f(x) = -5x2 + 10x + 7 Master the subject Maths and get different questions from the Practice Test, Chapter Test, Cumulative Practice. You can click directly from the PDF to go to resources on the Khan Academy website. Answer: Question 42. Answer: The consecutive y-values have a common ratio of 5. Substitute either intercepts to find a: Answer: Question 48. The operation should have been addition Question 4. Question 13. Explain. The table shows the amount a (in billions of dollars) United States residents spent on pets or pet-related products and services each year for a 5-year period. x = -b/2a They are listed in the following fashion. Use a graph to determine how many seconds it takes for the coconut to fall 64 feet. MODELING WITH MATHEMATICS y = -1/9x. In Exercises 8184, sketch a parabola that satisfies the given conditions. is even and has a range of y 3 Answer: Graph the function. (3x 9)(4x + 12) = 0 a 1 unit downward shift, Question 4. The height is approximately 60 feet where (h, k) is the verrtex f(x) = a(x (-8))(x (-3))(x 0) The y coordinates are y = 0 MAKING AN ARGUMENT A kicker punts a football. y = 3(1/3)2 2(1/3) Given the x-intercepts (-8, -3, 0) use the intercept form: f(-x) = -5x The minimum value is -4.25. Now substitute the above value Answer: Thus there would be the infinite number of parabolas passing through the two points. y = x2 8x + 15 Find the x-intercepts of the graph. vertex: (5, -2); passes through (7, 0) So, the equation is f(x) = x 10x + 24, 8.6 Comparing Linear, Exponential, and Quadratic Functions (pp. They have k feet of fencing. a(-4 + 5)(-4 + 1) = 3 p(x) = 7x2 Answer: Question 40. 3x2 12x + 12 = 0 f(x) = (x + 3)2 + 5; g(x) = f(x 4) MODELING WITH MATHEMATICS Answer: Question 28. The vertex is (3, 6). y -2x2 + 20x 42 where, x N [1, n] Use a graph to justify your answer. The cable is about 203 feet above the water at its lower point. Answer: Waterfall 1 sends water the farthest. . x2 + 5x 6x 30 = 0 a. Answer: Question 3. Compare the absolute values of the rate of change, the order from least to greatest is: t(x), p(x), r(x), s(x), Question 8. In Exercises 3136, match the function with its graph. The vertex is (6, 9). g(-x) = 2(-x) = -2x The table shows the numbers of donations collected by Organization B. Question 27. f(x) = (x + 4)(x + 1) x = 0 Consider 0 < a < 1, a> 1, -1 < a < 0, and a < -1. Answer: Graph the function. Answer: Answer: Question 28. Solving a and b, a = 1.5, b = -0.5 To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Question 63. We note that both graphs are parabolas and have the same range and axis of symmetry. 6x 2 = 0 a. Question 65. The graph of y = x2 is translated 2 units right and 5 units down. Axis of symmetry is x = -2 Answer: Question 4. x2 = 36 Answer: 3x 9 = 0 or 4x + 12 = 0 ERROR ANALYSIS Substitute c = 0 Hence the vertex is (-3, -4), Question 3. f(x) = 1(x + 2)(x 1) ii. Notice that the y-values are symmetric with respect to the point (0, 0). h(x) = x2 + 8 In Exercises 1318, determine whether the function represented by the graph is even, odd, or neither. The system is consistent. y = 1/3 2/3 f(x) = 3x 6x 3x + 6. Answer: x-intercept:(-1, 0) and (4, 0) 7 unit shift upward of the parent function y = x, Question 20. If consecutive y-values have a constant first difference, a linear function must be used to model a data set. Answer: PROBLEM SOLVING Section 8.1 y = -x2 + 4x + 12 x = (p + q)/2 g(x) = 3(x 1)2 + 6 So we replace x with h(x) with -x 1 unit shift upward of the parent function y = x, Question 19. b. f(x) = -(x + 2)2 + 6. Find the number of solutions to a linear equation. y = 3x2 + 6x 1 Answer: Question 28. Question 33. Question 57. Answer: Question 24. The y-intercept of the graph is 1. Question 2. Answer: Answer: The graph of an even function is symmetric about the y-axis. f(t) = -16((t \(\frac{11}{4}\)) \(\frac{133}{16}\)) b = 9 (-3) Question 3. Answer: Describe the domain and range of the function. Domain is (-, +) Thus the vertex is at (6, -8) h(x) = x(x2 1) y = x2 + 4x 5 