What is the Equation of a Median, Slope, Negitive Angles, Altitude, Perpendicular Bisector?
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To find the median you must first put your data in order from least to greatest.  The median is the number that appears in the middle.  If for some reason you have two pieces of data in the middle you find the mean of those two numbers.\n\nSlope is (y2 - y1)/(x2 - x1)
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First off, a perpendicular bisector (by definition) is a line that cuts something in half.\n\nWe know that a triangle is composed of three lines and therefore (as I’m sure you’ve already presumed) has three perpendicular bisectors.\n\nSo lets try to find one.  Its rather difficult without a triangle to show you on but we’ll make do with words.\n\nFirst, find the midpoint of any given line of your triangle.  You can do this by measuring it (if it’s to scale) or by using a midpoint formula (you can only do this if your triangle is on a graph).  If measuring, find the length of the side and divide by two for the distance from the start of the line to the middle of it.  If it is on a graph you can use the formula: ((x1+x2)/2),((y1+y2)/2).  You’ve guessed it, this formula does the exact same thing as the first method but with numbers instead of with a ruler.  In case you’re wondering; x1 refers to the x value of the first point of the line, y1 refers to the y value of the first point of the line, x2 refers to the x value of the second point of the line, and y2 refers to the y value of the second point of the line.  You will end up with an answer that looks like: (x,y).  This is the coordinate of your midpoint!\n\nNow that you have the midpoint you must connect it to the opposite vertex of your triangle.  This is easily done by hand and with a ruler.  You’ll notice how this has divided the triangle into two exact halves.  If you’re doing this in the mathematically sound way (i.e. with many formulas and calculations) please keep reading, your task is much more laborious!  You need to find the slope between the midpoint (M) and your vertex (V).  So we must use the slope formula: slope=(y2-y1)/(x2-x1).  Where (x1,y1) are the coordinates of the midpoint and (x2,y2) are the coordinates of the vertex.  Now that your slope is achieved you need to find the y-intercept.  This is found by using the equation: y=mx+b.  Sub in your midpoint coordinates for x and y (since they are a point on this line) and rearrange the equation so you have an answer for b (the y-intercept).  Now that you have an equation for this bisector, draw it in and give yourself a pat on the back!\n\nRepeat this process for the next two lines in your triangle.  Here’s a hint though, you don't actually need to find the third bisector because it will just confirm what the last two have told you!  Besides, you only need to have two bisectors to find the intersection of the bisectors.\n\nSpeaking of which, now we are going to find the intersection.  If you’ve been doing it all by hand and ruler you simply just need to put a point where your bisectors have met and show that you have, indeed, found the intersection.  If you have to do it the arduous method (in which case I applaud you), please read on.  Since you have you have the equations for each bisector, this will be easy.  You are simply going to find where these two lines intersect.  If you have a Texas Instruments Graphing Calculator (or similar device), now would be the time to whip it out and graph these two lines.  If you don’t have this device, have no fear; algebra is here!\n\nIf you have a pretty good understanding of algebra or even just pre-algebra you’ll understand this part fairly quickly.  We have two equations and two unknowns.  We have to solve for x and y in these two equations.  This will give us the x-value and y-value that these two lines share.  I’m going to use the two following equations to aid both my instruction and your understanding.\n\nLets say the two lines are y=2x-3 and y=x+1.  We know that y=2x-3 in the first equation so we’ll sub it into the second equation.  Therefore 2x-3=x+1.  From here you need to move the xs to one side and the numbers to another, so: 2x-x=1+3 which become x=4 (don’t forget that the number’s sign (+ or -) is inversed when you change sides (change side, change sign).  Now that we know x, we can sub x’s value into the first equation.
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find the slopes of both lines and if there answers are opposite recipricals, then they are parrallel\n\nheres adn ex:\nslope = 2 and -1/2\n\nin other workds, if you multiply the two slopes, u should get -1
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Total Area = Base Area + Lateral Area\n\nLateral Area= pi x radius x height of the slant.\nHeigh of slant = sqrt(cone height^2 + radius^2)\n\nLateral Area = (pi)(r) * sqrt(cone height^2 + radius^2)\nBase Area = (pi)(r^2)\n\nTotal area = (pi)(r) * sqrt(cone height^2 + radius^2) + (pi)(r^2)
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1) Rearrange so\ny = -(5/3)x + (2/3)\nThis means the perpendicular to this line (which the point must lie on) is of the form\ny = (3/5)x + n \nlet (a,b) = the point we require, so\nb = -(5/3)a + (2/3)   equation 1\nand -5 = -4(3/5) + n so n = -(13/5)   equation 2\nand b = a(3/5) + n  equation 3\nsubstitution of equations 1 and 2 into 3 give:\n-(5/3)a + (2/3) = a(3/5) - 13/5\nso a = 49/34\nand consequently b = -59/34\nso the point is (49/34, -59/34)\n\n2) let h = height of box and l = width of box = length of box (square base)\nso volume, v = hl^2\nand material area, a =l^2 + 4lh = 1300 cm^2\nso h = (1300-l^2)/(4l)\nso now v = (1300l - l^3)/4\nfor max volume \ndv/dl = 0 \nso dv/dl = (1300 - 3l^2)/4\n(1300 - 3l^2)/4 = 0 when l = sqrt(1300/3)\nwe take only the positive solution as the negative is meaningless in this problem.\nto check this is indeed a maximum value (as oppose to a minimum) we derive d^v/dl^2:\nd^v/dl^2 = -3l/2 so for l = sqrt(1300/3) this is always negative confirming this is a maxima.\nso now, v  = (1300l - l^3)/4\nsubstitute l = 20.817 cm\ngives volume, v = 4510.28 cm^3
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direction\naverage speed\nconstant
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I only see equalities... and what are you supposed to do with them?\n\nAssuming you need to graph them, first put them in terms of y:\n1) y = -x + 2\nThis has a slope of -1 (diagonal downward) and a y-intercept of 2.\n\n2) y = -2\nThis has no slope (horizontal line) and goes through the y-intercept of -2.\n\n3) y = x + 2\nThis has a slope of 1 (diagonal upward) and a y-intercept of 2.\n\nThe lines are shown in the attached diagram... Now what do you want to do with them?
