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# Recent problems solved by 'user_dude2008'

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 Numeric_Fractions/187511: find the cardinal number for each set A={xlx is a letter in the word six} 1 solutions Answer 140655 by user_dude2008(1861)   on 2009-03-21 00:49:56 (Show Source): You can put this solution on YOUR website!A={x | x is a letter in the word six} = {s, i, x} 3 elements ----> cardinal number is 3
 Percentage-and-ratio-word-problems/187624: Mike invested $6000 for one year. He invested part of it at 9% and the rest at 11%. At the end of the year he earned$624 in interest. How much did he invest at each rate?1 solutions Answer 140654 by user_dude2008(1861)   on 2009-03-21 00:47:32 (Show Source): You can put this solution on YOUR website!"Mike invested $6000 for one year" ----> x+y=6000 ----> y=6000-x "He invested part of it at 9% and the rest at 11%. At the end of the year he earned$624 in interest" ----> 0.09x+0.11y=624 ----> 9x+11y=62400 9x+11y=62400 9x+11(6000-x)=62400 9x+66000-11x=62400 -2x+66000=62400 -2x=62400-66000 -2x=-3600 x=1800 He invested $1,800 at 9% y=6000-x y=6000-1800 y=4200 He invested$4,200 at 11%
 Complex_Numbers/187613: how do i simplify the properties of rational exponents?1 solutions Answer 140632 by user_dude2008(1861)   on 2009-03-20 20:44:50 (Show Source): You can put this solution on YOUR website!Post a problem so we can show you.
 Linear-systems/187604: This question is from textbook saxon algebra 2 Factor the expression. 64x^6+y^6 (8x^2)^3+(y^2)^3 (8x^2+y^2)(8x^4-8x^2y^2+y^4) Did I do this right?1 solutions Answer 140626 by user_dude2008(1861)   on 2009-03-20 20:28:29 (Show Source): You can put this solution on YOUR website!64x^6+y^6 (4x^2)^3+(y^2)^3 (4x^2+y^2)( (4x^2)^2 - (4x^2)(y^2) + (y^2)^2 ) (4x^2+y^2)( 16x^4 - 4x^2y^2 + y^4 ) Ans: 64x^6+y^6 factors to (4x^2+y^2)(16x^4-4x^2y^2+y^4)
 Trigonometry-basics/187606: This question is from textbook saxon algebra 2 Graph the periodic function. Determine the Domain and Range. Identify the period and amplitude. y=6sin(x)+1 amplitude=6 That's all I know. Please help!1 solutions Answer 140623 by user_dude2008(1861)   on 2009-03-20 20:25:39 (Show Source): You can put this solution on YOUR website!y=6sin(x)+1 ---> y=6sin(1x+0)+1 in form of y=a*sin(bx+c)+d amplitude: A=abs(a)=abs(6)=6 Amplitude is 6 Period: T=(2pi)/b=(2pi)/1=2pi Period is 2pi (360 degrees). Graph repeats every 2pi radians/360 degrees Graph: Domain: all real numbers Range: [-5,7] or
 Exponents-negative-and-fractional/187451: This question is from textbook 5^2 5^3 over 5^3 5^2 = 5^_1 solutions Answer 140506 by user_dude2008(1861)   on 2009-03-19 20:05:01 (Show Source): You can put this solution on YOUR website! Ans:
 Exponents-negative-and-fractional/187452: This question is from textbook I need help with this problem. Simplify each expression. 2^7 over 2^51 solutions Answer 140505 by user_dude2008(1861)   on 2009-03-19 20:02:39 (Show Source): You can put this solution on YOUR website! Ans:
 Rational-functions/187453: 5y^2=-401 solutions Answer 140504 by user_dude2008(1861)   on 2009-03-19 20:01:25 (Show Source): You can put this solution on YOUR website!5y^2=-40 y^2=-40/5 y^2=-8 y=sqrt(-8) or y=-sqrt(-8) Ans: y=2i*sqrt(2) or y=-2i*sqrt(2)
 Quadratic-relations-and-conic-sections/187456: This question is from textbook Find a parabola equation y-k=a(x-h)^2 if its Vertex(3,2) and it contains the point (1,3)1 solutions Answer 140503 by user_dude2008(1861)   on 2009-03-19 20:00:03 (Show Source): You can put this solution on YOUR website!y-k=a(x-h)^2 Vertex(3,2) ----> y-2=a(x-3)^2 contains the point (1,3) ----> 3-2=a(1-3)^2 ----> 1=4a ----> a=1/4 Equation:
 Rational-functions/187317: This question is from textbook Prentice Hall Mathematics Algebra 2 What are the steps in doing this problem? My algebra 2 teacher isn't very good at explaining 1 solutions Answer 140414 by user_dude2008(1861)   on 2009-03-18 20:44:24 (Show Source): You can put this solution on YOUR website!You need to post the entire problem. We dont have your books.
