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# Recent problems solved by 'RAY100'

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 Miscellaneous_Word_Problems/201626: 1 solutions Answer 151827 by RAY100(1637)   on 2009-06-30 12:55:55 (Show Source): You can put this solution on YOUR website!(1) d= (r-6)3 (2) d= (r+6)2 . 3(r-6) = 2(r+6) 3r-18 = 2r +12 r=30 . check,,d = (30-6)3 =24 *3 = 72 d= (30 +6) 2 = 36 *2 = 72,,,,ok
 logarithm/201623: This question is from textbook write 5log(3x-11)-7log(x)as a single logarithm1 solutions Answer 151825 by RAY100(1637)   on 2009-06-30 12:50:55 (Show Source): You can put this solution on YOUR website!Remember alogb= logb^a,,,,and log a - log b = log (a/b) . 5 log (3x-11) - 7 log(x ) . log (3x-11)^5 - log (x)^7 . log { (3x-11)^5 / (x)^7 } . check,,,,let x=5, both original and answer = -1.882
 Polynomials-and-rational-expressions/201384: How to solve this Multiplication of Rational Expression: ?1 solutions Answer 151684 by RAY100(1637)   on 2009-06-28 20:17:20 (Show Source): You can put this solution on YOUR website!we believe the numerator of second multiplier should be (21) not (2) Please confirm . { (x^2 +x-2) / (x^2 -7x) } * { (5x^2 -38x +21) / (x^2 +2x) } . factor . { (x-1)(x+2)/ (x)(x-7)} * { (5x-3)(x-7) / x(x+2) } . simply by canceling opposing like terms . { (x-1)(5x-3) } / x^2 . check by allowing x=1,,both original and answer are zero try allowing x=2,, both are 1.75,,,,ok
 Polynomials-and-rational-expressions/201274: This question is from textbook 2x/2x-3=?/8x^3-27 1 solutions Answer 151672 by RAY100(1637)   on 2009-06-28 19:10:43 (Show Source): You can put this solution on YOUR website!( 2x) / (2x-3) = ? / ( 8x^3 -27) . factor second den,,which is a difference of cubes . (2x) / (2x-3) = ? / (2x-3){4x^2 +2x(3) +9 } . 2x /1 = ? / ( 4x^2 +6x +9) . cross multiply . ? = 2x(4x^2 +6x +9) . ? = 8x^3 +12x^2 +18x . check for x=1,,both original and answer has ,,? =38,,,ok
 Graphs/201400: Hello! I need a help ASAP!!! Problem 3. In 1920, the record for a certain race was 46.4 sec. In 1990, it was 45.0 sec. Let R(t)= the record in the race and t= the number of the year since 1920. a) Find a linear function that the date b) Use the function in (a) to predict the record in 2003 and in 2006. c) Find the year when the record will be 44.56 sec Find a linear function that fits the data. R(t)= ?? What is the predicted record for 2003? What is the predicted record for 2006? In what year will the predicted record be 44.56 sec?? Thank you so much for your help!!! 1 solutions Answer 151625 by RAY100(1637)   on 2009-06-28 09:48:14 (Show Source): You can put this solution on YOUR website!As a linear relationship, it follows the form, y=mx +b. . In this case,,,R=mt +b,,,with points (0,46.4),,and (70,45) . m= (y2-y1) / (x2-x1) = - (46.4 -45) /(1990 - 1920) = -1.4 / 70 = -.02 . R = (-.02)t +b,,,,,@(0,46.4),,,46.4 = 0 +b,,,b=46.4 . Base eqn ,,,,R = -.02t +46.4 . @ 1990, t=1990-1920=70,,,R=-.02(70) +46.4 = 45,,,,,good check . @ 2003, t=2003-1920=83,,,R=-.02(83)+46.4 = 44.74 . @ 2006, t=2006-1920=86,,,R=-.02(86)+46.4 = 44.68 . Have a great day
 Probability-and-statistics/201354: This question is from textbook Mathematics Solve the following problems using the Russian peasant algorithm 25 X 17 48 X 39 and 120 X 42 1 solutions Answer 151598 by RAY100(1637)   on 2009-06-27 18:58:45 (Show Source): You can put this solution on YOUR website!25 * 17 . 12,,,,34,,,,,even(12), not add 6,,,,,68,,,,,even (6), not add 3,,,,,136 1,,,,,272 . ,,,,,,408 (136 + 272) ,,,,,close to 425 . . 48 * 39 . 24,,,,,78, even(24), not add 12,,,,,156, even(12), not add 6,,,,,,312, even(6), not add 3,,,,,,624, 1,,,,,,1248 . ,,,,,,,1872,,(624 +1248),,,,exactly 1872 . . 120 * 42 . 60,,,,,,84, even (60), not add 30,,,,,168, even(30), not add 15.,,,,336 7,,,,,,672 3,,,,,1344 1,,,,,2688 . ,,,,,,5040,,,,(336+672+1344+2688),,,exactly 5040 . again, first column divide by 2,(drop remainders),,second column multiply by two. Cross out even numbers in first column , and mates in second column. Then add remaining second column.
