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# Recent problems solved by 'RAY100'

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 Radicals/201748: find the following ^3√y^3 . assume that the letters can represent any real number 1 solutions Answer 151980 by RAY100(1637)   on 2009-07-01 16:05:11 (Show Source): You can put this solution on YOUR website!cube root of y^3 = y
 Quadratic_Equations/201688: solve the equation by taking square root: 8x^2-3=-1551 solutions Answer 151979 by RAY100(1637)   on 2009-07-01 16:02:06 (Show Source): You can put this solution on YOUR website!8x^2 -3 = -155 . 8x^2 = -152 . x^2 = -152/8 = - 19 . taking sqrt of both sides . x= sqrt(-19) = 4.36 i,,,,,,,,where i = sqrt(-1)
 logarithm/201699: x^2 + 2^x = 1011 solutions Answer 151978 by RAY100(1637)   on 2009-07-01 13:59:27 (Show Source): You can put this solution on YOUR website!x= 6.017,,,,,by trial and error,,,assume x,,,calc eqn . check,,,6.017^2 +2^6.017=100.963 = 101
 Equations/201700: multiply (x+2)(x-3)(x+4)1 solutions Answer 151975 by RAY100(1637)   on 2009-07-01 13:40:42 (Show Source): You can put this solution on YOUR website!(x+2)(x-3)(x+4) . use FOIL first . (x+2) ( x^2 +4x -3x -12) . (x+2) ( x^2 + 1x -12) . now use distribution . x(x^2 +x -12) +2 ( x^2 +x -12) . x^3 +x^2 -12x +2x^2 +2x -24 . x^3 +3x^2 -10x -24 . checking,,,if x=0,,, original and answer = -24,,ok if x=1,,,both = -30,,,ok
 Travel_Word_Problems/201710: If a race car can go around a track in 5 minutes,then how long will it take to go around the track if it increases its speed by 20%? 1 solutions Answer 151971 by RAY100(1637)   on 2009-07-01 13:14:42 (Show Source): You can put this solution on YOUR website!v=d/t . (1) v=d/5 . (2) 1.2 v = d/t . from (2),,v=d/(1.2 t) = d /5,,,,,,from(1) . 1.2 t =5 . t= 5/1.2 = 4.17 min . checking,,,,let d=10, v= 10/5 =2 v2= 10/4.17 = 2.4 . 2.4 / 2 = 1.2,,,or 20 % higher,,,ok
 Geometric_formulas/201715: This question is from textbook geometry can you please help me solve((( An isometry maps a triangle into a________triangle.)))1 solutions Answer 151970 by RAY100(1637)   on 2009-07-01 13:05:00 (Show Source): You can put this solution on YOUR website!congruent
 Geometric_formulas/201716: This question is from textbook geometry can you please help me solve ((( An isometry maps an angle into a ________angle.)))1 solutions Answer 151969 by RAY100(1637)   on 2009-07-01 13:03:53 (Show Source): You can put this solution on YOUR website!congruent
 Inequalities/201713: The daily number v to an amusement park was always at least 852but never more than 1153. How is this expressed in an inequality?1 solutions Answer 151968 by RAY100(1637)   on 2009-07-01 12:54:25 (Show Source): You can put this solution on YOUR website!852 <= v <= 1153
 Linear_Equations_And_Systems_Word_Problems/201703: sanjay is now 1/2 as old as his brother. In 6 more years he will be 3/5 as old as his brother. Find the present age of each boy.1 solutions Answer 151936 by RAY100(1637)   on 2009-07-01 09:16:16 (Show Source): You can put this solution on YOUR website!Let s = Sanjay age,,,b= Brother's age . (1) s = (1/2) b . (2) ( s+6) = (3/5) (b+6) . subst (1) in (2) . (1/2) b +6 = (3/5)b + 18/5 . 6- 18/5 = (3/5 -1/2) b . 2.4 = .1 b . 24 = b,,,,,,s= 1/2 b = 1/2 *24 = 12 . check (1) 12 = 1/2 * 24 ,,,,ok . )2) 12 +6 = (3/5) ( 24 + 6 ) . 18 = 3/5 *30 =18 ,,,,,,ok
