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# Recent problems solved by 'xdragonfight'

 Surface-area/587618: find the area of a rhombus with a 45 degree angle and sides of 10 ft1 solutions Answer 374165 by xdragonfight(116)   on 2012-03-16 00:13:54 (Show Source): You can put this solution on YOUR website!Well, you know the formula for the area of a parellogram: A = bh (Area = Base times the Height) You know the base, 10. Draw the rhombus (any size will do, make it a convenient size). One of the bottom angles is 45 degrees, and the other is 135 degrees. Find the 45 degree angle (the acute, more closed angle). The base forms one side of that angle, and another side of the rhombus forms the other side of the angle. Where that other side of the rhombus goes up and touches the top of the rhombus, at that point draw an altitude down to the base. That will form a triangle, won't it? The Base, the other side of the 45 degree angle, and the altitude. Now, you know the altitude forms a 90-degree angle with the base, right? So your triangle has an angle of 90, one of 45, and the one that is left must be 45, so they all total 180 degrees, as the angles in every triangle do. So your triangle has two 45 degree angles. So it must be an isosceles triangle, right? It has two equal angles, and two equal sides, and the sides opposite those equal angles must be equal, right? So the two sides opposite those equal 45-degree angles are the altitude and the base. So the altitude and the base are equal, aren't they? And you already know the base is 10 feet. So the altitude must also be10 feet. So the base is ten feet, and the altitude is 10 feet. A=bh. Can you take it from there? Don't be afraid to go over this a few times until you see it clearly.
 logarithm/587477: use change of base formula to solve 2^2x = 901 solutions Answer 374136 by xdragonfight(116)   on 2012-03-15 19:04:19 (Show Source): You can put this solution on YOUR website!Solve 2x = 30. If this equation had asked me to "Solve 2x = 32", it would have been easy, because I could have converted the 32 to 25, set the exponents equal, and solved for "x = 5". But 30 is not a power of 2, so I can't set powers equal to each other. I need some other method of getting at the x, because I can't solve with the equation with the variable floating up there above the 2; I need it back down on the ground where it belongs. And I'll have to use logarithms to get at it. When dealing with equations, I can do whatever I like to the equation, as long as I do the same thing to both sides. And, to solve an equation, I have to get the variable by itself on one side of the "equals" sign; to isolate the variable, I have to "undo" whatever has been done to it. In this case, the variable x has been put in the exponent. The backwards (technically, the "inverse") of exponentials are logarithms, so I'll need to undo the exponent by taking the log of both sides of the equation. This is useful to me because of the log rule that says that exponents inside a log can be turned into multipliers in front of the log: logb(mn) = n · logb(m) When I take the log of both sides of an equation, I can use any log I like (base-10 log, base-2 log, natural log, etc), but some are sometimes more useful than others. Since the base in the equation "2x = 30" is "2", I might try log-base-2: log2(2x) = log2(30) xlog2(2) = log2(30) x(1) = log2(30) x = log2(30) But I can't evaluate this in my calculator unless I apply the change-of-base formula: x = log2(30) = ln(30)/ln(2) What would happen if I just used the natural log in the first place? 2x = 30 ln(2x) = ln(30) xln(2) = ln(30) x = ln(30)/ln(2) Either way, I get the same answer, but taking natural log in the first place was simpler and shorter.
