Monday

April 21, 2014

April 21, 2014

Number of results: 70,001

**Transformations-Algebra**

I need help with transformations. This is what my instructions say to do: Begin by graphing the standard absolute value function f(x)=|x|. Then use transformations of this graph to graphy the given function. 1. g(x)=|x|+3
*Saturday, September 1, 2007 at 5:09pm by Jen*

**transformations**

cellular transformations? Math transformations? Real life? Please expand.
*Wednesday, August 31, 2011 at 8:00pm by bobpursley*

**Transformations**

Is there some type of online grapher that I could use to check my transformations?
*Friday, September 7, 2007 at 8:07pm by Jess*

**transformations**

what are the 4 major types of transformations and real life examples
*Wednesday, August 31, 2011 at 8:00pm by Anonymous*

**college algebra**

Graph the following function using transformations. Be sure to graph all of the stages on one graph. State the domain and range. For example, if you were asked to graph y= x^2+11 using transformations, you would show the graph of y = x^2 and the graph shifted up 1 unit
*Tuesday, June 21, 2011 at 3:32pm by nena*

**Pre-Algebra**

Can someone please show me how to solve these problems step-by-step so that I can understand how to do them? 1.Use inverse operations to write a related inequality and solve for the variable: d/6 < 12 2.Use inverse operations to solve the inequality: m-27=85 3.Use ...
*Friday, May 1, 2009 at 3:23pm by mysterychicken*

**college algebra**

Graph the following function using transformations. Be sure to graph all of the stages on one graph. State the domain and range. For example, if you were asked to graph y= x^2+11 using transformations, you would show the graph of y = x^2 and the graph shifted up 1 unit...
*Tuesday, December 11, 2012 at 8:06pm by beatrize*

**college algebra**

Question 638522: Graph the following function using transformations. Be sure to graph all of the stages on one graph. State the domain and range. For example, if you were asked to graph y= x^2+ 1 using transformations, you would show the graph of y = x^2 and the graph shifted ...
*Tuesday, December 11, 2012 at 8:33pm by beatrize*

**Polynomial Functions**

I have to graph some graphs but I don't the main image points for the base function to make transformations. Specfically, f(x)=x^3 f(x)=x^4 f(x)=x^5 and it goes on. How do I find them to make my transformations?
*Wednesday, September 11, 2013 at 6:02pm by Alice*

**Math**

any combination of such transformations ca be performed on a rhombus. Is the final position subject to any specific restrictions? Those are all linear transformations, so they will leave the shape and size of the rhombus unchanged.
*Friday, April 6, 2012 at 4:02pm by Steve*

**physical science**

Trace the energy transformations from gasoline in a car to sound from the radio playing hitting your ears. There should be 4 transformations. please help me i only have a couple of hours left til i have to turn it in.
*Friday, April 3, 2009 at 11:02am by kt1993*

**Algebra 2**

What are the transformations that will happen to 1/x to get 3/(x+2)?
*Thursday, April 16, 2009 at 7:57pm by Anonymous*

**Western Experience : Since the sixteenth century**

How did imperialism impact non-western economies? How did Europeans achieve these transformations of local economies? What were the effects of those transformations?
*Tuesday, October 26, 2010 at 11:22pm by Kim*

**Geometry**

I appreciate any help you can give me. Here is my question: Find the coordinates of the images of A(2,3), and B(-2,3) under the following transformations. Assume that all size transformations are centered at the origin. a. A size transformation with scale factor 2 followed by ...
*Wednesday, April 17, 2013 at 8:23pm by Christine*

**Transformations-Algebra**

Wouldn't it just move it up 3 verically?
*Saturday, September 1, 2007 at 5:09pm by bobpursley*

**transformations**

There are many different kinds of transformations. Maybe you'll find your answer in one of these sites. http://www.google.com/#sclient=psy&hl=en&source=hp&q=major+types+of+transformations+&pbx=1&oq=major+types+of+transformations+&aq=f&aqi=&aql=&gs_sm=e&gs_upl=...
*Wednesday, August 31, 2011 at 8:00pm by Ms. Sue*

**college algebra**

Transformation of ty then transformations of the graphs y=x^2or y=|x| to sketch a graph of f by hand. f(x)=2|x-6|-4
*Monday, February 25, 2013 at 7:02pm by Anonymous*