 Angles/201706: find angle A if it supplements angle B which is equal to 70-x1 solutions Answer 151934 by RAY100(1637)   on 2009-07-01 09:06:36 (Show Source): You can put this solution on YOUR website!A + B = 180,,,,def supplementary . B= (70-x),,,,given . A +(70-x) =180 . A + (70-x) = 180 . A = 180 -70 +x . A= 110 +x . check, x=10, (70-x) =60,,,A=120,,,answer,,,110+10=120,,,,ok
 Radicals/201707: Divide, and, if possible, simplify: sqrt 56ab^3 / sgrt 7a1 solutions Answer 151933 by RAY100(1637)   on 2009-07-01 09:00:09 (Show Source): You can put this solution on YOUR website!sqrt 56ab^3 / sqrt 7a . sqrt{ 56ab^3 / 7a } . sqrt { 8b^3) . sqrt{ 4 *2 *b^2 *b } . 2 b sqrt( 2b) . check let b=1,,both answer and original = 2.828,,,,ok
 Equations/201409: Solve the inequality. ((3x)/(7-x)) > x 1 solutions Answer 151921 by RAY100(1637)   on 2009-06-30 23:34:26 (Show Source): You can put this solution on YOUR website!(3x) /(7-x) > x 3x > x(7-x) 3x> 7x -x^2 0> -x^2 +4x 0> x(-x +4) . x<0,,,,x>4 . check ,,x<0,,use x=-1, -3/8 > -1,,,,,ok . 0less than x less than 4,,use x= 1,,,3/6>1,,,,,,not true . x>4,,,use x=5,,,15/2 > 5,,,,,ok . therefore ,,,x<0,,,x>4 .
 Equations/201416: Solve the inequality. ((-7x+5)/(6x^2+3)) > 0 1 solutions Answer 151920 by RAY100(1637)   on 2009-06-30 23:19:49 (Show Source): You can put this solution on YOUR website!(-7x+5) / (6x^2 +3) >0 . (-7x+5) >0 . 5> 7x . 5/7 >x
 Exponential-and-logarithmic-functions/201660: This question is from textbook log(square root of 1-x) - log(square root of x+2)=logx First I sqared both sides and got log 1-x -log x+2=log x squared then i performed the quotient property of logs and got log(1-x/x+2)=log x squared then I got 1-x =x squared (x-2) then I got X cubed - 2x+ x-1=01 solutions Answer 151918 by RAY100(1637)   on 2009-06-30 23:12:03 (Show Source): You can put this solution on YOUR website!Good work,,,,but watch signs for last 2 steps . log{ (1-x) / (x+2) } = log (x^2) . (1-x) / (x+2) = x^2 . (1-x) = (x^2) (x+2) . 1-x = x^3 + 2x^2 . 0 = x^3 +2x^2 +x -1
 Percentage-and-ratio-word-problems/201662: A small airplane used 4 3/8 gallons of fuel to fly an 1 1/4 hour trip. How many gallons were used for each hour?1 solutions Answer 151916 by RAY100(1637)   on 2009-06-30 22:56:20 (Show Source): You can put this solution on YOUR website!4.75 gal / 1.25 hr = 3.5 gal /hr
 Polynomials-and-rational-expressions/201489: Simplify 3^wtimes3^5^-wtimes3 thank you1 solutions Answer 151914 by RAY100(1637)   on 2009-06-30 22:54:02 (Show Source): You can put this solution on YOUR website!3^w * 3^5^-w *3^1 . 3^w * 3^(-5w) *3^1 . 3^(w -5w +1) . 3^(-4w+1) . check, w=o, original and answer = 3 w=1,,both = 1/3^3 w=2,,both = 1/3^7,,,,ok
 Geometry_Word_Problems/201641: How do I figure out the diagonal measurments of a square?1 solutions Answer 151881 by RAY100(1637)   on 2009-06-30 16:59:55 (Show Source): You can put this solution on YOUR website!(1) diagon separates a square into 2 equal triangles. legs = "s",, diagonal =d,,,,as it is a right triangle(square corner),, use pythagorous,,c^2 = a^2 +b^2,,,with a = b =s,,,c=d, . d^2 = s^2 +s^2 =2s^2,,,,d = sqrt 2 s^2 = s*sqrt2,,,,, . . or (2) recognize that the triangles are ,,,45-45-90, with side ratios, 1-1-sqrt2,,or s-s-s*sqrt2,,,and see d= s*sqrt2