 Average/187318: Solve. (x – 2)^ = 101 solutions Answer 140413 by user_dude2008(1861)   on 2009-03-18 20:43:36 (Show Source): You can put this solution on YOUR website! Ans: which really means: or
 Exponential-and-logarithmic-functions/187263: we are doing solving equations by using logarithms. im stuck. 8^x=10 1 solutions Answer 140371 by user_dude2008(1861)   on 2009-03-18 15:55:00 (Show Source):
 Numeric_Fractions/187185: x/2+(1-x)/3=11 solutions Answer 140351 by user_dude2008(1861)   on 2009-03-18 13:37:42 (Show Source): You can put this solution on YOUR website!x/2+(1-x)/3=1 3x+2(1-x)=6 3x+2-2x=6 x+2=6 x=6-2 Ans: x=4
 Linear-equations/187137: The length of a rectangle is 2 cm more than four times the width. If the perimeter of the rectangle is 34 cm, what are its dimensions?1 solutions Answer 140350 by user_dude2008(1861)   on 2009-03-18 13:35:16 (Show Source): You can put this solution on YOUR website!"length of a rectangle is 2 cm more than four times the width" ---> L=4W+2 "the perimeter of the rectangle is 34 cm" ---> P=2L+2W ---> 34=2L+2W 34=2L+2W 34=2(4W+2)+2W 34=8W+4+2W 34-4=8W+2W 30=10W W=3 L=4W+2 L=4(3)+2 L=12+2 L=14 Ans: length = 14 cm, width = 3 cm
 Square-cubic-other-roots/187233: i dont know how to multiply squarroots and i have homework due tomorow and i will get a week of detention if it is not dont i need some one to explain it to me so i can do it.!!!????1 solutions Answer 140348 by user_dude2008(1861)   on 2009-03-18 13:08:10 (Show Source): You can put this solution on YOUR website!You need to post the problem or problems.