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First pair both x values are the same so it is a vertical line through -5 on the x-axis. Which would mean it has no slope (undefined)\n\nSecond pair has identical y-values so it is a horizontal line (slope=0) through 3 on the y-axis\n\nFor the third pair us the formula \ny=mx+c which describes any straight line (m=slope, c= a constant distinguishing the line from others with the same slope in different locations on a graph)\n3=m(-8)+c      (a)\n2=m(-6)+c      (b)\nSimultaneous equations!\nc=3+8m           (a)\n2=-6m+3+8m   (sub (a) into (b))\n2m=-1\nm=-1/2  \nSo the slope = -1/2\n\nThis formula can be used for any problem like this using the same method.
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Note that I am using properties of standard form of an equation of a line (Ax+By=C) below.\n\nslope of a line from an equation in standard form is -(A/B);\n\nso the slope of your original line is -3/2.  Slope of a line perpendicular is the opposite reciprocal of the slope, so 2/3. \n\nUsing -(A/B), the left side of the equation will be:\n\n2x-3y; to find the right side, plug the point in:\n\n2(3)-2(2) = 6-4 = 2\n\nSo, an equation is 2x - 3y = 2
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this is the slope intercept form equation\n\ny=mx + b\n\nwhere m is the slope and b is where the line crosses the y axis\n\nfor example\n\ny= 1/2x + 2
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x=(1--2)  or (1+2)\ny=(5-3)\n\ny/x=slope\nx=3\ny=2\nslope is 2/3
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put it in standard form :\n\ny < -1/2x + 3/2 \nand \ny > 2/3x + 2\n\nthen you know the first line passes thru the y axis at 3/2 and the second at 2\n\nthe slopes are -1/2 and 2/3 .... then shade below the line on the first one cuz y is less than .\n\nthen shade above the second line because y is greater than
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There are three medians in a triangle, not just one.\n\na) is your answer.
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slope= mx+b\nslope=1/2x\nequation= y=1/2x-3.5\ny-int: -3.5
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x=-3 is the equation for the line.\n\ny=mx+b where m is slope and b is y-intercept.\n\nm=change in y/change in x= [(-3)-1]/[(-3)-(-3)]\nm=-4/0\nWhen you divide by zero the answer is undefined, so slope is undefined.\n\nOnly vertical lines have undefined slopes, so the equation for the line is x=-3. This means that no matter what value you pick for y, x will be equal to -3.
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(x - 99)(x -101)(x - 103)(x - 105) + 16 = 0\n(x - 102 + 3)(x -102 + 1)(x - 102 - 1)(x - 102 - 3) + 16 = 0\n[(x - 102)² - 3² ] [ (x - 102)² - 1] + 16 = 0\nLet (x - 102)² = y \n(y - 5 - 4)(y - 5 + 4) + 16 = 0\n(y - 5)² - 4² + 16 = 0\n(y - 5)² =0 --> y = 5\n(x - 102)² = 5\n\nx = 102 + sqrt(5)\nx = 102 - sqrt(5)
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The midpoint of that segment is (3, -2) - all you do is take the average of the x coordinates and the average of the y coordinates.\n\nThe slope of that segment is found by\n\nm = (y2 - y1)/(x2 - x1)\n= (1 - (-5))/(4 - 2)\n= 6/2\n= 3\n\nSince you're looking for a line perpendicular to this one, take the slope, invert it, and change the sign.  So the slope of the new line will be -1/3.\n\nNow you have a point and a slope for the new point: m = -1/3, and point (3, -2).  Use the point-slope formula to find the equation of the line:\n\ny - y1 = m(x - x1)\ny - (-2) = (-1/3)(x - 3)\ny + 2 = (-1/3)x + 1\ny = (-1/3)x - 1