 Exponents/201356: This question is from textbook Mathematics For Technical trades Here is another problem I have an cannot figure out. Using the formula L=2C + 1.57(D+d)+ D+d/4C find L for D = 8",d=5",and C=19". 1 solutions Answer 151595 by RAY100(1637)   on 2009-06-27 18:34:12 (Show Source): You can put this solution on YOUR website!L= 2C +1.57(D+d) + (D+d) / (4C) . Please check to assure this is the problem . substituting, C=19, D= 8,,d= 5 . L = 2(19) +1.57{ (8) +(5) } + { (8) + (5) } / { 4(19) } . L= 38 +1.57(13) + (13)/ (76) . L= 38 + 20.41 + .1711 . L = 58.58
 Numbers_Word_Problems/201360: One number is less than another. If the sum of the first number and twice the scond number is 45, find the two numbers.1 solutions Answer 151594 by RAY100(1637)   on 2009-06-27 18:22:53 (Show Source): You can put this solution on YOUR website!Let x . x +2y =45 . x,,,,,,,y . 1,,,,,,,22 3,,,,,,,21 5,,,,,,,20 7,,,,,,,19 9,,,,,,,18 11,,,,,,17 13,,,,,,16 15,,,,,,15,,not true as x not less than y . These are just positive integers. Negative integers, and decimals add many more possible combinations. . Perhaps the problem has other limitations ??
 Triangles/201372: This question is from textbook Discovering Geometry An Investigative Approach 1) why does constructing an equilateral triangle is easy by just copying the given equilateral triangle? 2)In a triangle, what is longer: a median or an altitude? Are they ever the same length? Explain your answers. 3) how can you measure angle by not using your protectors? pls help me... its due monday pls.1 solutions Answer 151593 by RAY100(1637)   on 2009-06-27 18:11:27 (Show Source): You can put this solution on YOUR website!1) to construct a new equilateral triangle of side "s", start with the existing equilateral triangle, Extend 2 sides until they are "s" long, connect these points. . 2)altitude is perpendicular distance from the vertex to the opposite side . Median is the distance from the vertex to the opposite side . They are equal in isosceles(when base is odd length) or equilateral triangles . 3)Construction easily makes 180 degree and 90 degree angles. bisection or repeated bisection yields, 45, 22.5, 11.25, etc angles Adding or subtracting from each other yields combinations. . a 30-60-90 triangle has sides of 1-2-sqrt3. Constructing a 30 degree or 60 degree is readily done using length ratios of 1 &2. Bisecting these repeatedly yields 15, 7.5, 3.75, etc. degrees. These can be added or subtracted to find numerous angles.
