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# Recent problems solved by 'RAY100'

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 Linear-equations/239938: solve the system of equations using the addition method 9x-5y=4 27x-15y=81 solutions Answer 175940 by RAY100(1637)   on 2009-11-17 14:45:49 (Show Source): You can put this solution on YOUR website!To use the addition method we first must multiply the 1st eqn by 3 . (1) (9x -5y =4) * 3 = 27x -15y =12 . (2) 27x -15y =8 . . If we subtract (1) from (2), we will get 8=12,,,which is never true . Therefore we have no solutions . . another way to look at this is that both eqns are the same except for the y intercepts, therefore they are parallel lines,,,also with no solution .
 Linear-equations/239933: determine the slope and y intercept of the line represented by the given equation 9x-12y=1081 solutions Answer 175937 by RAY100(1637)   on 2009-11-17 14:29:59 (Show Source): You can put this solution on YOUR website!9x-12y=108,,,,,lets put in slope intercept form,,,,y=mx+b . subtract 9x both sides . -12y = -9x +108,,,,,,now,,,divide both sides by -12 . y= (9/12)x - 9 . . now slope = m = 9/12 = 3/4 . and y intercept = b = (-9) . .
 Inverses/239934: y+9=121 solutions Answer 175936 by RAY100(1637)   on 2009-11-17 14:24:41 (Show Source): You can put this solution on YOUR website!y +9 = 12,,,,,,,subtract 9 both sides . y=3 . . check ,,,,3+9 =12,,,,,ok
 Polynomials-and-rational-expressions/239926: how do i find all double roots of s^3-27s=0 showing all the steps?1 solutions Answer 175935 by RAY100(1637)   on 2009-11-17 14:23:01 (Show Source): You can put this solution on YOUR website!s^3 -27s =0 . s(s^2 -27) = 0 . s=0 . s^2 -27= 0 . s^2 =27 . s = +/- sqrt 27 . s= +/- sqrt(9*3) . s= +/- sqrt 9 * sqrt3 . s = +/- 3sqrt3 . . . check,,s=0,,,,,0=0,,,ok . s=+3sqrt3...(3sqrt3)^3 -27(3sqrt3) =0,,,ok . s=-3sqrt3....(-3sqrt3)^3 -27(-3sqrt3) = 0,,,,,ok .
 Radicals/239928: Simplify √x^1001 solutions Answer 175934 by RAY100(1637)   on 2009-11-17 14:15:37 (Show Source): You can put this solution on YOUR website!sqrt x^100 . sqrt x^(2*50) . (sqrt x^2)^50 . x^50 . . check,,let x=4, 2^100,,,vs 4^50,,,,= 1.26 * 10^30,,,ok .
 Radicals/239924: Solve: √7/9 - √7/251 solutions Answer 175932 by RAY100(1637)   on 2009-11-17 14:09:38 (Show Source): You can put this solution on YOUR website!sqrt7(1/9-1/25) . sqrt7 (25-9)/(9*25) . sqrt7 (16)/ (225) . 16/225 * sqrt7 . .
 Radicals/239920: Solve: 7√5 - 5√7 - √5 + √7 1 solutions Answer 175930 by RAY100(1637)   on 2009-11-17 14:00:42 (Show Source): You can put this solution on YOUR website!7sqrt5 -1 sqrt5 -5sqrt7 +1 sqrt7 . 6sqrt5 -4 sqrt7 .
 Polynomials-and-rational-expressions/239905: please help me solve this equation: 1 solutions Answer 175925 by RAY100(1637)   on 2009-11-17 13:27:50 (Show Source): You can put this solution on YOUR website!5v =0,,,,,,v=0 . 7v-5=0 7v =5 v=5/7 . 5v-1=0 5v=1 v=1/5 .