 Quadratic_Equations/201636: Hi, Could you help me to find a way to this problem?!Tanks=) One number is 6 less than a secound number.The product of the numbers is 48 more than the square of the smaller number.Find the two numbers. I tryed to solve with this way but i couldnt finish it: 1 solutions Answer 151879 by RAY100(1637)   on 2009-06-30 16:52:43 (Show Source): You can put this solution on YOUR website!(1) x =y-6,,,,,,x = smaller, y = larger . (2) xy = 48 + x^2,,,,,product means multiply . subst (1) in (2) . y(y-6) = 48 + (y-6)^2 . y^2 -6y = 48 + y^2 -12y +36 . 6y = 84 . y = 14 . . x=y-6 = 14-6 = 8 . check in (2),,14 * 8 = 48 + 64 = 112,,,,ok
 Equations/201556: Evaluate the function. Given that f(x) = (1)/(4-8x) , find f(r - 3). A) (1)/(1-8r) B) (1)/(28-8r) C) (1)/(28+b) D) (1)/(r-3-8x) 1 solutions Answer 151875 by RAY100(1637)   on 2009-06-30 16:42:48 (Show Source): You can put this solution on YOUR website!f(x) = 1/(4-8x) . f(r-3) = 1/ { 4-8(r-3) } . f(r-3 = 1/ (4-8r+24) . f(r-3) = 1/ (28 -8r),,,,,,or B
 Geometric_formulas/201599: This question is from textbook geometry can you please help me slove ((( True of false Two right circular cones with radii 4 and 8, and heights 10 and 20, respectively, are similar. )))1 solutions Answer 151871 by RAY100(1637)   on 2009-06-30 16:11:21 (Show Source): You can put this solution on YOUR website!In solid figures, if linear dims are proportional, figures are similar. . Scale factor by radius are,,4/8 = 1/2,,,by height,,10/20 =1/2,,,, . Therefore they are similar
 Exponents/201628: Dear tutor,I 've checked one of the problems which was like my question but I couldn't mach the answer with mine.could you help me in this way ? Choose the answer Of if : a.) b.) c.) d.) e.)1 solutions Answer 151849 by RAY100(1637)   on 2009-06-30 14:33:32 (Show Source): You can put this solution on YOUR website!x + 1/x =8 (x^2 +1 ) / x =8 x^2 +1 = 8x x^2 -8x +1 =0 . using quadratic eqn,, x= 7.873,,.127 , substitute either in . X^4 +(1/x^4) = 3842 . checking answers, this matches (E) (8^4 -2^8 +2)
 Geometric_formulas/201600: This question is from textbook geometry can you please help me solve (((Find the center of the circle with equation (x-3)^2+(y+4)^2=25.)))1 solutions Answer 151848 by RAY100(1637)   on 2009-06-30 14:10:45 (Show Source): You can put this solution on YOUR website!(x-3)^2 +(y+4)^2 =25 . Remember form is,,,,(x-h)^2 +(y-k)^2 = r^2,,,(h,k) is center . in our case, h=3,,,k=-4,,,r=5,,,or center is (3,-4)
 Exponential-and-logarithmic-functions/201601: Determine where the graph of the function is concave up and concave down (if you need to enter use infinity or - infinity) f(x)=x^3-15x^2+12x+6 concave up concave down can someone help please thanks 1 solutions Answer 151847 by RAY100(1637)   on 2009-06-30 14:05:32 (Show Source): You can put this solution on YOUR website!y= x^3 -15x^2 +12x +6 . y' = 3x^2 -30x +12 . to find vertex, set slope(y') =0 . 3x^2 -30x +12 =0 3(x^2 -10x +4) =0 . solve using quadratic eqn,,,x= 9.58,,,.417 . to find y,,,substitute in original eqn,,,,(9.58,-376.5),,,(.417,,8.47) . since this is a positive cubic,,rises to right,, 1st vertex,,,(.417,8.47) is concave down,,,and second vertex (9.58, -376.5) is concave up . checking,,,(.5,8.375) (.3,8.277),,,ok cc down (9.5,-376.4),(9.7, -376.3) ,,,,ok cc up