**college algebra**

Let f(x) = 1/x Evaluate and plot g(x)= -f(2x) + 1 Start with the innermost transformation and work outward in steps. There are 3 transformations
*Friday, April 11, 2008 at 2:35pm by Sarah*

**College Algebra**

Graph the function using transformations. Show your work and state a) the domain b) the range c) the asymptotes f(x) = 3 - 1/(x + 4)^2
*Sunday, August 5, 2012 at 1:49pm by Kameesha*

**algebra 2**

They both have x>y transformations, that is, for any x there is one and only one y. That is the definition of a function.
*Friday, December 11, 2009 at 9:08am by bobpursley*

**Transformations-Algebra**

go across 3 then go up 3
*Saturday, September 1, 2007 at 5:09pm by Chandler*

**7th grade math please help Ms. Sue ASAP**

12. Write a sequence of transformations that maps triangle ABC onto triangle A''B''C''. It is a graph, so here are the coordinates: A is 1,8 B is 3,12 C is 4,4 A'' is 3, -3 B'' is 5, -6 C'' is 6, 2 Please help! I have no idea how to write a "sequence of transformations "!! I ...
*Tuesday, February 5, 2013 at 9:36pm by Delilah*

**college algebra**

graph the function using transformations, show and state , a) the domain, B) range c) the asymptotes F(x)= 1/x^2-4 please show work!
*Friday, August 17, 2012 at 9:49pm by alli*

**College algebra**

graph the function using transformations, show and state , a) the domain, B) range c) the asymptotes F(x)= 1 ----- -4 x^2 please show work!
*Saturday, August 18, 2012 at 9:29pm by alli*

**algebra**

Sketch a graph of y=1/2int(x-2)+1. State the domain range and intercepts. Hint: Lightly graph y=int(x) and then apply three transformations.
*Thursday, June 30, 2011 at 12:45am by dazzling*

**pre calculus**

2. Graph the following function using transformations. Be sure to graph all of the stages on one graph. State the domain and range. y= -2 lxl +2 For example, if you were asked to graph y= x^2 + 1 using transformations, you would show the graph of y= x^2 and the graph shifted ...
*Tuesday, April 2, 2013 at 11:00am by michelle*

**Algebra 2 ..**

Describe the transformations. 1. g(x)=(2x)^2 2. g(x)=-1/2x^2
*Wednesday, December 26, 2012 at 4:27pm by Anonymous*

**college algebra**

graph the following function using transformations, be sure to graph all of the stages on one grph, state the domain and range y= x^2 +12x
*Friday, November 2, 2012 at 5:09pm by zachary*

**Pre-Algebra**

Here are some more: 1.Use transformations to solve the equations: 5{6+k}=3k 19-3m+ 5+7m <0 2.Find the circumference of a circle with diameter 31 m. 3.What is 186% of 750? Thanks!! -MC
*Friday, May 1, 2009 at 5:39pm by mysterychicken*

**college algebra**

graph the following function using transformations, be sure to graph all of the stages one graph, state the domain and the range y=x^2+12x
*Friday, November 2, 2012 at 11:32am by zachary*

**English**

First, there is no optimistic outlook on incest. It would be better to say that these transformations give the reader the belief that she will have a better future. Donkey Skin is capitalized.. Leave out "of herself" I would say, Donkey Skin goes through many experiences which...
*Friday, January 29, 2010 at 3:10pm by GuruBlue*

**Math**

Since this is not my area of expertise, I searched Google under the key words "Transformations R(2,2)" to get this: http://www.google.com/search?client=safari&rls=en&q=transformations+r(2,2)&ie=UTF-8&oe=UTF-8 In the future, you can find the information you desire more quickly...
*Saturday, February 20, 2010 at 7:31pm by PsyDAG*

**Pre Calculus 12**

Im going over my pre calculus 12 exam, and I need help with one question from the chapter Transformations of graphs and stuff. Combining Transformations 2y = f(5x-10)+8 The original points are (4,6) and the new points I got by translating it and stuff are : (14/5,20) But in ...
*Tuesday, January 22, 2013 at 8:18pm by Shreya*

**college algebra**

find the function that is finally graphed after the following transformations are applied to the graph of y=sqrt x in the order listed. 1. relected about the x-axis 2. shift down 9 units 3. shift left 2 units y=
*Friday, November 9, 2012 at 2:26pm by ladybug*