 Travel_Word_Problems/239890: How far would one travel @ 20 mph for 35 seconds?1 solutions Answer 175924 by RAY100(1637)   on 2009-11-17 13:25:37 (Show Source): You can put this solution on YOUR website!Distance = Velocity * Time . D = 20 mi / hr * 35 sec * 1 hr / 3600 sec . D= .1944 mile * 5280 ft / 1 mi . D= 1026.67 ft . . . check,,,v = (1026.67 ft * 1 mi/5280 ft) /(35 sec* 1hr/3600sec)= 20 mi / hr,,,,ok
 Coordinate-system/239903: write the coordinates of the point that is 9 units to the left of the y-axis and 6 units about the x-axis.1 solutions Answer 175920 by RAY100(1637)   on 2009-11-17 13:16:16 (Show Source): You can put this solution on YOUR website!(-9,6)
 Polynomials-and-rational-expressions/239902: please help me solve this eauation: 1 solutions Answer 175919 by RAY100(1637)   on 2009-11-17 13:15:02 (Show Source): You can put this solution on YOUR website!50r^2 +40rd + 8d^2 . (10r +4d)(5r +2d) . 2(5r+2d)(5r+2d) . . . note, factors of 50 = 50*1, 25*2, 10*5 . factors of 8 = 8*1, 4*2 . .
 Miscellaneous_Word_Problems/239895: Find the sum of 40 percent of 1/4 and 50 percent of 1/5.1 solutions Answer 175918 by RAY100(1637)   on 2009-11-17 13:09:19 (Show Source): You can put this solution on YOUR website!40% * (1/4) + 50% * (1/5) . .4*.25 + .5*.2 . .1 + .1 . .2
 Exponential-and-logarithmic-functions/238133: 4*(-3((-1)^2-3)^21 solutions Answer 175006 by RAY100(1637)   on 2009-11-12 13:47:52 (Show Source): You can put this solution on YOUR website!we presume last right bracket is after the last 2 . 4[ -3{ (-1)^2-3 }^2 ] . 4[ -3{ 1-3 }^2 ] . 4 [ -3{2}^2 ] . 4[ -3 {4} ] . 4[ -12 ] . -48 . .
 Polynomials-and-rational-expressions/238115: x^6+x^4+x^2+11 solutions Answer 175004 by RAY100(1637)   on 2009-11-12 13:40:41 (Show Source): You can put this solution on YOUR website!We can partially factor with "grouping" . x^6 +x^4 +x^2 +1 . x^4(x^2+1) +1(x^2+1) . (x^4+1)(x^2+1) . any further factoring would require imaginary numbers .
 Probability-and-statistics/238130: a six sided die is weighed so that the probability of "4" is 4 times as likely as getting any other number. what is the probability of getting a "1" or a "3"?1 solutions Answer 175003 by RAY100(1637)   on 2009-11-12 13:34:50 (Show Source): You can put this solution on YOUR website!with a "normal" die,,,each side has equal chance, with 6 total possibilities. With the weighted die,,#4,,, has 4 chances,,making the total 4+5=9 . All of the unweighted sides have a probability of 1/9 . . The weighted side has a probability of 4/9. .
 Inequalities/238131: 2x+5<131 solutions Answer 175001 by RAY100(1637)   on 2009-11-12 13:29:45 (Show Source): You can put this solution on YOUR website!2x + 5 < 13,,,,,,,,,subtract 5 both sides . 2x < 8,,,,,,,,,,,,divide both sides by 2 . x<4,,,,,,,answer . . check, let x =3,,,,,,,,2(3) + 5 < 13,,,,,,11<13,,,,ok .
 Numbers_Word_Problems/238128: If one number exceeds another number by 13 and the larger number is 3/2 times the smaller number, what is the smaller number?1 solutions Answer 174999 by RAY100(1637)   on 2009-11-12 13:26:31 (Show Source): You can put this solution on YOUR website!Let x = smaller number,,,,,,,and y= larger number . (1) y=x+13 . (2) y= 3/2 * x,,,,,,,,,subst . x+13 = 3/2 * x,,,,,,,subtract x both sides . 13 = 1/2 * x,,,,,,,,,,multiply by 2 both sides . 26 = x,,,,,,, . y= x+13 = 26 +13 = 39,,,,,,,, . . check,,(1) 39 = 26 + 13,,,,,ok . (2) 39 = 3/2*26 = 39,,,,,,ok . .