 Square-cubic-other-roots/201301: Solve the following equation 2y – 3/2 = sqrt 729 / 4 + y 1 solutions Answer 151590 by RAY100(1637)   on 2009-06-27 17:48:56 (Show Source): You can put this solution on YOUR website!2y -3/2 = sqrt 729 /(4+y) . (2y-1.5)(y+4) = 27 . 2y^2 +8y -1.5y -6 -27 =0 . 2y^2 +6.5y -33 =0 . Use quadratic eqn to solve . a= 2,,,,,b= 6.5,,,,,c=-33 . y=[ -(6.5) +/- sqrt{ (6.5)^2 -4 (2)(-33) } ] /2(2) . y= [ -6.5 +/- sqrt{ 306.25} ] /4 . y= [ -6.5 +/- 17.5] / 4 . y = -6,,+ 2.75 . check by inserting in original eqn,,,,,ok
 Polynomials-and-rational-expressions/201362: Find the quotient and remainder for (x^4-2x^2+3) divided by (x+1)1 solutions Answer 151588 by RAY100(1637)   on 2009-06-27 17:35:03 (Show Source): You can put this solution on YOUR website!( x^4 -2x^2 +3) / ( x+1) . .,,,,,,,,,,,,,,,,,,,x^3 -x^2 -x +1 +(2)/(x+1) ,,,,,,,,,,,,______________________________ ,,,,,,x+1,,!,,x^4 +0x^3 -2x^2 +0x +3 .,,,,,,,,,,,,,x^4 +x^3 ,,,,,,,,,,,,,,________ ,,,,,,,,,,,,,,,,,,,-x^3 -2x^2 ,,,,,,,,,,,,,,,,,,,-x^3 -1x^2 ,,,,,,,,,,,,,,,,,,,__________ ,,,,,,,,,,,,,,,,,,,,,,,,,-x^2 +0x ,,,,,,,,,,,,,,,,,,,,,,,,,-x^2 -1x ,,,,,,,,,,,,,,,,,,,,,,,,,________ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+1x +3 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+1x +1 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,_____ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+2 . Polynomial division is similar to regular long division,, divide, multiply, subtract, bring down,,,,,,repeat . To check, multiply quotient by divisor aand add remainder . (x^3 -x^2 -x +1) * (x+1) = x^4 -2x^2 +1 . adding remainder(+2) = x^4 -2x^2 +3,,,,,,ok . .
 Equations/201321: Solve the inequality. (c+4)(c-2)(c-7)>01 solutions Answer 151558 by RAY100(1637)   on 2009-06-27 11:57:27 (Show Source): You can put this solution on YOUR website!(c+4)(c-2)(c-7) > 0 . lets solve as equality first . (c+4)(c-2)(c-7) =0 . c+4=0,,,,c=-4 . c-2=0,,,,c=2 . c-7=0,,,,c=7 . in order,,,,,-4,,,,2,,,,,,7 . now lets check numbers before and after each of these against original inequality . for x less than (-4),,, let x=-5,,, -84 >0,,,, not true . for -4 less than x less than 2,,,let x=0,,,,,56>0,,,,,ok . for 2 less than x less than 7,,,,,let x= 3,,,,,-28>0,,,, not true . for x>7,,,,,let x = 8,,,,,72>0,,,ok . therefore ,,,,-4less than x less than 2,,,,x>7,,,are answers
 Equations/201337: solve the inequality 4k^3-6k^2(< or =)4k1 solutions Answer 151557 by RAY100(1637)   on 2009-06-27 11:35:32 (Show Source): You can put this solution on YOUR website!4k^3 -6k^2 < = 4k . lets solve as equality first . 4k^3 -6k^2 = 4k . 4k^3 -6k^2 -4k =0 . 2k ( 2k^2 -3k -2) = 0 . 2k (2k+1)(k-2) =0 . 2k =0,,,,k=0 . 2k+1 =0,,,,k= (-1/2) . k-2 = 0,,,,k=2 . Now on number line we have,,, (-1/2),,,,(0),,,,,(2) . Now lets check if numbers before and after each of these satisfy original inequality . for x< (-1/2),,,,let x = -1,,,,-10 <= -4,,,,ok . for (-1/2) < x < 0,,,let x= (-.25),,,-.3125 <=-1,,,,not true . for 0 less than x less than 2,,,,,let x=1,,,,-2 <= 4,,,,ok . for x>2,,,,let x= 3,,,,,54<=12,,,,,not true . Therefore,,,,,x<=(-1/2),,,,,0<=x<=2,,,,,answer
 Equations/201335: Find the slope and the y-intercept of the line. 2x-4y=-121 solutions Answer 151556 by RAY100(1637)   on 2009-06-27 10:59:52 (Show Source): You can put this solution on YOUR website!Many different ways to solve this ,,,but lets just match form, y=mx +b . 2x -4y = -12 . -4y = -2x -12 . y = (1/2)x + (3),,,,,or m=1/2,,,b=3 .