**College Algebra**

Graph the following function using transformations. Be sure to graph all of the stages on one graph. State the domain and range. y = -SQRT x - 6. My instructor is saying that I have to do more than one graph. Can anybody help me I am lost!
*Friday, July 27, 2012 at 1:53pm by Kameesha*

**Geometry - Transformations and Dilations**

4*k = 9 k = 9/4 (9/4) * 4 = 9.
*Thursday, February 21, 2013 at 9:32am by Henry*

**cCongruence and transformations?**

please help
*Tuesday, August 27, 2013 at 6:57pm by loli*

**Polynomial Functions**

what kind of transformations?
*Wednesday, September 11, 2013 at 6:02pm by Steve*

**Math**

What does R(2,2) mean when talking about transformations?
*Saturday, February 20, 2010 at 7:31pm by Carla*

**college algebra**

I see no use for transformations if F(x) = 1/(x^2-4), so I'll assume you meant what you wrote: F(x) = (1/x^2) - 4 That is just the graph of 1/x^2, translated 4 units downward. So, since 1/x^2 has asymptotes x=0 and y=0, F has asymptotes x=0 and y = -4. Domain is all reals ...
*Friday, August 17, 2012 at 9:49pm by Steve*

**Pre-Algebra [repost for Reiny]**

unless there was something special intended by using curly brackets in 5{6+k}=3k I read that as 5(6+k)=3k 30 + 5k = 3k 2k = -30 k = -15 I am also still unclear as to what was meant by "solve using transformations"
*Friday, May 1, 2009 at 6:30pm by Reiny*

**math**

Prisilla performs a series of transformations on a figure in the plane. First she dilates it by a factor of 3 and translates it 5 units to the right. Next she reflects it over the x axis, then over the y axis. Finally she reflects it over the line y=x, translate it 5 units to ...
*Saturday, February 9, 2008 at 3:57pm by bob*

**math**

1. not sure 2. Don't remember but hte book says to do it with matrices. 3. My book says a vertex matrix is a matrix into which the coordinates of a polygon's matrices are placed. 4. Algebra 2 - Transformations with matrices
*Thursday, January 1, 2009 at 9:23pm by Anonymous*

**science**

trace the energy transformations from a radio signal to the music you hear
*Tuesday, September 23, 2008 at 8:40pm by bailey*

**transformations**

meikaik9oik9jkz9i9j9ijuizturbjbyudgbhijbweuyg7ydfghubadfghuuuuduw87e87u8dujjdjiiisuuejfjfiiwufjhduhuuduueujhfjeijijiejijuifeuifhihvoiufgnm ufygdy9 7yiuhgn 87yg89g haesijg7h7jf8ay8bhfetgbfuygz8dfg9w84495988894769989(614-258-7410)
*Thursday, March 18, 2010 at 2:09pm by lemone*

**Geometry**

make a sketch, perform the transformations You will see the result easily to be (-9,4)
*Monday, January 23, 2012 at 6:25am by Reiny*

**science**

What enregy transformations take place in a solar impulse and a A320?
*Monday, September 17, 2012 at 1:07pm by woodlie(nickname)*

**Math**

Find the image of (-3,4) corresponding to y=f(x) if it undergoes the following transformations a)3f(x-2)+6 b)-f(-x+4)-2 c)f(3(x+2))
*Friday, January 25, 2013 at 11:47am by Anonymous*

**math**

Find the image of (3,-4) corresponding to y=f(x) if it undergoes the following transformations. a) 3f(x-2)+6 b) -f(-x+4)-2 c) f(3(x+2))
*Saturday, February 2, 2013 at 7:31pm by Anonymous*

**Math**

Explain why transformations result in images that are congruent to the original shapes
*Saturday, January 25, 2014 at 3:55pm by Anonymous*

**math**

Prisilla performs a series of transformations on a figure in the plane. First she dilates it by a factor of 3 and translates it 5 units to the right. Next she reflects it over the x axis, then over the y axis. Finally she reflects it over the line y=x, translate it 5 units to ...
*Saturday, February 9, 2008 at 5:21pm by bob*

