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# Recent problems solved by 'xcentaur'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359, >>Next

 Rational-functions/33923: Rationalize the denominator and simplify. √5+1 ------ 2+√21 solutions Answer 20411 by xcentaur(357)   on 2006-04-18 14:00:03 (Show Source): You can put this solution on YOUR website! expand the numerator -xC
 Linear_Equations_And_Systems_Word_Problems/33973: John and Jim needed to meet to discuss changes in a construction project. They were 880 miles apart. If they met after 8 hours and both went the same speed, how fast did each go?1 solutions Answer 20408 by xcentaur(357)   on 2006-04-18 13:49:32 (Show Source): You can put this solution on YOUR website!880 miles=distance 8hours=time speed=distance/time each one travelled half the distance so speed=440/8=55 mph -xC
 Trigonometry-basics/34015: The angular velocity of a merry-go-round is 35 radians/minute. If the diameter is 38 feet, find the linear velocity of a person standing on the very edge of the merry-go-round.1 solutions Answer 20407 by xcentaur(357)   on 2006-04-18 13:48:37 (Show Source): You can put this solution on YOUR website!angular velocity (w)=35 radians/min=35/60 rad/second=0.5833 rad/s diameter=38 feet hence radius (r)=19 feet velocity? v=0.5833(19)=11.0833 =11.1 feet/s(rounding off) -xC
 logarithm/34047: i need help in solving these questions, i do not understand them.1 solutions Answer 20406 by xcentaur(357)   on 2006-04-18 13:40:45 (Show Source): You can put this solution on YOUR website!sure,post the questions and we'll get to them
 Divisibility_and_Prime_Numbers/34044: one quart of paint is exactly enough for two coats of paint on a 9foot by 10 foot wall how many quarts of paint are needed to apply one quart of paint to a 10 foot by 12 foot wall? 1 solutions Answer 20405 by xcentaur(357)   on 2006-04-18 13:39:20 (Show Source): You can put this solution on YOUR website!1 quart ------------ 9(10)=90 ?? quarts ------------ 10(12)=120 cross multiply x(90)=1(120) x=120/90=4/3=1.33 quarts of paint required -xC
 Graphs/34018: 5. Show and explain the process of solving the following application problems using equations: a. A cable 200 ft. long is cut into two pieces so that one piece is 12 ft. longer than the other. How long is each piece? b. A boat travels 24 miles upstream in 3 hours. It then takes 3 hours to go 36 miles downstream. Find the speed of the boat in still water and the speed of the current. c. A service station wishes to mix 40L of a 78% antifreeze solution. How many liters of a 75% solution and a 90% solution should be used in forming the mixture? 1 solutions Answer 20404 by xcentaur(357)   on 2006-04-18 13:37:51 (Show Source): You can put this solution on YOUR website!a. A cable 200 ft. long is cut into two pieces so that one piece is 12 ft. longer than the other. How long is each piece? let the first pc be x ft long then second piece is (x+12) together they make up 200 feet so x+x+12=200 2x+12=200 2x=200-12=188 x=188/2=94 b. A boat travels 24 miles upstream in 3 hours. It then takes 3 hours to go 36 miles downstream. Find the speed of the boat in still water and the speed of the current. let speed of boat in still water be x,and speed of current downstream be y then upstream the speed of the boat will be (y-x) miles per hour distance=24 miles in 3 hours at speed of (y-x) speed=(y-x)=distance/time=24/3=8 speed downstream is (x+y) speed=(x+y)=dstnce/time=36/3=12 so we have 2 equations and 2 variables, y-x=8 AND x+y=12 y=8+x AND y=12-x y=8+x=12-x 8+x=12-x x+x=12-8 2x=4 x=2 so speed of boat is 2 mph y=8+x=10 mph which is speed of current c. A service station wishes to mix 40L of a 78% antifreeze solution. How many liters of a 75% solution and a 90% solution should be used in forming the mixture? let x litres be taken of the 75% solution let y litres be taken of the 90% solution then (x+y)=40 as we need 40litres of the solution so y=40-x now we can write our equation as, x(75%)+y(90%)=40(78%) x(75/100)+y(90/100)=40(78/100) 75x+90y=40(78) 75x+90y=3120 75x+90(40-x)=3120 75x+90(40)-90x=3120 -15x+3600=3120 -15x=3120-3600 -15x=-480 x=32 y=40-x=8 so you need 32 litres of 75% solution,and 8liters of 90% solution Hope this helps, -xC