 Equations/201339: Solve the inequality (-6x+2)/(3x^2+7) >01 solutions Answer 151555 by RAY100(1637)   on 2009-06-27 10:49:52 (Show Source): You can put this solution on YOUR website!(-6x+2) (3x^2+7) > 0 . lets solve eqn as if it were equal to zero . (-6x+2) (3x^2 +7) = 0 . -6x+2 = 0 . -6x = -2 . x= + 1/3,,,,,zero . 3x^2 +7 =0 . 3x^2 =-7 x^2 = -7/3 x= +/- 1.53 i,,,,imaginary therefore not a Real Number Solution . The only Real answer is x= +1/3 . If we had solved this part of the problem with the inequality problem with the inequality sign, -6x+2 >0, the answer would be x < 1/3. . Lets check by picking test points on either side of + 1/3 . Smaller than + 1/3, use 0, . substituting,,,(-6(0)+2)(3(0)^2 +7) = 2*7=14,,,,or 14 > 0 ,,,,ok . Larger than +1/3 ,,,use 1 . subst,,,,,(-6(1)+2)(3(1)^2 +7) = (-4)(10) = -40,,,,or -40>0,,,,not true . Therefore ,,,,,x< 1/3,,,,is valid answer .
 Equations/201322: Find an equation of the line satisfying the given conditions. Through (-4,3); perpendicular to -8x+5y=771 solutions Answer 151554 by RAY100(1637)   on 2009-06-27 10:24:59 (Show Source): You can put this solution on YOUR website!For this problem, lets first find the slope of the original equation, using y=mx +b form, and then define the slope of the second eqn as, m2=-1/m1,perpendicular. Finally, we can define the eqn of the second line from the slope and the given point. . -8x +5y =77 5y = 8x +77 y = (8/5)x + 77/5 . or from form ,,,,y= m x +b,,,m = (8/5) . m2= - 1/m1 = (-5/8) . Second eqn is , y= mx +b,,,,y = (-5/8) x +b . As it contains the point ( -4,3),,,,substitute . (3) = (-5/8) (-4) + b . 3 = 20/8 +b . 24/8 - 20/8 = 4/8 =1/2 = b . subst m,,and b,,in form eqn,, y = (-5/8)x + (1/2) . mult thru by 8 . 8y = -5x + 4 . checking, subst ( -4,3),,,,8*3=(-5)(-4) +4 = 24 ,,,,ok
 Quadratic_Equations/201334: Please help. I'm not sure I have this done correctly. 3/-5-x - x/x-3=01 solutions Answer 151547 by RAY100(1637)   on 2009-06-27 08:57:47 (Show Source): You can put this solution on YOUR website!Please review to assure correct problem . 3/(-5-x) - x/(x-3) . just rearrange the first term, to get better den . -3/(x+5) -x /(x-3) . LCD = (x+5)(x-3) . [ -3 (x-3) -x(x+5)] / (x+5)(x-3) . [ -3x +9 -x^2 -5x ] / (x+5)(x-3) . [ -x^2 -8x +9 ] / (x+5)(x-3) . [ -1 ( x^2 +8x -9) ] / ( x+5)(x-3) . [-1 (x-1)(x+9)] / [ (x+5)(x-3) ] . checking let x=0 in original and answer,,,both = -3/5,,,,ok doing same for x=1, both = zero,,,ok
 Proportions/201295: If the ratio of the corresponding diagonals of two similar figures is 4 : 9 ,then what is the ratio of their perimeters?1 solutions Answer 151545 by RAY100(1637)   on 2009-06-27 08:41:43 (Show Source): You can put this solution on YOUR website!Remember with similar figures, that have proportional sides, . length and perimeter varies as Scale Factor ^1 . Area varies as SF^2 . and Volume varies as SF^3 . in our case SF = 4/9, perimeters have this same ratio, 4/9
 Equations/201133: 3+3/7+5=21 solutions Answer 151500 by RAY100(1637)   on 2009-06-26 15:10:40 (Show Source): You can put this solution on YOUR website!3+3/7 + 5 = 2 . Please review what the problem is ?? . if it is (3+3) / (7+5) = 6 / (12) = 1/2 .
