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# Recent problems solved by 'RAY100'

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 Exponential-and-logarithmic-functions/200908: The half life of cobalt-60 is 5.3 years. a.) find its decay rate b.) If you initially have 15 grams of this material, how long until only 10 grams remain? I am having trouble can someone help1 solutions Answer 151226 by RAY100(1637)   on 2009-06-24 09:35:59 (Show Source): You can put this solution on YOUR website!Remember, x = x(0) * 2^(-t/h),,,,where x(0) is initial amount at t=0,,t=time(yrs), and h = half life (yrs) . x = x(0) *2^(-t/5.3),,,,,,,(a) . subst in given values . 10 = 15 *2^( - t/5.3) . 10/15 =2/3 = 2^(-t/5.3) . take log both sides,,,,,remember log (a^b) = b(loga) . log (2/3) = log (2^(-t/5.3) ) = (-t/5.3)log2 . log(2/3) / log2 = (-t/5.3) . -.585 = - t/5.3 . 3.10 = t,,,,,,,,,,(b) . check . 10 = 15 *2^(-3.1/5.3) =10,,,,,,ok .
 Polynomials-and-rational-expressions/200991: -3-{x-3x-y}-y 1 solutions Answer 151225 by RAY100(1637)   on 2009-06-24 09:16:17 (Show Source): You can put this solution on YOUR website!-3-{ x-3x-y} -y . -3 -1{x-3x-y} -y . distribute (-1) . -3 -x +3x +y -y . -3 +2x . 2x-3 .
 Rational-functions/200867: 9x^2+4y^21 solutions Answer 151224 by RAY100(1637)   on 2009-06-24 09:10:19 (Show Source): You can put this solution on YOUR website!9x^2 +4y^2 . very interesting problem. . If this was ,, 9x^2 -4y^2 ,, just factor difference of squares,,, (3x+2y)(3x-2y). To use this form on the positive, lets rewrite the eqn . (9x^2 - (-4) y^2 . (3x+sqrt(-4)y) (3x- sqrt(-4)y) . (3x+2iy) (3x - 2iy) . check using FOIL . F = 9x^2,,,,O= -6ixy,,,I = +6ixy ,,,,L = -4i^2 y^2 = 9x^2 +4y^2,,(i^2 = -1),,,,,ok
 Equations/200895: please help. what is 20am-m+ma ?1 solutions Answer 151177 by RAY100(1637)   on 2009-06-23 17:37:34 (Show Source): You can put this solution on YOUR website!20am -m +ma . m(20a -1 +a) . m( 21a -1) . 21am -m .
 Polynomials-and-rational-expressions/200903: x/x+1 + 5/x = 1/x^2+x1 solutions Answer 151176 by RAY100(1637)   on 2009-06-23 17:22:17 (Show Source): You can put this solution on YOUR website!x/(x+1) + 5/x = 1/ ( x^2 +x) . LCD = x (x+1) = x^2 +x,,,,,,,,,,multiply thru . x(x) + 5(x+1) = 1 . x^2 +5x +5 =1 . x^2 +5x +4 =0 . (x+1) (x+4) =0 . x = -1,,-4 . check for (-4),,,,(-4)/(-4+1) +5/(-4) = 1/ { (-4)^2 +(-4) } . (-4/ -3 ) - ( 5/4) = 1 / 12 . ( 16 -15 ) /12 = 1/12 . 1/12 = 1/12 ,,,,,,,,,,ok .. for (-1),,,,,start with,,,,,x^2 +5x +4 =0,, (-1)^2 +5(-1) +4 =0,,,, 1 -5 +4 =0,,,,,,ok .