 Linear-equations/587480: 3/2m = m+71 solutions Answer 374135 by xdragonfight(116)   on 2012-03-15 19:04:02 (Show Source): You can put this solution on YOUR website!3/2m=m+7 -m -m .5m=7 7/.5=14 m=14
 Percentage-and-ratio-word-problems/587478: how do you turn 7.95 and 7.99 into a fraction? 1 solutions Answer 374134 by xdragonfight(116)   on 2012-03-15 18:58:29 (Show Source): You can put this solution on YOUR website!7.95=159/20 and 7.99=799/100
 test/587132: 3|x-2|=18 Solve for x1 solutions Answer 373995 by xdragonfight(116)   on 2012-03-14 23:05:34 (Show Source): You can put this solution on YOUR website!THERE IS 2 SOLUTION !! 3x-6=18 and 3x-6=-18 3x-6=18 +6 +6 3x=24 24/3=8 x=8 ok here 2nd solution 3x-6=-18 +6 +6 3x=-12 x=-4 so u will put ur answer as -4 and 8
 Complex_Numbers/587131: 2x + 3> 131 solutions Answer 373994 by xdragonfight(116)   on 2012-03-14 22:52:28 (Show Source): You can put this solution on YOUR website!2x+3>13 -3 -13 2x>10 divide everything by 2 2x/2=x 10/2=5 x>5
 test/587130: 3|x-2|=18 How to do please show steps1 solutions Answer 373993 by xdragonfight(116)   on 2012-03-14 22:49:49 (Show Source): You can put this solution on YOUR website!THERE IS 2 SOLUTION 3x-9=18 and 3x-9=-18 hope you know how to solve these 2 when u put the answer u have to put both solution
 Surface-area/587103: what are the side lengths of a rectangle whos perimeter is 66 and its area is 216 1 solutions Answer 373991 by xdragonfight(116)   on 2012-03-14 22:42:46 (Show Source): You can put this solution on YOUR website!2L+2W=66 LxW=216 so start with 2L+2W=66 lets solve for W 2L+2W=66 -2L -2L 2W=66-2L divide everything by 2 2w/2=w 66/2=33 -2L/2=-L so new equation is w=33-L ok lets start on the 2nd equation LxW=216 replace W with (33-L) Lx(33-L)=216 -L^2+33L=216 so L=9 ok lets find W now 2(9)+2W=66 2W=48 W=24 L=9 24x9=216
 Reduction-of-unit-multipliers/587117: how to find the slope of y+7=8x 1 solutions Answer 373990 by xdragonfight(116)   on 2012-03-14 22:32:29 (Show Source): You can put this solution on YOUR website!y+7=8x subtract 7 y+7=8x -7 -7 y=8x-7 y=mx+b slope=M so 8 is the slope
 Quadratic_Equations/587121: Solve: 1=3x^2+2x1 solutions Answer 373989 by xdragonfight(116)   on 2012-03-14 22:30:23 (Show Source): You can put this solution on YOUR website!x=1/3 check if its right 3(1/3)^2+2(1/3)
 Reduction-of-unit-multipliers/587120: how to find the slope of 8y-x=48 1 solutions Answer 373988 by xdragonfight(116)   on 2012-03-14 22:28:30 (Show Source): You can put this solution on YOUR website!8y-x=48 subtract -x postive - negative= postive 48-(-x)=x+48 8y=x+48 divide everything by 8 8y/8=y, x/8=(1/8)x, 48/8=6 so the new equation is y=(1/8)x+6 y=mx+b M=slope so (1/8) is the slope
 test/587115: Hi I need help solving this. Please help! Solve the quadratic equation: 25n^2=16 thank you1 solutions Answer 373987 by xdragonfight(116)   on 2012-03-14 22:25:27 (Show Source): You can put this solution on YOUR website!25n^2=16 x=4/5 or .8 check it if its right 25(.8)^2
 Quadratic_Equations/587112: Solve: 3x^2=13x-41 solutions Answer 373986 by xdragonfight(116)   on 2012-03-14 22:22:15 (Show Source): You can put this solution on YOUR website!3x^2=13x-14 x=2 and 1/3 check if its right 3(2+1/3)^2=13(2+1/3)-14
 Linear-equations/587113: 3x+2 x=51 solutions Answer 373985 by xdragonfight(116)   on 2012-03-14 22:20:28 (Show Source): You can put this solution on YOUR website!3x+2 x=5 3(5)+2= 17
 Equations/587114: 5=x35 what does x equal1 solutions Answer 373984 by xdragonfight(116)   on 2012-03-14 22:19:53 (Show Source): You can put this solution on YOUR website!x=5 divde by 35 x=5/35