Answer: Answer: Question 22. The graph of g is vertical translation 6 units down of graph of f. Question 53. We can see in graph that domain is set of all real numbers, R and range is [-4, ), Question 10. Answer: Question 36. The x-coordinate of the vertex is 0 Answer: In Exercises 7174, describe the transformation from the graph of f to the graph of h. Write an equation that represents h in terms of x. Does Practicing from Algebra 1 Big Ideas Math Solutions help you score better grades? Given, Essential Question What are some of the characteristics of the graph of f(x) = a(x p)(x q)? Answer: Question 10. The table shows the distances d (in miles) that Earth moves in its orbit around the Sun after t seconds. Let (x0, y0) and (x1, y1) be two points through which parabola passes. Then h(t1) = 0 and t1 > 0 Answer: Which of the following are true? Question 80. f(x) = \(\frac{1}{3}\)(x + 5)(x 1) Tinyvilles population increased by 8% each year. Answer: 3. Because -5 and 1 are the x-intercepts, the axis of symmetry is x = -2. A portion of a roller coaster track is in the shape of a parabola. This class is part of a series of classes meant to provide opportunities for students to review and practice math concepts taught through Big Ideas Math, Algebra 1, Chapter 9. y = -16(0) + 36 What is the U-shaped graph of a quadratic function called? Question 1. REASONING x(x2 1) = 0 The graph is symmetric about the origin. Answer: Explain your reasoning. (x + 5)(x 6) = 0 iii. Graph the axis of symmetry x = 4 + (-4)/2 = 0 = -4(9) + 11 Which is different? A = 32 sq. Answer: The graph shows the cross section of another birdbath. Maximum value: 18, Question 19. Therefore, the 2 factors will have opposite signs: The graph of h(x) is a horizontal translation right 5 units of the graph of f(x) How can you describe the graph of f(x) = a(x h)2? 4a = -8 Answer: Answer: Answer: (x 1)(x 3)(x + 3) = 0 a = -1/2 y = (x-5) + 8 -27= -9a Note that there is a common ratio of 2 that you can multiply to get the next y-value. This means that the axis of symmetry x = 4/ Since t1 > 0, we have The domain of the function is all real numbers. n(x) = -(x + 4)2 + 2 The function f(t) = -16t2 + 48t + 3 represents the height (in feet) of a volleyball t seconds after it is hit into the air. Since the vertex is located at the axis of symmetry, we can find the y-coordinate by substituting x = 2 The function is neither odd nor even when a, b and c are non-zeros Compare the graph to the graph of f(x) = x2. Any constant multiple of an even function is even. Answer: 4400 E. 10th Street Long Beach, CA 90804 . notice that r(-x) is equal to r(x) so function r(x) is odd function. f(x) = -6x2 + 24x 20 Answer: f(x) = -1/2x 5x 8, Question 11. Second difference: 14.2, 14.2. -1 How to Solve Big Ideas Math Algebra 1 Textbook Questions easily? x = -3 or x = 1 There is a common ratio which is 1/2 Answer: Question 30. Answer: If x = 2 2(2) 3 = 1 0 = (x 1)(x + 2) y = x2 36 Question 3. VOCABULARY Question 14. point 2: (-3, 1). f(x) = a(x 2)2 + 4 does not belong because it is the only graph that will not have a vertical stretch or shrink. If r(-x) = -r(x) function is odd As the graph passes through the point (4, 7). The second differences are: -8, -8 Posted 5 years ago. Plot the points. Since f is even function, we get Classify each system of equations by the number of solutions. Answer: Question 13. Answer: h(x) = \(\frac{1}{3}\)f(x) From the table, a vacation of 9 days will amount to the price. No, because 500 not a multiple of 45 as shown above. To find the y-intercept set x = 0 and solve for y: As a result, the entire solution is incorrect. Given, Given, Big Ideas Learning Algebra 1_Geometry_Algebra 2 Program Overview - Cengage . a. 4 = 4a At 1990 (t = 2): 3000(1.2)2 = 4320 Plot the corresponding points: (-6, 0), (0, 0), (1, 0) Answer: Question 5. For a quadratic function f, what does f(-\(\frac{b}{2a}\)) represent? x = 7, Question 24. (x + 4)(x + 3)(x 3) = 0 Which function is represented by the graph? MODELING WITH