 5! 4 h:! 4! or 7! ( 1, 1, ) a: = 0, = 1, or = 5 b: = 6 or = 1 c: Answers will var a, b, and c: Answers will var a: About $564,40 b: In 05 c: About $6,585 Selected Answers 01 CPM Educational Program. All rights reserved. 1
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