 Expressions-with-variables/236987: what is the answer to 3-4q=10q+10?1 solutions Answer 174321 by RAY100(1637)   on 2009-11-09 16:49:24 (Show Source): You can put this solution on YOUR website!3-4q=10q+10,,,,,,,add 4q,,,,subst 10,,,,,both sides . -7 = 14q,,,,,divide by 14 . - 1/2 = q . . check,,,,3-4(-1/2) = 10(-1/2) +10 = 5,,,,,ok .
 Signed-numbers/236975: Hello, I can't figure out these 2 problems using Pemdas. Use each operation only once per problem (addition, subtraction, division and multiplication).Thank you!!! 12___6___4___2=24 12___6___4___2=141 solutions Answer 174320 by RAY100(1637)   on 2009-11-09 16:46:08 (Show Source): You can put this solution on YOUR website!12 + 6 * 4 / 2 . 12 + 24/2 . 12 + 12 . 24 . . . 12-6 +4 * 2 . 12-6 + 8 . 6+8 . 14 .
 decimal-numbers/236973: 72.9301 in word form .414783 in word form 470.03072 in word form1 solutions Answer 174314 by RAY100(1637)   on 2009-11-09 16:22:16 (Show Source): You can put this solution on YOUR website!seventy two and nine thousand three hundred one , ten thousandths . four hundred and fourteen thousand, seven hundred eighty three, millionths . four hundred seventy and three thousand seventy two, hundred thousandths .
 Trigonometry-basics/236936: PLEASE HELP ME SOLVE THIS TRIGONOMETRIC FUNCTIONS: GIven that sin0=4/5 and 0 lies in quadrant ll,find the following value. tan 01 solutions Answer 174310 by RAY100(1637)   on 2009-11-09 16:14:52 (Show Source): You can put this solution on YOUR website!sin o = 4/5 = .800 . use arc sine to find ,,,,,o= 53.13 degrees,,,(2nd function sin on calc) . This shows that sin 53.13 = .8,,,ok,,,but there is no 53.13 degrees in Quadrant 2 . Using the 180 degree ref line,,,,o' = 180- 53.13 = 126.87 degrees . checking sin 126.87 = .8,,,,ok . Now tan 126.87 = - 1.333 ,,,,,, . OR -4/3 .
 Angles/236969: A ray that divides an angle in two equal parts is called a(n) _____________.1 solutions Answer 174308 by RAY100(1637)   on 2009-11-09 16:05:54 (Show Source): You can put this solution on YOUR website!bisector
 Graphs/236970: how to solve 6x+3 when x=21 solutions Answer 174307 by RAY100(1637)   on 2009-11-09 16:04:54 (Show Source): You can put this solution on YOUR website!6x +3 for x=2 . 6(2) +3 . 12 +3 . 15 . .