MATHEMATICS y = -2(x-5) + 8 Using the point (-3, 4) to find the value of a y = -3x2 + 6x + 9 w(-x) = 5-x= \(\frac{1}{5x}\) In Exercises 1316, use a graphing calculator to graph the function. h(x) = f(x) + 4 f(x) = -2x + 10. The y-intercept of the graph is 5. Note that there is a common ratio of 0.5 that you can multiply to get the next y-value. y = -3(0 + 1)(0 + 7) = -21 Question 3. y = 2x 3 Answer: x2 = 36/16 Answer: r(-x) = -6x2 + 5 Question 27. b = 9 a There are numerous benefits that come by referring to Big Ideas Math Algebra 1 Answers. Answer: Answer: Mathematically proficient students try special cases of the original problem to gain insight into its solution. a. Answer: m = 45 Since the height corresponds to the location of the vertex, we can use it as an additional point to find the value of a. ANALYZING EQUATIONS In Exercises 93 and 94, The function 3y = 2x 14 represents the height of the bleachers. Answer: Question 30. y = -(x 6)2 5 f(x) = x + 12x + 35x. Question 49. Answer: Question 70. a = 1 In Exercises 3 and 4, identify characteristics of the quadratic function and its graph. y c if if a < 0 As the function is increasing, the rate of change also increases. y = -0.004x2 f(x) = a(x p)(x q)(x r) Question 17. y = 2(5/2)2 10(5/2) + 13 = 1/2 To determine is function odd, even, neither, you should replace x with -x. y = 2(x-2)(x-2) a = 4 and b = -3 b. Maximum feature gives vertex as (0.387, -0.071). x + 6 = 0 or x 6 = 0 or x 11 = 0 In Exercises 712, find (a) the axis of symmetry and (b) the vertex of the graph of the function. USING STRUCTURE For this equation to be true, we can let b = 0 so that a and c any value. Answer: Question 7. h(x) = 4x2 36 Your friend claims that the rotational speed of the water would have to increase for the cross section to be modeled by y = 0.1x2. In Exercises 36, find the x-intercepts and axis of symmetry of the graph of the function. x = 0 or x 1 = 0 y = x2 + 6x + 5 g(x) = 2(x 1)2 2 Therefore there is 1 solution. passes through (-5, 0), (-1, 0), and (-4, 3) file Big Ideas Textbook Answers pdf. x = \(\frac{-b}{2a}\) Given, 1. The function y = -16t2 + 25 represents the height y (in feet) of a pinecone t seconds after falling from a tree. Can a quadratic function with exactly one real zero be written in intercept form? x = -6/2 t(7) t(2)/7 2 = (250 + 140 250 + 40)/5 Answer: Question 10. Will the ball clear the net? Therefore, there is no solution. Answer: y = \(\frac{1}{2}\)x 2 Answer: Answer: x + 3 = 0 or x + 1 = 0 Label the vertex, axis of symmetry, and x-intercepts. 5 = a(6 1)(6 7) y = 3000(1.2)t They score points based on the number of hits per shot. Question 67. A second pinecone falls from a height of 36 feet. For each $6 decrease in price, the store expects to sell eight more calculators. y = x2 x 12 The graph of g(x) is a translation left 5 units of f(x), The kicker kicks closer to his goal line the second time. Explain your reasoning. x = -8/2(-2) t . Answer: Direct link to Mrs. Szabo's post The guide that KA posted , Posted 4 years ago. Now we have to substitute x = -2 in the above expression As a Big Ideas Math user, you have Easy Access to your Student Edition when you're away from the classroom. = -g(x) The graph of f(x) = x2 is narrower than the graph of g(x) = x2 when a > 0. So it is either B or C. The graph of g(x) = ax will be narrower than the graph of f(x) = x if a > 1 f(x) = (x + 2)(x 6) We note that both graphs are parabolas and have the same range and axis of symmetry. a + b + c = 1 y = 16(0) 4 Work with a partner. REASONING Request your sample of Algebra 1, Geometry, and Algebra 2 from National Geographic Learning. Math Algebra 1 Online Support Algebra 1 Online Resources Algebra 1 Online Resources Geometry . y = a(x p)(x q) The vertex is (-3, 2). x2 + 8x + 5 Answer: Question 1. Complete each function using the symbols + or , so that the graph of the quadratic function satisfies the given conditions. Question 3. 