 Polynomials-and-rational-expressions/200904: a^-1+b^-1 / a^2-b^2/ab1 solutions Answer 151175 by RAY100(1637)   on 2009-06-23 16:59:49 (Show Source): You can put this solution on YOUR website!a^-1b^-1 / a^2 -b^2 / ab . please check to assure correct problem. . (a^-1 *b^-1) / (a^2 -b^2) / (ab) . as with fractions, invert and multiply instead of divide . ( a^-1 * b^-1) * ( ab) / (a^2 -b^2) . a^-1 = 1/a,,,,,,b^-1 = 1/b . ( 1/ab) * (ab) / ( a^2 -b^2) . 1/ ( a^2 - b^2 )
 Miscellaneous_Word_Problems/200900: This question is from textbook elementary algebra Suppose that a board 20 feet long is cut into two pieces. Four times the length of the shorter piece is 4 feet less than three times the length of the longer piece. Find the length of each piece.1 solutions Answer 151139 by RAY100(1637)   on 2009-06-23 10:55:03 (Show Source): You can put this solution on YOUR website!Let x=short length,,,,y= long length . (1) x + y = 20,,,,,y = 20 -x (2) 4x = 3y-4 . substitute (1) in (2) . 4x = 3( 20-x) -4 4x = 60 -3x -4 7x =56 x=8 . substitute in (1) . y= 20 -8 y=12 . check (1) 8+12 =20,,,,ok (2) 4(8) = 3( 12) -4 32 =32,,,,,,,,,,,,,,,,,,,,,,ok
 Inequalities/200912: Okay this is from a worksheet and im lost.... [6-2/3y]-4=81 solutions Answer 151137 by RAY100(1637)   on 2009-06-23 10:45:14 (Show Source): You can put this solution on YOUR website!Solving ALGEBRA problems,,, use order of operations in reverse,,,PEMDAS opposite . [ 6-2/3y] -4 =8,,,,,,,,add 4 both sides [ 6-2/3y] = 12,,,,,,,,,,subtract 6 both sides -2/3y = 6,,,,,,,,,,,,,,,,,divide by - 2 and mult by 3,,both sides y = - 6 (3/2),,,,,,,,,,,,,simplify y= -9 . check [ 6-2/3(-9)] -4=8 [6+6] -4 = 8 12-4=8 8=8,,,,,ok
 Functions/200918: 3^x -4=21 solutions Answer 151136 by RAY100(1637)   on 2009-06-23 10:36:26 (Show Source): You can put this solution on YOUR website!3^x -4 =2 . 3^x = 6 . take log both sides . log(3^x) =log 6 . or ,,,,,,x log 3 = log 6 . x= log 6 / log 3 . x= 1.631 . check,,,,,,3^(1.631) =6,,,,,ok . . if problem was ,,,,,3^(x-4) = 2 . (x-4) log 3 = log 2 . x-4 = log2/log3 = .631 . x= 4.631 . check 3^(4.631-4) =2,,,,, ok
 Polynomials-and-rational-expressions/200831: Find the binomial factors for the following trinomial and check using the FOIL method. 9y^2-12y+41 solutions Answer 151081 by RAY100(1637)   on 2009-06-22 13:07:12 (Show Source): You can put this solution on YOUR website!9y^2 -12y +4,,,,,,,,,factors of 9(9-1, 3-3) factors of 4(4-1, 2-2),,, (+) third term means signs are the same, and factor multiples add,,,,(-) 2nd term means, signs are (-). . ( 3y-2) (3y-2) . F = 3y*3y= 9y^2 . O= 3y*-2 = -6y . I = 3y *-2 = -6y . L = -2*-2 = +4 . combining middle terms ,,, 9y^2 -12y +4 .
 Polynomials-and-rational-expressions/200832: Find the binomial factors for the following trinomial and check using the FOIL method. 7k^2-9k-101 solutions Answer 151080 by RAY100(1637)   on 2009-06-22 12:59:51 (Show Source): You can put this solution on YOUR website!7k^2 -9k -10,,,,,,,,,Factors of 7(7*1),,,factors of 10 (10*1,,,5*2),,,,,(-) last term means difference of factor multiples,,,,,,,,(-) middle term means largest factor multiple (-) . (7k +5)(k-2) . F = 7k*k = 7k^2 . O = 7K *-2 = -14 k . I = k*5 = 5k . L= 5*-2= -10 . combining middle terms,,,, 7k^2 -9k -10 .
 Polynomials-and-rational-expressions/200833: Find the binomial factors for the following trinomial and check using the FOIL method. 4n^2-5n-61 solutions Answer 151079 by RAY100(1637)   on 2009-06-22 12:52:40 (Show Source): You can put this solution on YOUR website!4n^2 -5n -6,,,,,factors of 4( 4*1, 2*2),, factors of 6 (6*1,,3*2),,,last term (-) means difference of . middle terms, or factors,,,, 2nd term (-) means largest factor multiple is (-) . (4n+3)(n-2) . F = 4n *n = 4n^2 . O = 4n * -2 =-8n . I = n*3 =3n . L = 3*-2 = -6 . combining middle terms ,,,,4n^2 -5n -6
 Distributive-associative-commutative-properties/200844: Please help me how to solve this and teach it to me step by step: 10(y-6)1 solutions Answer 151078 by RAY100(1637)   on 2009-06-22 12:44:51 (Show Source): You can put this solution on YOUR website!10 (y-6) . 10*y -10*6 . 10y -60 .
