Without repeating over lines and crossing over lines, what is the mathematical way? SUch as a box with a x in it is.
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Suppose the shape is represented by a graph ( http://mathworld.wolfram.com/Graph.html ). You want to find a path through the graph that passes through every edge without travelling on an edge more than once. This is an easy problem in graph theory, and such a path is called an Euler path. An Euler path through a connected graph exists if and only if the graph contains at most two vertices with odd degree (the number of edges the vertex has). This is a trivial theorem.\nSuppose a graph is connected, which means there exists some path between any pair of vertices. For each vertex, there is some number of edges connected to it. Suppose the number of edges is even for all the vertices. Then there is no problem drawing an Euler path through these edges. Explain why (Examine the problem at each vertex).\nFrom the above, the only possible problems must come from vertices with odd degree. Without loss of generality, we proceed by adding vertices of odd degree to the nice graph described above. Adding one vertex is no problem, we start at that vertex, travel along the one additional edge and then we're in a nice graph that already contains an Euler path, since the vertex we left at the start now has even degree, for all intents and purposes. \nIf we add two vertices of odd degree, we are alright as well, with the exception that any path must start at one of these vertices and end at the other. Show this by labelling each odd degree vertex with little "in" and "out" signs on the edges.\nIt should now be obvious that we can't add any more vertices with odd degree for the simple reason that a path that doesn't double back on itself can only have 2 endpoints. Adding more vertices doesn't change the fact that you put your pencil down at one odd vertex and you're required to lift it back up at one other odd vertex. After that, the game is up.
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Yahoo's formatting messes this up, but if you cut-and-paste it into Word or Notepad, then use font Courier New it should make more sense.\n\nFirst question\n\n  1      1     11\n---- + ---- = ----\n 3x      2     12\n\n  4       6x     11x\n----- + ----- = -----\n 12x     12x     12x\n\n\n4 + 6x = 11x\n  - 6x = -6x\n-------------\n4      =  5x\n\ndivide both sides by 5\n\n 4\n--- = x = First answer\n 5\n\n\n******\nSecond question\n\n1.5x + 9 =  4.5\n     - 9 = -9.0\n----------------\n1.5x     = -4.5\n\ndivide both sides by '1.5'\n\nx        = (-4.5)/(1.5) = (-3)\n\nx = -3 = Second answer
372111
Wait a minute everybody!\nthose vertical lines,( lyl ) could mean absolute value!!\nHelloooo?\nso the answerSSS could be 9 and -9\nsheesh!
431354
Start with a graph of:\nf(x) = x\n\nThat's a straight line going through the origin with a slope of 1.  It should look like a 45 degree angle if you draw it correctly.\n\nNow to transform this to:\nf(x) = | x |\n\nYou have to think of each value smaller than 0.  Rather than -1, for example, you'll have 1.  Rather than -2, you'll have 2, etc.  This is like "mirroring" the graph that is below the x-axis so that it is above the x-axis.\n\nThis results in a "V" shape.  A slope of -1 down to the origin, then a slope of 1 from the origin.\n\nFinally:\nf(x) = | x | - 2\n\nFor every value that results, you now subtract 2.  For example, x = 0, gives -2, rather than 0.  This is true for every point x, making every point y smaller by 2.  It would look like you shifted the whole graph down 2 units.\n\nSo it would be "V" like before, but it would go down at a slope of -1, cross the x-axis at -2, and continue to (0, -2).  Then it would slope up (m=1) through the x-axis at 2 and continue upward.\n\nYou can go to the first link and type 'abs(x) - 2' in the box.  The resulting graph is shown as the 2nd link.
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Intersect = upside down U - ∩\nUnion = right side up U \nIs an element of = kind of a cross between a sideways U with the lines pointing to the right with a third line in the middle and a letter E\nIs not an element of = the same with a diagonal line running from the upper right to the lower left\nIs a subset of = a sideways capital U with the legs pointing to the right - "is a subset of" without the middle line\nIs proportional to = imagine the infinity sign with the rightmost curve cut off so that the lines go straight out to the right \nLogarithms - the word log with a subscript number representing the base followed by the number like log(2)8 = 3 - the 2 would be written as a subscript\nUnunseptium = Uus - note that this element (atomic number 117) is only theoretical and has not yet been discovered
676409
In a hexagram shape, like so...\n\n----o----\no-o-o-o\n--o---o-\no-o-o-o\n----o----
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I think that you want x element of [-6,4)\n\nYou wanted closed on the left and open on the right, is that true?\n\nJust remember that for intervals:\nopen   ( )\nclosed [ ]\n\nAnd you can match them up: [-6,4)
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The Edifier has it right, but darned if I can follow the notation. You really need to see this written out like a textbook to understand what's going on.\n\nClick the link below in "sources" to see the answer hosted at my website www.calculus-help.com. Right now, Yahoo! answers, as far as I can tell, doesn't allow graphics, which makes it tricky to answer ANY math questions.\n\nPlease don't post math answers, guys, if the poster knows the answer but can't get there, and you get something completely different.