 Linear_Algebra/201135: Find each value 1. f(3) if f(x) = 7 - x^ 2(squared) 2. f(0) if f(x) = x - 3x^ 2 (squared)1 solutions Answer 151498 by RAY100(1637)   on 2009-06-26 14:57:41 (Show Source): You can put this solution on YOUR website!f(3) = 7-x^2 = 7 -(3)^2 = 7-9 = -2 . f(0) = x-3x^2 = (0) -3(0)^2 = 0 .
 Geometric_formulas/201143: This question is from textbook geometry can you please help me answer. ((( ture of false All lateral faces of regular pyramids are congruent rectangles. )))1 solutions Answer 151494 by RAY100(1637)   on 2009-06-26 14:44:16 (Show Source): You can put this solution on YOUR website!Lateral Faces of pyramids are triangles ( not rectangles) therefore false
 Inequalities/201253: WRITE Dh AND SOLVE THE INEQUALITIY 12X-7X+10>01 solutions Answer 151491 by RAY100(1637)   on 2009-06-26 14:21:50 (Show Source): You can put this solution on YOUR website!12x -7x +10 > 0 5x +10 >0 5x > -10 x> -2
 Inequalities/201270: solve for x. With correct inequality symbol, then the number 10x+2-5x-6>-2(6-x)1 solutions Answer 151489 by RAY100(1637)   on 2009-06-26 14:17:10 (Show Source): You can put this solution on YOUR website!10x +2 -5x -6 > -2(6-x) . 10x +2 -5x -6 > -12 +2x . 5x -4 > -12 +2x . 3x > -8 . x> -8/3
 Inequalities/201158: 6-3/6x<8 The final solution I came to was X<5/2 I'm lost1 solutions Answer 151487 by RAY100(1637)   on 2009-06-26 14:08:45 (Show Source): You can put this solution on YOUR website!Please check the problem . (1) ( 6-3) / (6x) < 8 (3) / (6x) < 8 3 < 48 x 3/48 1/16< x . (2) 6 -(3/6)x < 8 -(1/2)x < 2 -x < 4 x > -4,,,note inequality flip . . (3) 6 - {3/(6x) } < 8 -{3/(6x)} < 2 -3 < 12x -3/(12) < x - (1/4) < x .
 Equations/201256: Evaluate the expression. Write answer without exponents. (4/9)1/21 solutions Answer 151477 by RAY100(1637)   on 2009-06-26 12:47:24 (Show Source): You can put this solution on YOUR website!(4/9)1/2=4/9*1/2=4/18=2/9
 Equations/201255: Evaluate the expression. Write answer without exponents. -2^-5 1 solutions Answer 151476 by RAY100(1637)   on 2009-06-26 12:36:32 (Show Source): You can put this solution on YOUR website!(-2)^-5 =1/(-2)^5=1/-32 = (-1/32)
 Problems-with-consecutive-odd-even-integers/201145: The sum of two numbers A and B is 3. The sum of their cubes is 36, What is the sum of their squares decreased by the product of the two numbers?1 solutions Answer 151388 by RAY100(1637)   on 2009-06-25 15:07:41 (Show Source): You can put this solution on YOUR website!(1) A + B = 3,,,,,,,,B=(3-A) (2) A^3 + B^3 =36 . A^3 + (3-A)^3 =36 . side problem (3-A)^3 = (3-A) (3-A)(3-A) (3-A) ( 9-6A +A^2) 27 -27A +9A^2 -A^3 . subst in . A^3 +(27 -27A +9A^2 -A^3) =36 9A^2 -27A -9 =0 9(A^2 -3A -1) =0 (A^2 -3A -1) =0 . To factor use quadratic eqn . a=1,,,,,b=-3,,,,,c=-1 . A =[ -(-3) +/- sqrt((-3)^2 - 4 (1)(-1)] / 2(1) . A= [3 +/- sqrt{ 9+4} ]/2 . A= [3 +/- 3.6]/2 . A= 3.3, -.3,,,,, . B= 3-3.3 =-.3,,,,or B= 3-(-.3) = 3.3 . ( A^2 +B^2) - AB =? . { (3.3)^2 +(-.3)^2 } - (3.3)(-.3) = ? . 11+10 = ? . 21=?