 Numbers_Word_Problems/587047: The sum of 2 numbers is 40. When the greater number is divided by the smaller, the quotient is 4 and the remainder is 5. Find the numbers.1 solutions Answer 373983 by xdragonfight(116)   on 2012-03-14 22:16:51 (Show Source): You can put this solution on YOUR website!first number=x 2nd number= y The sum of 2 numbers is 40 so x+y=40 x/y = 4+5/y x = 4y+5 x+y=40 4y+5+y=40 5y+5=40 5y=35 y=7 x=4y+5=4(7)+5=28+5=33 Answers: numbers are 33 and 7
 Equations/587083: 8-12x=6*(1+x) 1 solutions Answer 373978 by xdragonfight(116)   on 2012-03-14 22:00:50 (Show Source): You can put this solution on YOUR website!8-12x=6(1+x) 8-12x=6+6x -6x -6x 8-18x=6 -8 -8 -18x=-2 divide -2 by -18 -2/-18=2/18 =1/9
 Graphs/587085: How do you graph y=3/4x-2 1 solutions Answer 373977 by xdragonfight(116)   on 2012-03-14 21:58:25 (Show Source): You can put this solution on YOUR website!make a graph go to your y-int wwhich is -2 so draw a point at (0,-2) then go up 3 point go right 4 points because is 3/4
 Equations/587099: 12.5 + .5y = .75x + 71 solutions Answer 373976 by xdragonfight(116)   on 2012-03-14 21:56:48 (Show Source): You can put this solution on YOUR website!isnt there suppose to be 2 equations? LOL IF THERE IS 3 VERABLES THEN THERE WILL BE 3 EQUATION
 Proportions/587091: use the porportion x over z = 6 over 5. complete each statment x+z over z 1 solutions Answer 373975 by xdragonfight(116)   on 2012-03-14 21:54:19 (Show Source): You can put this solution on YOUR website!x/z=6/5 x=6 z=5 lawl x+z/z=(6+5)/5 =11/5
 Systems-of-equations/587092: i need your help on y=5x+7 y=6x1 solutions Answer 373974 by xdragonfight(116)   on 2012-03-14 21:51:34 (Show Source): You can put this solution on YOUR website!y=6x so just replace y with (6x) so 6x=5x+7 don't tell me u can't solve 6x=5x+7
 Polynomials-and-rational-expressions/586663: -10n^2+35n=0 1 solutions Answer 373843 by xdragonfight(116)   on 2012-03-13 23:48:26 (Show Source): You can put this solution on YOUR website!N=3.5 check it if its right -10(3.5)^2+35(3.5)
 Numeric_Fractions/518749: The length of a rectangular field is 18m longer than the width. The field is enclosed with fencing and the divided into two parts with a fence parallel to the shorter sides. If 216m of fencing are required, what are the dimensions of the outside rectangle? 1 solutions Answer 345263 by xdragonfight(116)   on 2011-10-20 21:31:16 (Show Source): You can put this solution on YOUR website!x=36
 Numbers_Word_Problems/515236: the difference of 2 positive numbers is 4 and the sum of their squares is 401 solutions Answer 343865 by xdragonfight(116)   on 2011-10-14 22:54:13 (Show Source): You can put this solution on YOUR website!6-2=4 6^2+2^2=40
 Travel_Word_Problems/515242: I was wondering how long it would take to walk 1,050 miles?1 solutions Answer 343864 by xdragonfight(116)   on 2011-10-14 22:52:52 (Show Source): You can put this solution on YOUR website!if you walk 5miles per hour then it take 210 hours
 Rectangles/514945: how do i do this problem, the length of a rectangle is 8 cm more than its width. The perimeter is 24 cm. Find the length and width of the rectangle 1 solutions Answer 343632 by xdragonfight(116)   on 2011-10-14 08:13:49 (Show Source): You can put this solution on YOUR website!L=10 W=2 2(2)+2(10)=24 10-2=8
 Pythagorean-theorem/514947: 1 1/2 miles long and 2 3/4 miles wide what is the area?1 solutions Answer 343631 by xdragonfight(116)   on 2011-10-14 08:11:14 (Show Source): You can put this solution on YOUR website!A=LxW A=1 1/2 X 2 3/4 A=33/6