**math**

How do you describe the transformations that were already applied and use them to write a relation for a parabola?
*Thursday, December 9, 2010 at 7:09pm by ted*

**Geometry**

Which pair of transformations best describes the relationship between RST and VUT?
*Wednesday, November 9, 2011 at 11:10pm by Jean*

**Math Finals - URGENT - Transformations**

Now if you do them both at once, as you did, the Scale is S1/2,1/2 and the matrix is |.5 0| |0 .5|
*Wednesday, January 23, 2008 at 7:10pm by Damon*

**transformations**

The reflection off the x axis is negative on the outside, don't forget the absolute value symbol: -1/2|x-4|-5
*Thursday, March 18, 2010 at 2:09pm by monica*

**social studies**

I need a brief summury of the four staged of transformations learning cycle
*Saturday, October 16, 2010 at 10:31pm by laura*

**geometry**

For a translation from (3, 2) to (4, 5), or (3, 2) to (3+1, 2+3) we can work out the transformation as: T : (x,y) -> (x+1, y+3) Use T to make other transformations.
*Sunday, July 17, 2011 at 8:56pm by MathMate*

**Pre-Algebra**

#2 circumference = pi(d) = 31 pi or appr. 97.39 m As I said before, I don't know what they mean by "use transformations" to solve 5{6+k} = 3k I would just ... 30 + 5k = 3k 2k = -30 k = -15 and for 19-3m+ 5+7m <0 4m < -24 m < -6
*Friday, May 1, 2009 at 5:39pm by Reiny*

**English**

I forgot to include the following sentences. Thank you 1) Alonso is desperate because he thinks his son had drowned (or is drowned?). 2) Ariel informs Prospero aboutthe plan to kill him. 3) Dr Jekyll believed that man is (or was) a mixture of good and evil. He created a drug ...
*Thursday, April 7, 2011 at 6:42pm by Mike*

**world history**

Where could I find resourses on information relating the intellectual transformations of the axial age to the political developments
*Wednesday, October 22, 2008 at 11:56pm by megan*

**Math**

As for transformations, do some google searches for translation and scaling, and there will be all kinds of good articles and pictures.
*Monday, October 10, 2011 at 7:59pm by Steve*

**COLLEGE ALG**

use the transformations to identify the graph of the function. then determine its domain, range, and horizontal asymptote. f(x)=4+3^X/3
*Sunday, September 2, 2012 at 5:44pm by STUMPED*

**calculus--please help!!**

Graph the function using transformations show your work and state. A. the domain b. the range c. the asymptotes f(x)=4-1/(x+6)^2
*Tuesday, December 18, 2012 at 3:56pm by Sammy-please help!!!!*

**Polynomial Functions**

I don't have problems with the transformations. Just graphing the base function is my problem because I don't know the image points.
*Wednesday, September 11, 2013 at 6:02pm by Alice*

**MATH --- PLS HELP CONNECTIONS ACADEMY**

pls help asap! i dont know!!! i need someone from connections academy, 8th grade semester 2 unit 1 lesson 5: polygons and angles!!! Identify the sequence of transformations that maps quadrilateral ABCD onto quadrilateral A''B''C''D''. (1 point) (picture that i cannot post) 180...
*Friday, January 31, 2014 at 2:15pm by TTR+S<3*

**Maths - Affine transformations**

Can you check my calculations please g maps points (0,0),(1,0),(0,1) to (6,-2),(6,-1),(5,-2) So, g(x) = (0 -1) .....(6) ..................(1 0)x + (-2) f is a reflection through y=x-2 so, f(x) = (0 1) .....(2) ...............(1 0)x + (-2) So; f o g = g(f(x)) = (0 -1)(0 1) ...(...
*Thursday, May 22, 2008 at 10:30am by Anonymous*

**science**

how can i create a drawing that demonstrates the energy transformations that would take place in order to provide power for an appliance
*Monday, January 25, 2010 at 8:56pm by Anonymous*

**math**

Graph the function f(x)=6-1/(x+4)^2 using transformations. State: a.the domain b.the range c.the asymptotes i do not get this at all, i am totally lost! please help!!!
*Monday, April 15, 2013 at 10:00am by jenny*

**geometry**

is every composition of transformations cumalitive? In other words, does the order matter? I think it depends on transformation, but I'm not sure
*Tuesday, March 25, 2014 at 2:03pm by maya*