 logarithm/187163: e^x+1 = 201 solutions Answer 140298 by user_dude2008(1861)   on 2009-03-17 23:38:01 (Show Source): You can put this solution on YOUR website!e^x+1 = 20 e^x = 20 - 1 e^x = 19 Ans: x = ln(19)
 logarithm/187165: log(x^2+19) = 21 solutions Answer 140297 by user_dude2008(1861)   on 2009-03-17 23:36:32 (Show Source): You can put this solution on YOUR website!log is assumed to be base 10 log(x^2+19) = 2 x^2+19 = 10^2 x^2+19 = 100 x^2 = 100 - 19 x^2 = 81 x=-9 or x=9
 logarithm/187166: log(2x^2+3x) = log(10x+30)1 solutions Answer 140296 by user_dude2008(1861)   on 2009-03-17 23:33:53 (Show Source): You can put this solution on YOUR website!log(2x^2+3x) = log(10x+30) 2x^2+3x = 10x+30 2x^2+3x - 10x - 30 = 0 2x^2-7x-30 = 0 (x-6)(2x+5) = 0 x-6=0 or 2x+5=0 Ans: x=6 or x=-5/2
 logarithm/187167: log(x^3) = (log x)^21 solutions Answer 140295 by user_dude2008(1861)   on 2009-03-17 23:29:56 (Show Source): You can put this solution on YOUR website!log(x) assumed base 10 log(x^3) = (log x)^2 3*log(x) = (log x)^2 Let z=log(x) 3*z = z^2 0 = z^2-3z 0 = z(z-3) z = 0 or z = 3 log(x) = 0 or log(x) = 3 x=1 or x=1000 Ans: x=1 or x=1000
 real-numbers/187168: sum of three consecutive numbers is 18.what are these numbers?1 solutions Answer 140294 by user_dude2008(1861)   on 2009-03-17 23:26:35 (Show Source): You can put this solution on YOUR website!"sum of three consecutive numbers is 18." ----> x+(x+1)+(x+2)=18 x+(x+1)+(x+2)=18 x+x+1+x+2=18 3x+3=18 3x=15 x=5 --> x+1=6, x+2=7 Ans: nums are 5, 6, and 7 Check: 5+6+7=18
 Square-cubic-other-roots/187078: square root of 4q-3 =31 solutions Answer 140228 by user_dude2008(1861)   on 2009-03-17 16:23:52 (Show Source): You can put this solution on YOUR website!sqrt( 4q-3 ) = 3 4q-3 = 3^2 4q-3 = 9 4q = 9+3 4q = 12 q = 12/4 q = 3 Ans: q = 3
 Linear_Algebra/187019: I have tried to get some of these but I have a problem of being just a little off and then blowing the whole deal. Please help. Write standard form and identify a, b, and c. 4x² + 4 = 2x + 3 I need to solve this equation. x(x-3) = 40 Would it be -5,-8? Find the x-intercepts Y = x² +4 And yet another one. Y = x² -4x -32 Find the ordered pair for the vortex. Y = 2x² -4x +6 Could it be (4,1)? Solve the specified variable. a/(l-r) for r Could it be r = a/s ? 1 solutions Answer 140227 by user_dude2008(1861)   on 2009-03-17 16:22:12 (Show Source): You can put this solution on YOUR website!"Write standard form and identify a, b, and c. 4x² + 4 = 2x + 3 " 4x² + 4 = 2x + 3 4x² + 4 - 3 = 2x 4x² + 4 - 3 - 2x = 0 4x² - 2x + 1 = 0 Now in standard form: ax^2+bx+c = 0 ---> a = 4, b = -2x, and c = 1 ---------------------------------------------------------- x(x-3) = 40 x^2-3x=40 x^2-3x-40=0 (x-8)(x+5)=0 x = 8 or x = -5 close...off by a sign ---------------------------------- x-intercepts: Y = x² +4 0 = x² +4 x^2 = -4 x = sqrt(-4) x = 2i or x = -2i -------------------------------- x-intercepts: Y = x² -4x -32 0= x² -4x -32 (x-8)(x+4)=0 x=8 or x=-4 ------------------------------------------------ 2x² -4x +6 ---> a=2, b=-4, c=6 x = -b/2a x=-(-4)/(2(2)) x=4/4 x=1 y=2(1)^2-4(1)+6 y=2(1)-4(1)+6 y=2-4+6 y=4 Vertex: (1,4) ... mixed up coordinates --------------------------------------------------- can't solve a/(l-r) since it is not equation