 logarithm/34026: This question is from textbook college algebra i am having a hard time answering these problems. 1. x=8log(100,10) 2. logx (1/16)=-2 3. log(x)=square root log(x)1 solutions Answer 20400 by xcentaur(357)   on 2006-04-18 13:17:59 (Show Source): You can put this solution on YOUR website!1. we know that OR therefore, so we get, x=8(1/2)=4 2. logx (1/16)=-2 take x to the other side,so we get therefore,x=4 3. log(x)=square root log(x) square both sides, [log(x)]^2=[log(x)] using property of logs we get, 2logx=logx 2logx-logx=0 logx=0 now look at this, log8 to the base 2=*3* so 8=2 raised to *3* instead of 3 if we put 0,instead of 8 we will get 1 so any number raised to zero becomes one,so we get x=1 hope this helps, -xC
 Exponents/33935: 3/4 n=16 2/5 n=30 -7/15 =21/10 n.5/16=15/141 solutions Answer 20396 by xcentaur(357)   on 2006-04-18 13:02:38 (Show Source): You can put this solution on YOUR website!you have provided the data,what is the question?
 Equations/34040: -(x+6)+4x=3(x-1)+71 solutions Answer 20390 by xcentaur(357)   on 2006-04-18 12:35:44 (Show Source): You can put this solution on YOUR website!-(x+6)+4x=3(x-1)+7 opening brackets, -x-6+4x=3x-3+7 3x-6=3x+4 take everything to one side 3x-3x-6-4=0 0-10=0 -10=0 which cannot be true please check your question,then post again -xC
 Linear-equations/34025: what does it mean when it says to write a rule for each function? I have the following x f(x) -1 -9 0 -5 1 -1 2 3 I get 1 for x and 4 for f(x) am I going in the right direction?1 solutions Answer 20389 by xcentaur(357)   on 2006-04-18 12:34:31 (Show Source): You can put this solution on YOUR website!when it says to write a rule for each function, you have to write an expression which will give you the required value for f(x) when you substitute x meaning, x f(x) -1 -9 0 -5 1 -1 2 3 So here you should put (-1) in the expression and you should get (-9) So you would have to multiply by 9 Sample functions are below,please try to find other ways of doing this as well,because the same expression can be written in at least 3 different ways x y f(x) -1 -9 (9x) 0 -5 (x-5) 1 -1 (-x) 2 3 (x-1) -xC
 Linear-equations/34032: This question is from textbook Elementary and Intermediate Algebra how do I solve this one? -1/4x=3/4 1 solutions Answer 20388 by xcentaur(357)   on 2006-04-18 12:27:50 (Show Source): You can put this solution on YOUR website!-(1/4)x=3/4 OR (-1)/4x=3/4 -(1/4)x=3/4 if you mean negative one-fourth of x,then we get, -1x=3 [multiplying through out by 4] then x=-3 if you mean -1x divided by 4,then we get, -1x=(3/4)*4 -1x=3 x=-3 luckily both answers work out to the same -xC
 Volume/33966: A box has a volume of 7500 cm3 and a surface area of 2600cm2. what are the length, width, and height of the box?1 solutions Answer 20387 by xcentaur(357)   on 2006-04-18 12:27:40 (Show Source): You can put this solution on YOUR website!let length be x cm,breadth be y cm,height be z cm then volume=x*y*z=7500 then surface area=2(xy*yz*zx)=2600 We only get 2 equations,please check your question for any missing data or assumptions you are required to make,and post again -xC
 Linear-equations/34037: This question is from textbook how do I get x alone to solve it? 3(x-4)=2(x-8)+5x1 solutions Answer 20386 by xcentaur(357)   on 2006-04-18 12:22:06 (Show Source): You can put this solution on YOUR website!3(x-4)=2(x-8)+5x open the brackets 3x-12=2x-16+5x 3x-12=7x-16 taking everything to one side 3x-12-7x+16=0 remember on taking terms to the other side,their sign reverses now we get -4x+4=0 -4x=-4 x=1 xC