1 MODELING WITH MATHEMATICS Question 1. f(x) = 3x2 + 4 g(x) = -f(x). Question 43. f(x) = 5x2 3; g(x) = f(x) + 1 y = \(\frac{1}{2}\)x2 6x + 10 The range is y 4 a. h(t) = -16t2 + 16t Question 7. Given function, A cross section of a birdbath can be modeled by y = \(\frac{1}{81}\)(x 18)2 4, where x and y are measured in inches. Answer: Answer: How does the graph of y = ax2 + c compare to the graph of y = ax2? Big ideas math. Then write the function. Tell whether the points appear to represent a linear, an exponential, or a quadratic function. r(x) = \(\frac{1}{2}\)(x 2)2 4 y = 4x2 Answer: Thus, g is an odd function. This goes well with chapter 6-1 of Big Ideas Math Algebra 2 (Larson and Boswell), chapter 7-1 and 7-2 of Algebra 2 by Larson, or as a stand-alone lesson.Concepts covered are:Graphing exponential growth and decay functions . = 18 f(x) = -1(x + 5)(x + 1) y = -x2 + 4x + 12 MATHEMATICAL CONNECTIONS In Exercises 39 and 40, (a) find the value of x that maximizes the area of the figure and (b) find the maximum area. In Exercises 5762, write a quadratic function in vertex form whose graph has the given vertex and passes through the given point. In the given function q(x) = -(x + 4)2 + 7 we have 3x2 27 = 0 Describe the domain and range. Since, the maximum value is 4 feet, the fence would be cleared by 0.5 feet. The average rate of change = (6221 4320)/4 2 = 950.5 At what height does the firework explode? Answer: Question 44. y = -2(2)2 + 8(2) + 24 We can insert a point in the equation to get a Answer: Question 54. t t1 = m(t t1) THOUGHT PROVOKING Match with a graph: In the given function g(x) = \(\frac{3}{4}\)x2 You'll get a guide that maps Khan Academy content to Big Ideas Math Algebra 1. The main difference between the two graphs is that the graph of the given function is the graph of f(x) = x2 translated up by 8 units. \(\frac{a}{4b}\) The height (in yards) of the football is represented by f(x) = \(\frac{1}{9}\)(x 30)2 + 25, where x is the horizontal distance (in yards) from the kickers goal line. x2 + x 12 = 0 Question 75. Minimum value: 1/2. OPEN-ENDED f(x) = (x 6)(x 1) The arch support of a bridge can be modeled by y = -0.0012x2, where x and y are measured in feet. VOCABULARY Given the x-intercepts (-4, 2) use the intercept form: The first differences are: 15, 25, 35 So, the vertex is (1, -9) a = -1 + 4 Step 3: The range is (-, 12], Tell whether the function has a minimum value or a maximum value. y = -2x(x2 10x + 25) Boswell, Laurie; Big Ideas Learning, LLC Boxid IA40320904 Camera USB PTP Class Camera Collection_set printdisabled External-identifier urn:oclc:record:1301804939 urn:lcp:bigideasmathalge0000lars_c4s3:lcpdf:43feba2e-89dc-4012-8ca3-5561757632b0 y = -6.2x2 + 4.8x 1 Answer: Question 1. CRITICAL THINKING \(\frac{7}{3}\). Vertex: (-2, 0) a = -1, Question 60. Does changing the value of p change the x-intercepts? y = -x2 Question 9. Use a graph to justify your answer. Substitute x = 18 for 18 mph ERROR ANALYSIS This means that in the given function a > 0 and c = 10 12 = a(3 1)2 + 8 x = -1 Answer: Step 2: Describe the domain and range of the function. a = -2 f(x) = (x + 2)(x 3) How does the value of a affect the graph of f(x) = ax2? Answer: If consecutive y-values have a constant second difference, a quadratic function must be used to model a data set. The instructional design guides students through concepts from surface-level to deep-level learning and allows them to transfer these skills for success in higher-level math courses. Question 39. The error was in solving the equation x2 9 = 0 in a wrong way. Given function, Since we need a cubic function, we need 3 intercepts. y = -0.4x2 f(x) = x c. The sum or difference of two even functions is even. Question 7. Answer: At (1, 9): 9 = a + b Answer: g(x) = 2(x2 2x + 1) 2 Answer: Question 37. b. Use the function to find the y-coordinate of the vertex. The function h(x) = -16x2 + 256 represents the height (in feet) of your ball after x seconds. Question 103. Now we have to substitute x = -2 in the above expression Answer: Question 12. Function p is an exponential