 Percentage-and-ratio-word-problems/187051: Suppose a population of initial size 100 grows at the rate of 8% per year forever. What is the size of the population at the end of year 1? What is the size of the population at the end of year 2? What is the size of the population at the end of year 3? What is the size of the population at the end of year n (for any integer n)? What algebraic equation would you need to solve to find the number of years x that it would take for our population to reach 200? Use a calculator to solve to x. I am truly not even sure how to get started on this problem, any and all help would be greatly appreciated. Thanks1 solutions Answer 140202 by user_dude2008(1861)   on 2009-03-17 13:45:51 (Show Source): You can put this solution on YOUR website!" initial size 100 grows at the rate of 8% per year forever" ---> What is the size of the population at the end of year 1? Ans: 108 people at end of yr 1 ------------------------------------------------------ What is the size of the population at the end of year 2? Ans: 116 people at end of yr 2 ------------------------------------------------------ What is the size of the population at the end of year 3? Ans: 125 people at end of yr 3 ------------------------------------------------------ What is the size of the population at the end of year n? ------------------------------------------------------ find the number of years x that it would take for our population to reach 200? Ans: takes about 9 yrs for pop. to reach 200 people
 Rate-of-work-word-problems/187008: raphael can load a large shipping truck in 15 hours. working together, raphael and jana can load the same truck in 6 hours. how long would it take to load the truck by herself? 1 solutions Answer 140169 by user_dude2008(1861)   on 2009-03-17 00:13:12 (Show Source): You can put this solution on YOUR website!Use equation t(1/rate1 + 1/rate2) = 1 rate1 = raphael's rate = 15 hrs, rate2 = janas rate = x t(1/15+1/x)=1 t is given as t=6 ----> 6(1/15+1/x)=1 1/15+1/x=1/6 2x+30=5x 30=3x x=10 Ans: jana can load the truck in 10 hrs
 Expressions-with-variables/186988: (A squared + A + b)(A squared-A-B)1 solutions Answer 140163 by user_dude2008(1861)   on 2009-03-16 23:46:50 (Show Source): You can put this solution on YOUR website!(A^2 + A + B)(A^2-A-B) (A^2 + A + B)(A^2-(A+B)) Let X=A+B (A^2 + X)(A^2-X) A^4-X^2 A^4-(A+B)^2 A^4-(A^2+2AB+B^2) A^4-A^2-2AB-B^2 Ans: (A^2 + A + B)(A^2-A-B) = A^4-A^2-2AB-B^2
 Exponential-and-logarithmic-functions/187005: 8^3t=32^4t-11 solutions Answer 140162 by user_dude2008(1861)   on 2009-03-16 23:44:03 (Show Source): You can put this solution on YOUR website!8^(3t)=32^(4t-1) 2^(3(3t))=2^(5(4t-1)) 2^(9t)=2^(20t-5) 9t=20t-5 -11t=-5 t=5/11 Ans: t=5/11
 Exponential-and-logarithmic-functions/187004: 3^2-8x= 9^3x+1 1 solutions Answer 140161 by user_dude2008(1861)   on 2009-03-16 23:42:23 (Show Source): You can put this solution on YOUR website!3^(2-8x)= 9^(3x+1) 3^(2-8x)= 3^(2(3x+1)) 3^(2-8x)= 3^(6x+2) ---> 2-8x=6x+2 ---> x=0 Ans: x=0
 Quadratic_Equations/186995: A = 3 pie a^2 solve for a1 solutions Answer 140160 by user_dude2008(1861)   on 2009-03-16 23:40:31 (Show Source): You can put this solution on YOUR website!A = 3pi*a^2 A/(3pi) = a^2 Ans: a = sqrt( A/(3pi) ) or a = -sqrt( A/(3pi) )
 Angles/187001: A diagonal walk through a small rectangular garden 9 meters by 12 meters can be built at $10 per linear meter. How much will the walk cost1 solutions Answer 140159 by user_dude2008(1861) on 2009-03-16 23:39:16 (Show Source): You can put this solution on YOUR website!9^2+12^2=x^2 81+144=x^2 225=x^2 x=sqrt(225) x=15 .... diagonal walk is 15 meters 15 (meters) * ($10/meter) = $150 Ans:$150
 Quadratic_Equations/187002: please solve by factoring. y^2-4y=451 solutions Answer 140158 by user_dude2008(1861)   on 2009-03-16 23:37:21 (Show Source): You can put this solution on YOUR website!y^2-4y=45 y^2-4y-45=0 (y-9)(y+5)=0 y-9=0 or y+5=0 Ans: y=9 or y=-5