 Functions/33240: Please help: If g(x)= 2x^2-5x-7 Find g(-1), g(2), g(-3), g(4) Thanks1 solutions Answer 19635 by xcentaur(357)   on 2006-04-11 01:46:38 (Show Source): You can put this solution on YOUR website!g(x)= 2x^2-5x-7 to find g(-1), substitute x=-1 so we get g(-1)=2(-1)^2-5(-1)-7(-1) =2(1)+5+7=14 g(2)=2(4)-5(2)-7=8-5-10=-7 and so on -xC
 Linear_Equations_And_Systems_Word_Problems/33015: For some reason I can not set up these kind of word problems: According to data from the US dept of defense and congressional research service, the estimated annual cost y (in thousands of dollars) per active duty service member in the us armed forces in year x is given by the equation: 6000x-2000y+136000=0 (4< x < 18) where x=4 corresponds to 1994. find the year in which the estimated annual cost per service member is (a) \$92,000 (b) 110,000 -i have tried setting up the equation by substituting 4 for x and then entering both equations in my TI 83. I believe it's an intersection answer between two equations, however, i am not getting anywhere and i have attemped four other similar questions hoping i something would click. There are also no examples in the text i am using to assist. Thank you for any help you may provide. erin mcavoy1 solutions Answer 19481 by xcentaur(357)   on 2006-04-09 16:50:01 (Show Source): You can put this solution on YOUR website!6000x-2000y+136000=0 (4< x < 18) where x=4 corresponds to 1994 It reduces to y=3x+68. x=4,y=3(4)+68=12+68=80 x=5,y=3(5)+68=15+68=83 x=6,y=86 x=7,y=89 x=8,y=92------------->(a) x=9,y=95 x=10,y=98 x=11,y=101 x=12,y=104 x=13,y=107 x=14,y=110----------->(b) x=15,y=113 x=16,y=116 x=17,y=119 x=18,y=122 If you substitute x=0,we get y=68.Multiply this by 1000 and we get a credible figure,considering it as 1990. Then for x=18,y=122 ie in the year 2008, a figure of \$122000 seems to make sense. That would make 1998 and 2004 your answers,though of course we have no logical reasoning to back this up. If this is a valid question,and you do manage to solve this,drop a mail at: xcentaur[at]hotmail[dot]com Hope this helps, xC
 Expressions-with-variables/33029: -a^2+9a-2a^2-9-10a1 solutions Answer 19477 by xcentaur(357)   on 2006-04-09 16:15:22 (Show Source): You can put this solution on YOUR website!-a^2+9a-2a^2-9-10a group like terms (-a^2-2a^2)+(+9a-10a)+(-9) -3a^2-a-9 xC
 Numeric_Fractions/33050: This question is from textbook strategies for problem solving x+4=t over 71 solutions Answer 19476 by xcentaur(357)   on 2006-04-09 16:15:19 (Show Source): You can put this solution on YOUR website!x+4=t over 7 x+4=t/7 7(x+4)=t 7x+28=t 7x+28-t=0 xC
 Functions/32891: Hi I am having some trouble with this problem from my College pre-calculus class. Given the following rational function, Complete each of the following: a. Find the zeros of the function. b. Find the y-intercepts. c. Find the horizontal and vertical asymptotes. 1 solutions Answer 19475 by xcentaur(357)   on 2006-04-09 16:13:14 (Show Source): You can put this solution on YOUR website! Hi I am having some trouble with this problem from my College pre-calculus class. Given the following rational function, Complete each of the following: a. Find the zeros of the function. b. Find the y-intercepts. c. Find the horizontal and vertical asymptotes. Thats all well and good,but what's the function? If you'd like a more general answer,please post again or try Google -xC
 Radicals/33042: (2sqrt5-2sqrt3)(sqrt10+sqrt6)1 solutions Answer 19474 by xcentaur(357)   on 2006-04-09 16:12:46 (Show Source): You can put this solution on YOUR website!(2sqrt5-2sqrt3)(sqrt10+sqrt6) opening the brackets, -xC