 Probability-and-statistics/201603: Card Figure: 1 A , 2 B's, & 3 C's. Die 1/6 Referring to the figure in, think about first picking a card and then rolling the die. Give the probability in simplest form. P(C number greater than 4)=1 solutions Answer 151842 by RAY100(1637)   on 2009-06-30 13:33:22 (Show Source): You can put this solution on YOUR website!P(C, number greater than 4) = 3/6* 2/6 = 6/36 or 1/6
 Probability-and-statistics/201604: Card Figure: 1 A , 2 B's, & 3 C's. Die 1/6 Referring to the figure, think about first picking a card and then rolling the die. Give the probability in simplest form. P(B,number less than 5)1 solutions Answer 151839 by RAY100(1637)   on 2009-06-30 13:30:12 (Show Source): You can put this solution on YOUR website!P(B, Number less than 5) = 2/6 * 4/6 = 8/36 or 2/9
 Probability-and-statistics/201605: Card Figure: 1 A , 2 B's, & 3 C's. Die 1/6 Referring to the figure, think about first picking a card and then rolling the die. Give the probability in simplest form. P(A,not 2)=1 solutions Answer 151836 by RAY100(1637)   on 2009-06-30 13:27:31 (Show Source): You can put this solution on YOUR website!P(a,not 2) = 1/6 * 5/6 = 5/36
 Sequences-and-series/201608: find the 6th term of the sequence which has a first term of 5 and has a common ratio of 4.21 solutions Answer 151834 by RAY100(1637)   on 2009-06-30 13:23:55 (Show Source): You can put this solution on YOUR website!Geometric series has form,,,,a(n) = a(1) * r^(n-1) . a(1) =5,,,,r=4.2,,,,,n= 6 . a(6) = 5*4.2^ 5 = 6534.56 . checking,,5,,21,,,88.2,,370.44,,1555.848,,6534.56,,,,,ok
 Sequences-and-series/201609: which is the 9th term of the sequence which has a first term of 1 and has a common ratio of 1.51 solutions Answer 151833 by RAY100(1637)   on 2009-06-30 13:19:00 (Show Source): You can put this solution on YOUR website!Please see problem # 201610,,,Thanks
 Sequences-and-series/201610: which is the 9th term of the sequence which has a first term of 1 and has a common ratio of 1.51 solutions Answer 151832 by RAY100(1637)   on 2009-06-30 13:16:33 (Show Source): You can put this solution on YOUR website!Geometric sequence has form,,,,a(n) = a(1) r^(n-1) . given,,,a(1) =1,,,r=1.5 . a(n) = 1* 1.5^(n-1) . for n=9,,,,,a(9) = 1*1.5^8 = 25.629 . checking,, 1,,1.5,,2.25,,,3.375,,5.0625,,7.59375,,11.390,,17.086,,25.629,,,,,ok
 Polynomials-and-rational-expressions/201613: What is the largest four-digit number such that the second digit is one-fourth of the third digit, the third digit is twice the first digit, and the last digit is the same as the first digit? Thank you! 1 solutions Answer 151829 by RAY100(1637)   on 2009-06-30 13:09:47 (Show Source): You can put this solution on YOUR website!Let,,w,x,y,z,,,be four digits in order. . x=1/4 y . y=2w,,,,therefore x = 1/4 * 2w = w/2 . z=w . rewriting the digits,,,,,w,,w/2,,,2w,,,w . 2w is "largest" digit,,,,like to set to 9 but also have a digit, (w/2) ,,,therefore 2w =8 is largest possible. . restating digits,,,4,,,2,,,8,,,4, . checking, numbers match criteria.
 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