 Travel_Word_Problems/514205: On a 600 mile road trip, two people drive the car. One person drives three times as long as the other. How many miles has the longer driver driven?1 solutions Answer 343336 by xdragonfight(116)   on 2011-10-13 00:33:13 (Show Source): You can put this solution on YOUR website!12 times
 Money_Word_Problems/514228: This year's salary, 60,000, is a 10% increase over last year's salary. What was last year's salary?1 solutions Answer 343335 by xdragonfight(116)   on 2011-10-13 00:32:13 (Show Source): You can put this solution on YOUR website!60000-6000=54000 60000(.1)=x .1=10%
 Mixture_Word_Problems/514225: A 90 pound mixture of two different types of nuts costs \$370. If type A costs \$3 a pound and type B costs \$5 a pound, how many pounds of each type were used?1 solutions Answer 343334 by xdragonfight(116)   on 2011-10-13 00:29:09 (Show Source): You can put this solution on YOUR website!Type B : 50 pounds 50x5=250 Type A : 40 pounds 40x3=120 120+250=370\$
 Coordinate-system/514209: graphing linear equation using slope intercept form y=3x+41 solutions Answer 343333 by xdragonfight(116)   on 2011-10-13 00:21:14 (Show Source): You can put this solution on YOUR website!Y=3X+4 THE Y INTERCEPT(b)=(0,4) NOW SET Y=0 & SOLVE FOR X 0=3X+4 3X=-4 X=-4/3 THUS THIS POINT IS (-4/3,0) NOW PLOT THESE 2 POINTS & DRAW THE LINE THROUGH THEM WITH A SLOPE (m) OF 3. [THIS IS THE RED LINE]. --------------------------------------------- Y=-3X-4 HAS A Y INTERCEPT OF (0,-4) NOW SET Y=0 & SOLVE FOR X 0=-3X-4 -3X=4 X=4/-3 THUS THIS POINT IS (-4/3,0) NOW PLOT THESE 2 POINTS AND DRAW A LINE THROUGH THEM WITH A SLOPE (m) OF -4/3 [THIS IS THE GREEN LINE] (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = 3x +4 and y = -3x -4). Answer by rapaljer(4420) (Show Source): You can put this solution on YOUR website! In contrast to the last problem that I posted about graphing straight lines, these two lines are given in SLOPE-INTERCEPT FORM (y=mx+b). In these cases, you can immediately identify the slope and the y-intercept of each line. The number term is always the y-intercept, and the coefficient of x is always the slope, which can be written as a fraction that we call the "RISE OVER THE RUN". Then you can graph them as follows: y=3x-4 The y intercept is -4, and the slope m=3, which means . Start by graphing the y-intercept by going DOWN 4 units on the y-axis. Then starting with your pencil on this point,GO UP 3 units, then go to the RIGHT 1 unit, and put the next point. Connect these two points with a line, and continue the line in both directions. y=-3x-4 The y intercept is -4, and the slope m=-3, which means . Start by graphing the y-intercept by going DOWN 4 units on the y-axis. Then starting with your pencil on this point,GO DOWN 3 units, then go to the RIGHT 1 unit, and put the next point. Connect these two points with a line, and continue the line in both directions. If you want to see the point of intersection for these equations, then graph the two lines on the same graph, and see where the lines cross. This point is the point of intersection of the two lines. For additional help on most AMU topic in algebra, see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for the topic "Math in Living Color", choose a level of math, either Basic, Intermediate, or College Algebra, and look for the topic you need help with. If you can't find what you need, send me an Email, and maybe I can help you find the right page on my website!!! R^2 at SCC