 Radicals/33045: 5/sqrt7+sqrt31 solutions Answer 19473 by xcentaur(357)   on 2006-04-09 16:07:54 (Show Source): You can put this solution on YOUR website!"5/sqrt7+sqrt3" do you mean, OR Please check your question, and post again -xC
 Polynomials-and-rational-expressions/32923: This question is from textbook algebra Solve the Problem... Five divided by the difference of a number and 7 equals the quotient of 10 and the sum of the number and 6. Find the number.1 solutions Answer 19472 by xcentaur(357)   on 2006-04-09 16:06:49 (Show Source): You can put this solution on YOUR website!let the number be x Five divided by the difference of a number and 7 equals the quotient of 10 and the sum of the number and 6 5/(x-7)=10/(x+6) cross multiply 5(x+6)=10(x-7) 5x+30=10x-70 100=5x x=20 xC
 Linear-equations/32901: This question is from textbook elementary algebra how do solve by graphing: x+y=-1 3x-y=-71 solutions Answer 19470 by xcentaur(357)   on 2006-04-09 15:55:29 (Show Source): You can put this solution on YOUR website!x+y=-1......[1] 3x-y=-7.....[2] Take the first equation,substitute x=0,-1,1,2,-2 and so on, and calculate y you will have all these values of x and y as pairs x=0,y=-1 x=-1,y=0 x=1,y=-2 and so on plot these on the graph as (x,y)=(0,-1),(-1,0),(1,-2) etc Then draw a straight line through the points,connecting them Repeat for the second equation The lines will meet at a particular point.From the graph paper,look up the co-ordinates of the point,and there you have your solution. It should work out to (x,y)=(-2,1) Hope this helps, xC
 Radicals/33043: (sqrt2+3sqrt3)(sqrt12-4sqrt8)1 solutions Answer 19469 by xcentaur(357)   on 2006-04-09 15:49:41 (Show Source): You can put this solution on YOUR website!(a+b)(c-d) = ac-ad+bc-bd Opening the brackets we get, xC
 Linear_Algebra/33030: The linear equation y = 5 graphs as a __________________ line. Can you explain how I solve this please? Thanks Penalope1 solutions Answer 19467 by xcentaur(357)   on 2006-04-09 15:45:46 (Show Source): You can put this solution on YOUR website!y=5 means that for all values of x,y will take on value '5' meaning x could be 0,-1,1,2,-2,etc but y will always be 5 try to imagine this on a graph paper if you manage to,you will see this becomes a straight line passing through the y-axis at the point y=5 Like this, So it would be a straight line parallel to the x-axis passing through point 5 on the positive y-axis Hope this helps, xC
 Expressions-with-variables/33032: m+5n-(3m+4n)1 solutions Answer 19466 by xcentaur(357)   on 2006-04-09 15:43:36 (Show Source): You can put this solution on YOUR website!m+5n-(3m+4n) m+5n-3m-4n -2m+n
 Expressions-with-variables/33033: 7p+q-(7q-6p)1 solutions Answer 19465 by xcentaur(357)   on 2006-04-09 15:41:13 (Show Source): You can put this solution on YOUR website!7p+q-(7q-6p) 7p+q-7q+6p 13p-6q
 Expressions-with-variables/33031: -b^2-b+7b+2b^2-6b1 solutions Answer 19464 by xcentaur(357)   on 2006-04-09 15:41:12 (Show Source): You can put this solution on YOUR website!-b^2-b+7b+2b^2-6b group like terms (-b^2+2b^2)+(-b+7b-6b) b^2+0 b^2 xC
 Expressions-with-variables/33036: -2(5u+v)-v1 solutions Answer 19462 by xcentaur(357)   on 2006-04-09 15:36:06 (Show Source): You can put this solution on YOUR website!-2(5u+v)-v -10u-2v-v -10u-3v
 Linear_Algebra/33034: Can you help solve this and explain how? Find the midpoint between these points: (2, 3) and (8, 1) Thank you. Penalope 1 solutions Answer 19461 by xcentaur(357)   on 2006-04-09 15:35:41 (Show Source): You can put this solution on YOUR website!(2, 3) and (8, 1) ==> (a,b) and (c,d) Midpoint is given by: ( (a+c)/2,(b+d)/2 ) So we get, (5,2) Hope this helps, xC
 Expressions-with-variables/33035: 7r+3(s-2r)1 solutions Answer 19460 by xcentaur(357)   on 2006-04-09 15:34:13 (Show Source): You can put this solution on YOUR website!7r+3(s-2r) 7r+3s-6r r+3s