59954
if all the lines are equal in every way (duplicate) then you can put a measurment (dimension) from the existing line to a datum or border whichever you choose and then put a callout like 3@12.00' (3 lines at 12.00 feet)in the dimensionwith a arrow pointing at the line.\n\njeff
509409
You put a round bracket "()" on the number line when the sequence doesn't include the number where that bracket goes. For example, if the final answer you get is "all the numbers between 2 and 8, excluding 2 and 8" then you use the round brackets. You'll know your answer excludes a number or numbers because it will be "bigger than" or "smaller than" only, not "bigger than or equal to" or "smaller than or equal to", in other words, ther will be no line underneath the inequality sign. \nNow, if you do get something like "x is bigger than or equal to  8 and smaller than or equal to 2" than you know your answer includes 2 and 8, so you use the brick bracket, "[ ]". Good luck.
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thats not a big issue.....u can rearrange the letters to numbers...for example if the problems lists the coordinates as a,b,c,d etc....mark a=1, b=2, c=3 atc....\nhope this helps
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y = 7\n\na horizontal line
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x is always assumed horizontal <---> left right\ny is always assumed vertical /&#92;  &#92;/   up down
135600
160. double X. because X is an inscribed angle. sry it took so long, i had to draw it =)
14645
In the given qts, the data provided is typical for using an orthodox yet nice method called L.P.P. (Linear programming) which is actually a graph method with the cartesian co-ordinates. I am sorry but i won't be able to provide you with the graph solution. Here is the theory of the required solution.\n\nLet the no of matches per box in the first case be x\nLet the no of matches per box in the second case be (x-y) where y is the number of matches decremented per box.\n\nNumber of matches in first case = 24x\nNumber of matches in second case = 28(x-y)\n\nHowever number of match boxes are equal\nHence, 24x = 28(x-y)\n       24x = 28x - 28y\n       28y = 4x\n        7y = x  ----------- (1)\n\nNote that since the total number of matches is not = 0\n hence,   x > y \n          x > 0\n          y > 0  \n and x,y are integers ----- (2)\n\nHence, x is minimum when y is minimum.\nMinimum integral value of y is 1\nHence minimum value of x = 7y = 7*1 = 7 ----- (3)\n\nFrom (1), (2) and (3), we conclude that...\n\nTotal number of matches required for the given qts should have a minimum value         \n   = 24x \n   = 24*7 \n   = 168   ........ (ANSWER)\n\nThe data provided by you is sufficent for finding minimum no of matches required since that's the limiting case. If you have a more precise condition in the given qts, a unique solution shall be obtained for the same. Graphs would have made the solution more interesting.\n\nI saw someone getting an answer as 672. It's possible if there is a condition in the given qts that "When the number of matches in each box are decremented, number of boxes required are 28. However, the number of matches placed in each box is found to be four less than the intial number of matches placed in each box". Then the solution would be like this :\n\nLet the no of matches per box in the first case be x\nHence, the no of matches per box in the second case be (x-4) \n\nNumber of matches in first case = 24x\nNumber of matches in second case = 28(x-4)\n\nHowever number of match boxes are equal\nHence, 24x = 28(x-4)\n       24x = 28x - 112\n        4x = 112\n         x = 28 \n\nClearly, like in the previous solution, in this case too, \n \n   x > 4\n  and its obvious that x > 0 and x is an integer.\n\nHence, the unique number of matches required in this case is \n         = 24x \n         = 24 * 28 \n         = 672 ... (ANSWER)\n\nI hope that this solution serves its purpose and helps you conquer this question satisfactorily.
94827
I'll do the fourth problem.\n\n-3x< -6  or x+5< -2\n\nfirst deal with one half- \n-3x< -6 (now divide by -3)\nx>2 (when you divide by a negative the sign is reversed)\n\nthen the second half- \nx+5<-2 (get x alone, so subtract five from each side)\nx< -7\n\nso you have:\n2 < x  or  x < -7\n\nto graph this there is a line with an arrow to the left of the first slash and another line to the right of the second slash\n\n<-----/-------0--/-->\n____-7______2
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Just graph it like an equality, and then your answer is everything either above (>) or below (<) the line.  For example, in the last inequality, the answer is everything above the line y = -2, not including the line itself.