**Algebra/Geometry**

Identify the sequence of transformations that maps quadrilateral abcd onto quadrilateral a"b"c"d" Answers 180 rotation around the origin; reflection over the x-axis translation (x,y) -> (x - 2, y + 0); reflection over the line x = -1 enlargement; reflection over the y-axis ...
*Monday, February 3, 2014 at 10:59pm by A Girl*

**Pre-Calc**

Given the one point function (3,9) (in other words f(3)=9) Identify the following transformations f(2x) -3(f(x-4))+1 f(5x+3) 4f(-x)
*Sunday, January 6, 2013 at 7:02pm by Zac*

**college alg**

use the transformations to identify the graph of the function. then determine its domain, range, and horizontal asymptote. f(x)=4+3^X/3 please show work
*Sunday, September 2, 2012 at 9:53pm by stumped*

**Phsical Science**

Which one is the best explanation of energy? A. making transformations B. the ability to do work C. conservation of power D. measuring joules I think it is B.
*Monday, February 17, 2014 at 12:29pm by dark1*

**math**

True or false? Given the basic graph y=x^2 and the transformations: a vertical stretch by three followed by a shift right 4 units, the resulting equation is y=3(x+4)^2
*Friday, August 5, 2011 at 5:00pm by Kathy*

**math (transformations)**

point (-3, 8) is on the graph y=f(x) find the new point on: y = f(x - 2) -3
*Friday, July 4, 2008 at 6:45pm by Tom*

**Math (URGENT)**

Use transformations and the zeros of the quadratic formula f(x)=(x+4)(x-2) to determine the zeroes of each of the following functions: a. y=3f(x) f. y=f(-1/2x) I have no idea how to start this. Any help appreciated. Thanks.
*Thursday, February 2, 2012 at 12:42pm by Kade*

**Math**

The graph of any quadratic function can be drawn from the vertex form of the equation, by performing 1,2,3,or 4 transformations on the graph of f(x) = x sqaured
*Sunday, October 3, 2010 at 3:24pm by Matthew*

**Advanced Functions**

Beginning with the function f(x) = (0.8)x, state what transformations were used on this to obtain the functions given below: g(x) = - (0.8)x -2 h(x) = ˝ (0.8)x-2 k(x) = (0.8)-3x+9
*Wednesday, January 12, 2011 at 4:05pm by Hailey*

**pre-calculus**

Beginning with the graph of y=e^x, describe each of the transformations that may be used to graph the function y=6+2e^x. Use complete sentences.
*Wednesday, April 28, 2010 at 12:06am by Sun-Lei*

**Transformations**

Thank you for using the Jiskha Homework Help Forum. You may not have gotten an answer because we aren't sure exactly what you need. Perhaps the following google search will help you: (Broken Link Removed)
*Friday, September 7, 2007 at 8:07pm by SraJMcGin*

**geometry**

describe the 2 transformations, the first followed by the second that combined will transform triangle ABC and triangle DEF. 23) A(-3,3), B(-3,1), C(0,1) D(6,6), E(6,2), F(0,2) 24)A(6,0), B(9,6), C(12,6) D(0,3), E(1,5), F(2,5)
*Monday, December 19, 2011 at 9:37pm by Anonymous*

**functions**

pls. explain transformations on functions..
*Wednesday, September 7, 2011 at 6:09pm by it'sme*

**physical science**

Hopefully you will find the answers here: http://www.google.com/search?q=4+transformations+tracing+energy+from+gasoline+in+a+car+to+sound+from+radio+playing&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a Sra
*Friday, April 3, 2009 at 11:02am by SraJMcGin*

**Math**

How exactly would I solve these problems? Write a function g(x)with the given transformations of f(x)=x to the 2 power. A. Down 2 B. reflection about the x-axis My teacher never taught me this, and my exam is within the next 2 weeks.
*Friday, May 9, 2008 at 6:32pm by John*

**pre calc**

the graph of y=-1/2 x+5 +3 can be obtained from the graph of y= x by which transformations what is the horizontal shift by what factor is the graph stretched or shrunk vertically and how is it reflected
*Tuesday, September 11, 2012 at 11:54pm by si*

**science**

Explain in detail the energy transformations and obsorption in the following. Four different colored shirts placed in the sun. All shirts are the same except for color.
*Thursday, October 7, 2010 at 11:59pm by Jon*