 Proportions/236956: The length of the skid mark of an automobile sliding to a stop is directly proportional to the square of the velocity. It was found that a car traveling 60 miles per hour left a skid mark 172 feet in length when attempting to stop. Find the length of the skid marks of a car traveling 50 miles per hour.1 solutions Answer 174304 by RAY100(1637)   on 2009-11-09 16:03:06 (Show Source): You can put this solution on YOUR website!Let L= skid length in ft,,,,v= veolcity in MPH . L=kv^2 . subst data given,,,,,172 = k (60)^2,,,,,,,k= 172/60^2 = .0477 . proportion becomes,,,L= .0477 v^2 . for v=50,,,,,L = .0477 * 50^2 = 119.44 ft . . checking,,,, 119.44/50^2 = .0477,,,,ok
 Linear_Algebra/236963: ```What is the point slope form with the table (X) 3,5, 7, 9 (Y)-6,2,10,18```1 solutions Answer 174301 by RAY100(1637)   on 2009-11-09 15:56:23 (Show Source): You can put this solution on YOUR website!Let m= {18-(-6)}/ { 9- 3} = 24 /6 = 4 . m= (y2-y1)/(x2-x1) . using the point slope eqn with extreme coordinate pairs . y-y1 = m (x-x1) . y-18 = 4(x-9) . y-18 = 4x -36,,,,,,,subtracting y,, and adding 36 to both sides . 18 = 4x -y . . checking, y=4x -18,,,,,,all coordinates match ,,,,,ok
 Equations/236961: 11+n=-2(1-n)1 solutions Answer 174296 by RAY100(1637)   on 2009-11-09 15:48:03 (Show Source): You can put this solution on YOUR website!11+n = -7(1-n),,,,,,distribute (-7) . 11+n = -7 +7n,,,,,,add 7,,,subtract 1n,,,,from both sides . 18=6n,,,,,,,divide by 6 ,,,,both sides . 3=n . . check,,,,,11+3 = -7(1-3) = 14,,,,,ok .
 Polynomials-and-rational-expressions/236889: -2x^4-5x^3+3x^2 please help i have a test at school need to know how to work this problem1 solutions Answer 174248 by RAY100(1637)   on 2009-11-09 12:34:22 (Show Source): You can put this solution on YOUR website!-2x^4 -5x^3 +3x^2 . x^2 ( -2x^2 -5x +3) . x^2 ( -2x +1)(x+3) . . x*x*(-2x+1)*(x+3) . .
 Exponents-negative-and-fractional/236879: solve for x 6x+1/5=65 1 solutions Answer 174246 by RAY100(1637)   on 2009-11-09 12:27:29 (Show Source): You can put this solution on YOUR website!6x +1/5 = 65,,,,,,,clear fractions by multiplying by 5 . 30 x +1 = 325 . 30 x = 324 . x= 10.8 . . check ,,,,,6(10.8) + .2 = 65,,,,,ok
 Geometry_Word_Problems/236877: im not sure why i cant pickout the most imporant info in these word problems please help... If the length of a rectangle is 1km longer than twice the width then what is the length if the areaa is 55 square kilometer?1 solutions Answer 174239 by RAY100(1637)   on 2009-11-09 11:31:09 (Show Source): You can put this solution on YOUR website!Let L = Length,,,,,W= Width . Area = A = L*W,,,,,but L= 2W + 1 . A= ( 2W+1) (W) = 2w^2 +W,,,,,and A= 55 . 2W^2 +W - 55 = 0,,,,,factor . (2W +11)(W-5) =0 . 2w+11=0,,,,W=-11/2,,,not realistic . W-5 =0,,,,W=5 and L= 2*5 +1 =11 . . check,,,,,,LW= 5*11=55,,,,,ok . 2*5 +1 =11,,,,,,ok .
 Rational-functions/234607: solve x+7/x-2 < 0.1 solutions Answer 172974 by RAY100(1637)   on 2009-11-03 13:48:42 (Show Source): You can put this solution on YOUR website!x +7/(x-2) <0 . multiply by (x-2) . x(x-2) +7 <0 . x^2 -2x +7 <0 . solve by quadratic formula . a=1,,,b--2,,,,c=7 . x=[ -(-2)+/- sqrt{(-2)^2 -4(1) (7)}]/2(1) . x=[ 2 +/- sqrt{4-28}]/2 . x= 1 +/- 2.45i,,,,, . returning to x^2 -2x +7<0 . (x-1 -2.45i)(x-1+2.45i) <0 . x-1-2.45i <0,,,,,x< 1+2.45i . x-1+2.45i <0,,,,,x< 1-2.45i .
 Linear-systems/232838: 9y-2x(6+4y)1 solutions Answer 171964 by RAY100(1637)   on 2009-10-29 11:16:57 (Show Source): You can put this solution on YOUR website!9y - 2x(6+4y) . 9y -2x*6 -2x*4y . 9y -12x -8xy . 9y -8xy-12x . .