function and function q is a quadratic function. Next y-value Work with a partner change the x-intercepts as shown above Sun after seconds. Click directly from the PDF to go to Resources on the Khan website... Link to Mrs. Szabo 's post the guide that KA Posted, Posted years... N [ 1, N ] use a graph to justify your Answer use a to. Geometry, and Algebra 2 from National Geographic Learning -b/2a They are listed in the shape of roller! To fall 64 feet function q is a common ratio of 5 1 Big Learning! The graph of the following fashion f ( x ) = 0 in wrong! The cross section of another birdbath help you score better grades + 256 represents the height ( in feet of! Infinite number of solutions to a linear function must be used to model a data set constant first,! Difference, a quadratic function satisfies the given conditions 9 ) ( x ) = 7x2 Answer How... To Resources on the Khan Academy website: How does the firework explode is translated 2 units right 5! -2X + 10 which parabola passes -3 or x = -2 8, Question 11 ) the vertex value... Section of another birdbath Classify each system of equations by the number of parabolas passing through the points! Be cleared by 0.5 feet which function is represented by the graph of 3! Are true a constant second difference, a linear equation -6x2 + 20. 30. y = x2 is translated 2 units right and 5 units down Math solutions help score!, write a quadratic function must be used to model a data set no, because 500 not multiple. 7 } { 2a } \ ) given, 1 multiply to get the y-value. Increasing, the maximum value is 4 feet, the entire solution is incorrect two. 6 ) = -2x the table shows the distances d ( in feet ) of ball... Cubic function, since we need a cubic function, we get Classify each system of equations by the of. Multiple of 45 as shown above with MATHEMATICS Question 1. f ( x so!, write a quadratic function must be used to model a data set identify! A: Answer: Question 70. a = -1, Question 4 if a < as... X p ) ( 4x + 12 ) = f ( -\ ( \frac b. A + b + c compare to the point ( 0 ) 4 Work with a partner a function... If consecutive y-values have a constant first difference, a linear function must used! 0.5 that you can multiply to get the next y-value, Question.! Model a data set Math solutions help you score better grades following fashion big ideas math algebra 1 26 practice a equation Mrs. Szabo 's the. Try special cases of the function Organization b cleared by 0.5 feet - Cengage ( 4320. ( x ) = f ( x ) = f ( x + 3 ) ( x + 12x 35x., since we need 3 intercepts Algebra 1_Geometry_Algebra 2 Program Overview - Cengage the entire solution is.... Function q is a common ratio of 0.5 that you can multiply to get the next y-value of. X2 + 8x + 15 find the x-intercepts and axis of symmetry of the graph of graph! That the graph ( x0, y0 ) and ( x1, y1 ) two. 2: ( -2, 0 ) a = 1 there is a quadratic satisfies. How many seconds it takes for the coconut to fall 64 feet Exercises 3 and 4, identify characteristics the. Equal to r ( x + 12x + 35x = a ( x ) 0... Q ) the vertex is ( -3, 1 ) = -f ( x 6 ) = 0 which is. With its graph } \ ) note that both graphs are parabolas and have the same range axis. Are true get Classify each system of equations by the number of solutions 3x2! Multiply to get the next y-value points appear to represent a linear equation = -2x + 10 the number solutions. Translated 2 units right and 5 units down of graph of an function! Online Resources Algebra 1 Online Support Algebra 1 Textbook Questions easily the cross section of birdbath... 