 Exponents/201152: This question is from textbook Mathematics For Technical trades A problem I have and cannot figure out is: Evaluate: 3{15-(8-5)}divided by 2squared times(3/2)= Please if you can help thats great Thank janet1 solutions Answer 151387 by RAY100(1637)   on 2009-06-25 14:36:50 (Show Source): You can put this solution on YOUR website!Remember the order of operations . PEMDAS, Parenthesis, Exponents, Multiply/Divide, lt to rt, Add/Subtract, lt to rt . 3{ 15 -(8-5) } / (2^2 *3/2),,,,check that we got 3/2 in right spot . 3{ 15 -3} / (4*3/2) . 3 { 12) / 6 . 36/6 . 6 . IF the (3/2) is separate . [3{ 15-(8-5)} / 2^2 ] * 3/2 . [3{15 -3} / 4] *1.5 . [ 3(12) /4 ] * 1.5 . (36/4) * 1.5 . 9*1.5 . 13.5 .
 Divisibility_and_Prime_Numbers/201146: This question is from textbook I do not understand how to factor a composite number into a product of prime numbers. For example: 1201 solutions Answer 151386 by RAY100(1637)   on 2009-06-25 14:14:33 (Show Source): You can put this solution on YOUR website!usually we use a "factor tree" to better visualize ( please excuse ,,,,) . ,,,,,,,,,,,,,,,,,,,,,,,,,120 ,,,,,,,,,,,,,,,,,,,,,,,,5,,,,24...........these are factors of 120 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,2,,,12........these are factors of 24 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,2,,,6......these are factors of 12 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,2,,3....these are factors of 6 . Therefore prime factors of 120 are 2,2,2,3,5,,(which multiply to 120) . better stated as 2^3, 3, 5 . Note we do not use the 1, in this factorization .
 logarithm/201176: This question is from textbook intermediate algebra Pg 560 62. Express as a single logarithm with a coefficient of 1. (The "b"s are tiny and below "log") 2 logbx-3(logby+logbz) 1 solutions Answer 151383 by RAY100(1637)   on 2009-06-25 14:00:27 (Show Source): You can put this solution on YOUR website!2log(b) x -3( log(b) y + log(b) z . remember a log c = logc^a . log(b)x^2 -log(b)y^3 -log(b)z^3 . remember log a +log b = log(a*b),,,and log a -log b =log(a/b) . log(b) { x^2 / y^3 * z^3 } . checking, let b=10,,, a=1, ,, b=2,,,c=3 . original eqn = -2.33,,,,answer = -2.33,,,,,ok
 Equations/201166: Part 1: Enter the dimensions of a rectangular box with a volume of 50x^3 - 3 - 2x + 75x^2. ____? Part 2 A rectangular box has a volume of 50x^3 -3 - 2x- 75x^2. In order for such a box to actually exist, the numerical value of x must be greater than____? (Use factorization from part 1 to solve.) 1 solutions Answer 151380 by RAY100(1637)   on 2009-06-25 13:25:57 (Show Source): You can put this solution on YOUR website!Vol = 50x^3 -2x +75x^2 -3 . looking for V = L * W * H . factor original eqn . 2x(25x^2 -1) +3(25x^2-1) . (2x+3)( 25x^2 -1) . (2x+3) (5x+1)(5x-1),,,,,sides of box . 2x+3 =0,,,,,x=-1.5 . 5x +1 = 0,,,,,x= -1/5 . 5x-1=0,,,,,,x= 1/5 . Smallest zero is (-1.5),, therefore x> -1.5