 Polynomials-and-rational-expressions/200852: Solve the equation: x+6/x=-51 solutions Answer 151077 by RAY100(1637)   on 2009-06-22 12:40:52 (Show Source): You can put this solution on YOUR website!please see problem # 200851,,,
 Polynomials-and-rational-expressions/200851: Solve the equation: x+6/x=-51 solutions Answer 151076 by RAY100(1637)   on 2009-06-22 12:38:25 (Show Source): You can put this solution on YOUR website!(x+6) / x = -5 cross multiply x+6 = -5x 6x +6 =0 6(x+1) =0 x=-1 check (-1) +6 = -5 (-1) 5=5,,,,,,,ok
 Numbers_Word_Problems/200850: If 4a+3b=27 and 3a+4b=29, then 7a+7b/2=?1 solutions Answer 151075 by RAY100(1637)   on 2009-06-22 12:34:27 (Show Source): You can put this solution on YOUR website!(1) 4a +3b =27 (2) 3a +4b = 29 . multiply (1) by 3,,,,and (2) by 4 . (3) 12a +9b = 81 (4) 12a +16b = 116 . (4) - (3) 7b = 35 b=5 . subst into (1) 4a +3(5) = 27 4a =12 a=3 . check (1) 4(3) +3(5) = 27,,,,,12 +15 =27 ,,,,,,ok (2) 3(3) +4(5) =29,,,,9+20=29,,,,,,,ok . subst into 7a + 7b/2 = 7(3) +7(5) /2 = 21 + 35/2 = 38.5 . or subst (7a +7b )/2 = (7*3 +7*5)/2= 56 /2 =28
 Polynomials-and-rational-expressions/200834: Find the binomial factors for the following trinomial and check using the FOIL method. 25y^2-30y+91 solutions Answer 151073 by RAY100(1637)   on 2009-06-22 11:01:11 (Show Source): You can put this solution on YOUR website!25 y^2 -30y +9 . (5y-3)(5y-3) . F = (5y)(5y) = 25 y^2 . O = (5y)(-3) = -15y . I = ((5y)(-3) = -15y . L = (-3)(-3) = +9 . combining middle terms ,,,,,, 25y^2 -30y + 9,,,,,ok
 percentage/200840: how do you change a decimal into a fraction, and a fraction into a decimal?1 solutions Answer 151072 by RAY100(1637)   on 2009-06-22 10:55:15 (Show Source): You can put this solution on YOUR website!Very good question. . Decimal to fraction . .5 = 5/10 = 1/2 . .25 = 25 /100 = 1/4 . .375 = 375 / 1000 = 3/8 ,,,,,,,( divided by 125) . To generalize, set decimal number over place value . . Fraction to decimal . Remember that 1/2 means "1 divided by 2" = .5 . 1/4 = 1 divided by 4 = .25 . 3/8 = 3 divided by 8 = .375 . also mixed numbers, either change to improper fraction and proceed as above, or just do fraction part and add back in whole number part.
 Square-cubic-other-roots/200821: (3 sqrt 3)^41 solutions Answer 151068 by RAY100(1637)   on 2009-06-22 10:44:34 (Show Source): You can put this solution on YOUR website!(3sqrt3)^4 ,,,,,,,,check = 729 . [ 3 * 3^1/2] ^4 . [ 3^1 1/2]^4 . [3^ 3/2]^4 . 3^ (12/2) . 3^6= 729,,,,,ok
 Polynomials-and-rational-expressions/200830: Multiply and if possible simplify: (x^2-6x+9/12-4x)(x^6-9x^4/x^3-3x^2)1 solutions Answer 151066 by RAY100(1637)   on 2009-06-22 10:28:10 (Show Source): You can put this solution on YOUR website![ { x^2-6x +9} / {12-4x} ] * [ { x^6 -9x^4} / {x^3 -3x^2}] . [ ( x-3)(x-3) / -4x (x-3) ] * [ ( x^4)(x^2 -9) / (x^2) ( x-3) ] . simplify by cancelling like terms, num and den . -x^4 (x^2 -9) / 4 x^2 . (-1/4) x^2 ( x+3)(x-3) . Check using x=2 in both original and answer, both = +5, ok
 Expressions-with-variables/200822: PLease help solve a^2 – 40 = 0 and w^2 + 49 = 01 solutions Answer 151063 by RAY100(1637)   on 2009-06-22 09:31:28 (Show Source): You can put this solution on YOUR website!a^2 -40 =0 . a^2 =40 . sqrt both sides . a= =/- sqrt 40 = +/- 6.325 . . w^2 +49 =0 . w^2 =-49 . w = +/- sqrt -49 = +/- 7 i .