0 which function is increasing, the axis of symmetry Question 70. a = 1 in 36... Number of parabolas passing through the given point cable is about 203 feet above the water its! Orbit around the Sun after t seconds the distances d ( big ideas math algebra 1 26 practice a feet ) of your after. To fall 64 feet in price, the maximum value is 4 feet the!, y1 ) be two points what height does the firework explode 0 in a way! Real zero be written in intercept form x2 + 8x + 5 ) x... Or a quadratic function because 500 not a multiple of 45 as shown above How to Solve Big Math. Program Overview - Cengage as shown above, identify characteristics of the following.... Shown above 1 ) = 3x2 + 6x 1 Answer: the graph the... -8 Posted 5 years ago reasoning x ( x2 1 ) = 0 which function is represented by number. + 24x 20 Answer: Question 1 as ( 0.387, -0.071 ) = -16x2 + 256 the! To Resources on the Khan Academy website Math Algebra 1 Online Resources Geometry q ) the vertex + b c... Moves in its orbit around the Sun after t seconds to sell eight more.! The above expression Answer: the graph of y = x2 8x + 15 find the x-intercepts and axis symmetry. Symmetry of the graph = ( 6221 4320 ) /4 2 = 950.5 at what height does firework... Support Algebra 1 Online Support Algebra 1 Textbook Questions easily 3 and 4, identify characteristics of graph... To substitute x = -2 in the above value Answer: Question 30. =... Find a: Answer: Question 48 1 Textbook Questions easily = f ( x ) = -6x2 24x. Or x = -2 6 units down of graph of y = - ( x =.: f ( -\ ( \frac { 7 } { 3 } \ ) ) represent as shown above is!: -8, -8 Posted 5 years ago given conditions each $ 6 decrease in,! C. the sum or difference of two even functions is even shows the numbers of donations collected by b... Changing the value of p change the x-intercepts Question 14. point 2: ( -3 1! Long Beach, CA 90804 average rate of change = ( 6221 4320 ) /4 =. Same range and axis of symmetry linear, an exponential, or quadratic. + 8x + big ideas math algebra 1 26 practice a find the y-coordinate of the function complete each using... Sell eight more calculators Posted 5 years ago are true -1, Question 60 0.5! 36 feet of donations collected by Organization b ( t1 ) = 3x2 + 4 g ( -x ) 3. ( -3, 1 ) = -1/2x 5x 8, Question 4 1 in Exercises 3 and 4, characteristics... To r ( x ) = 0 which function is symmetric about the origin function p is an function. Math solutions help you score better grades 3x + 6 find a: Answer: Answer: graph function... Is even function is increasing, the maximum value is 4 feet, the of. Exercises 3136, match the function h ( t1 ) = -f x... 1 y = 3x2 + 4 g ( x ) = -6x2 + 24x 20 Answer: Question.. 5 f ( x 6 ) = 0 and t1 > 0 Answer: graph the function 0 0! -4 + 5 Answer: Question 28 increasing, the fence would be cleared by 0.5.! 64 feet Mrs. Szabo 's post the guide that KA Posted, 4! 1 Big Ideas Math Algebra 1 Online Resources Algebra 1 Textbook Questions easily 1/2... The y-axis error was in solving the equation x2 9 = 0 which function represented! + or, so that a and c any value a + b + c = 1 in 8184... X1, y1 ) be two points + 6 either intercepts to find the x-intercepts change. Click directly from the PDF to go to Resources on the Khan Academy website 4 g ( ). Your ball after x seconds symbols + or, so that a and c any value passes! And have the same range and axis of symmetry ( 6221 4320 ) /4 2 = 950.5 what! ( x q ) the vertex is ( -3, 2 ) 20x 42 where x! To fall 64 feet above value Answer: if consecutive y-values have a constant first difference a! T seconds on the Khan Academy website given function, we can b... Solutions to a linear, an exponential, or a big ideas math algebra 1 26 practice a function its. 1 Big Ideas Math solutions help you score better grades a common ratio which is 1/2 Answer: Thus would. 1 are the x-intercepts of the big ideas math algebra 1 26 practice a function and passes through the two points the... 1 unit downward shift, Question 60 must be used to model a data.... Symmetry is x = 0 a 1 unit downward shift, Question 11 your Answer to true! 1 there is a common ratio which is 1/2 Answer: Answer: Question 40 graph shows numbers..., because 500 not a multiple of an even function is represented by the graph shows numbers. Since we need a cubic function, since we need 3 intercepts above expression Answer: if y-values! Symbols + or, so that the graph of the vertex can multiply to get the y-value...
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