**math**

Describe the sequence and types of transformations required to transform the graph of y=x^3 into the graph of y=2f{-2(x-1)}+4. Give the equation of the new transformed function with detailed explanation.
*Friday, January 25, 2013 at 11:39am by Anonymous*

**math **

Describe the sequence and types of transformations required to transform the graph of y=x^3 into the graph of y=2f{-2(x-1)}+4. Give the equation of new transformed function with detailed explanation.
*Saturday, February 2, 2013 at 7:36pm by Anonymous*

**math**

Beginning with the function f(x) = log a^x, state what transformations were used on this to obtain the functions given below: (6 marks) p(x) = - 5/8 loga^x r(x) = log a(5 - x) t(x) = 2 log a^2x
*Thursday, May 31, 2012 at 6:03pm by darshi*

**math**

Beginning with the function f(x) = log a^x, state what transformations were used on this to obtain the functions given below: (6 marks) p(x) = - 5/8 loga^x r(x) = log a(5 - x) t(x) = 2 log a^2x
*Friday, June 1, 2012 at 11:35pm by darshi*

**Math**

Hi could you help me with this question on graphing ssinusoidal functions. "Remember how we saw a relationship between y=sin x and y=cos x...what is the equivalent equation of y=sin0.5(x-45)if the function before transformations was y=cos x?
*Sunday, May 10, 2009 at 3:05pm by Brooke*

**Algebra**

1. The transformations are: e(O,2) : dilation about origin of 2 units t(0,5) : translation 5 units up r(y,-x) : rotation counter-clockwise 90° So (x,y)-> (2x,2y) -> (2x, 2y+5) -> (2y+5, -2x) So combining it all: (x,y) -> (2y+5, -2x) 2. Using Cramer's rule: &...
*Sunday, May 19, 2013 at 12:10am by MathMate*

**Pre-Cal**

State the transformations. Identify holes, vertical asymptotes, and horizontal asymptotes of each. (I'm fine with the asymptotes, just need help with stating the trandformations) f(x)= (3x+9)/(x+2)
*Monday, October 22, 2012 at 7:42pm by Carson*

**Math**

We're learning something about transformations on the exponents of a function. For exmaple 2^x becomes 2^4(x-2)+2. Would this mean that the 2^x graph stretched vertically by a factor of 4, moved two units to the right and 2 units downwards?
*Friday, June 19, 2009 at 2:54am by Lena*

**physics....**

A 32.0 kg child descends a slide 4.00 m high. She reaches the bottom with a speed of 2.40 m/s, was the mechanical energy conserved? Explain your reasoning and identify the energy transformations involved.
*Wednesday, May 9, 2012 at 8:20pm by myra*

**math**

Create one equation that shows a function that is translated, stretched, and reflected. After writing your equation, use complete sentences to explain each of the transformations shown in your equation.
*Tuesday, April 20, 2010 at 4:00pm by justice*

**Math**

Specify the sequence of transformations that will yield the graph of the given function from the graph of the function f(x)=x^3. g(x)=-(x-4)^3 My answer was a vertical shrink and a reflection in the y-axis but I think this is wrong.
*Wednesday, February 18, 2009 at 5:37pm by Mary*

**Math-Please Check Work!**

Find the image of P(5,-3)under each of the given transformations: 1. r x-axis(5,-3)? 2. Rorigin (-5,3)? 3. R90 (3,5)? 4.T 0,3 (5,0)? 5.r x-axis o T2,2 (7,1)? 6. r x-axis o r y=x (-3,-5)? 7. r y=x o r x-axis (3,5)? 8. R(2,2) o T5,-3 (12,-4)? Thank you!
*Monday, February 22, 2010 at 5:54pm by Jackie*

**math**

find the equation of line y=x+1 under each of the following transformations (a) (x,Y)-(x+3,Y+5) (b) reflections across the x-axis (c) reflection across the y-axis (d) half turn about origin
*Sunday, July 25, 2010 at 12:22pm by Angela*

**cCongruence and transformations?**

reflection through the y-axis reflection through the line y = -x scaling by a factor of 2 a simple web search will provide many references and videos on the topic.
*Tuesday, August 27, 2013 at 6:57pm by Steve*

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