 Expressions-with-variables/200823: Find b^2 - 4ac and the number of real solutions -3x^2 + 7x = 01 solutions Answer 151062 by RAY100(1637)   on 2009-06-22 09:27:05 (Show Source): You can put this solution on YOUR website!-3x^2 +7x +0 =0 , a= (-3),,,,,,b= (7),,,,,,,,,c=0 . Discriminant = b^2 -4ac = (7)^2 - 4 (-3) (0) = 49 . D > 0 ,,,,,therefore 2 real numbers as solutions,,,,,,0,,,2.3333 . if D = 0,,,,,, one solution . if D less than 0 = no real solutions
 Square-cubic-other-roots/200824: x^2 + x + sqrt x^2 + x – 2 = 01 solutions Answer 151059 by RAY100(1637)   on 2009-06-22 09:15:23 (Show Source): You can put this solution on YOUR website!x^2 +x +sqrtx^2 +x -2 = 0 . x^2 +x+x+x-2=0 . x^2 +3x -2=0 . use Quadratic Formula . a=1,,,,b= 3,,,,c=-2 . x=[ -(3) +/- sqrt { (3)^2 -4 (1) (-2) } ] / 2(1) . x= [ -3 +/- sqrt { 9 +8 } ] /2 . x= [-3 +/- 4.123 ] /2 . x= .5615,,, -3.562 . check by subst into original, with calc,,,,ok
 Expressions-with-variables/200825: b^4 + 13b^2 + 36 = 01 solutions Answer 151058 by RAY100(1637)   on 2009-06-22 09:00:08 (Show Source): You can put this solution on YOUR website!b^4 +13b^2 +36 =0 let a = b^2 a^2 +13a +36 =0 (a+9)(a+4) =0 subst back (b^2 +9)(b^2 +4) =0 . b^2 +9 =0,,,,, b^2 = -9,,,b= +/- 3i . b^2 +4 = 0,,,,,,b^2 = -4,,,,,,,,,b= +/- 2i
 Expressions-with-variables/200826: w^2 + 49 = 01 solutions Answer 151056 by RAY100(1637)   on 2009-06-22 08:50:18 (Show Source): You can put this solution on YOUR website!w^2 +49 (w+7i)(w-7i)
 Rational-functions/200759: x^3=4x=1 solutions Answer 151055 by RAY100(1637)   on 2009-06-22 08:47:59 (Show Source): You can put this solution on YOUR website!x^3 -4x x(x^2 -4) x(x+2)(x-2)
 Polynomials-and-rational-expressions/200651: 1. X^2-X-20/X^2-25/X^2-16/X^2-X-30 Please help me out April 1 solutions Answer 150981 by RAY100(1637)   on 2009-06-21 10:33:52 (Show Source): You can put this solution on YOUR website![ { X^2 -x -20} / {x^2-25} ] / [ {x^2 -16} / { x^2 -x -30} ] . As with fractions, to divide invert and multiply,,,a/b/c/d = a/b * d/c . [ { x^2 -x-20} / {x^2 -25}] * [ { x^2 -x -30} / {x^2 -16} ] . factor and simplify by cancelling like terms . [ { (x-5)(x+4)} / { (x+5)(x-5) } ] * [ { (x-6)(x+5) } / { ( x+4)(x-4)} ] . ( x-6) / (x-4),,,,,answer . check,, let x=1,,,,in original = 1.5,,,,,,,in answer = 1.5,,,,,,ok
 real-numbers/200582: please,solve this problem for me 2+4-6-3x2+(3x7)=? 1 solutions Answer 150978 by RAY100(1637)   on 2009-06-21 10:19:27 (Show Source): You can put this solution on YOUR website!Remember order of operations, PEMDAS, Parenthesis, Exponents, Multiply / Divide, lt to rt, and ADD / Subtract, lt to rt . 2+4 -6 -3*2 +3*7 . 2+4 -6 -6 +21 . 6 -6 -6 +21 . 0-6 +21 . -6 +21 . 15
 Equations/200745: Separate 152 into 2 parts such that if the bigger number is divided by the smaller number, the result is 5/2.1 solutions Answer 150974 by RAY100(1637)   on 2009-06-21 09:51:37 (Show Source): You can put this solution on YOUR website!(1) x+y= 152 (2) x/y = 5/2 = 2.5,,,,,,,x=(2.5y) . subst (2) into (1) . 2.5y + y = 152 3.5 y =152 y= 43.43,,,,,,answer . subst in (2) x = 2.5 * 43.43 = 108.57 . check (1) 108.57 +43.43 = 152,,,,ok (2) 108.57 / 43.43 = 2.5,,,,,,ok
 Polynomials-and-rational-expressions/200748: The sum of two numbers is 11 The sum of the squares of the two numbers is 73, find the two numbers.1 solutions Answer 150971 by RAY100(1637)   on 2009-06-21 09:40:25 (Show Source): You can put this solution on YOUR website!(1) x +y =11 (2) x^2 + y^2 =73 . from(1) y = (11-x) . subst into (2) . x^2 +(11-x)^2 =73 x^2 + (121 -22x +x^2 = 73 2x^2 -22x +48 =0 divide by 2 x^2 -11x +24 =0 factor (x-8)(x-3) =0 x= 8 , 3 . check (1) 8+3=11,,,,ok (2) 64 + 9 = 73 ,,,,,ok