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Recent problems solved by 'fractalier'

fractalier answered: 2101 problems
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 expressions/39315: simplify 4x-5(x-7) a -x + 35 b) -x-35 c) -x-7 d) 9x+351 solutions Answer 24996 by fractalier(2101)   on 2006-05-26 12:27:07 (Show Source): You can put this solution on YOUR website!4x - 5(x-7) = 4x - 5x + 35 = -x + 35 Choice a.
 expressions/39538: Simply each of the following expressions where possible (pg. 150) I can't really type it out on my computer but the numbers are on the left side of the letter. 6x2y3 + 9x2y3 ________________________________ 3x2y2 1 solutions Answer 24995 by fractalier(2101)   on 2006-05-26 12:24:27 (Show Source): You can put this solution on YOUR website!From (6x^2y^3 + 9x^2y^3) / 3x^2y^2 we can combine the numerator and cancel where we can...we get (6x^2y^3 + 9x^2y^3) / 3x^2y^2 = 15x^2y^3 / 3x^2y^2 = 5y
 Equations/39428: 2y/x^2+2x+1 + x/x^2-11 solutions Answer 24993 by fractalier(2101)   on 2006-05-26 12:21:56 (Show Source): You can put this solution on YOUR website!We factor denominators first and get 2y/x^2+2x+1 + x/x^2-1 = 2y / (x+1)^2 + x / (x+1)(x-1) The lowest common denominator is then (x-1)(x+1)^2 We convert both fractions to that denominator and combine and get 2y / (x+1)^2 + x / (x+1)(x-1) = 2y(x-1) / (x-1)(x+1)^2 + x(x+1) / (x-1)(x+1)^2 = [2y(x-1) + x(x+1)] / (x-1)(x+1)^2 = No further significant simplification can be done...
 Rational-functions/39541: The cost of producing a number of items x is given by C=mx+b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item). (a) if the fixed cost is \$40 and the variable cost is \$10, write the cost equation. (b) Graph the cost equation1 solutions Answer 24991 by fractalier(2101)   on 2006-05-26 12:17:15 (Show Source): You can put this solution on YOUR website!To get the cost equation, just plug in for m and b to get C = 10x + 40 To graph it, go to the point (0, 40) and plot a point. From that point, we have a slope of 10. We go up 10 and over 1, and plot another point. Then draw a line thru the points.
 Rational-functions/39542: Find the slope of the line through the given points. (2,4)and (6,-3)1 solutions Answer 24989 by fractalier(2101)   on 2006-05-26 12:14:59 (Show Source): You can put this solution on YOUR website!slope m is found by m = (y2 - y1) / (x2 - x1) m = (-3 - 4) / (6 - 2) m = -7/4
 Trigonometry-basics/39543: why should we take sin theta as opposite/hypotenuse is there any proof for it can u please send it to me on my email address1 solutions Answer 24987 by fractalier(2101)   on 2006-05-26 12:12:49 (Show Source): You can put this solution on YOUR website!It is merely how we define the term sin(theta). It is not a proof, it is a definition.
 Rational-functions/39544: find the constant of variation k. m varies directly with n; m=144 when n=81 solutions Answer 24986 by fractalier(2101)   on 2006-05-26 12:11:43 (Show Source): You can put this solution on YOUR website!We write the direct variation as m = kn then plug in m and n 144 = 8k and thus k = 16
 Probability-and-statistics/39324: what measure is always the same as the a. 50th percentile? b. 25th percentile? c. 75th percentile?1 solutions Answer 24978 by fractalier(2101)   on 2006-05-26 10:33:10 (Show Source): You can put this solution on YOUR website!In statistics, the 50th percentile corresponds to the median, the 25th percentile is the 1st quartile, and 75th percentile is the 3rd quartile...
 logarithm/39444: Solve 2/3^2x = 12.1 solutions Answer 24977 by fractalier(2101)   on 2006-05-26 10:28:06 (Show Source): You can put this solution on YOUR website!It is not clear exactly what the problem is but I assume you mean 2 / (3^2x) = 12 I will show you this one...if you meant something else, please repost... Okay, from 2 / (3^2x) = 12 we can rearrange the terms and get 3^2x = 2/12 = 1/6 take the log of both sides log 3^2x = log 1/6 now use the power rule 2x log 3 = - log 6 and x = (- log 6) / (2 log 3)
 Equations/39470: Solve each equation. identify each equation as a conditional equation, an inconsistent equation, or an identity. 1/2b - 1/2=1/4b1 solutions Answer 24976 by fractalier(2101)   on 2006-05-26 10:22:40 (Show Source): You can put this solution on YOUR website!Let us multiply all by 4b to clear the fractions, so we get 1/2b - 1/2 = 1/4b 4b[1/2b - 1/2 = 1/4b] 2 - 2b = 1 now subtract 2, then divide by -2 and get -2b = -1 b = 1/2 Must be a conditional equation, since an inconsistent equation has no solution, and an identity has an infinite number of solutions...
 Sequences-and-series/39510: write out the term of the geometric sequence that satisfies the given conditions. a1=-9,r=-9/10,n=51 solutions Answer 24975 by fractalier(2101)   on 2006-05-26 10:16:53 (Show Source): You can put this solution on YOUR website!Okay, our first tern is -9. After that, we just multiply each term by the common ratio, which is in this case -9/10, until we get 5 terms...so we get -9 81/10 -729/100 6561/1000 -59049/10000
 Linear-systems/39511: solve the equation 6-17/z -3/z^2=01 solutions Answer 24974 by fractalier(2101)   on 2006-05-26 10:14:20 (Show Source): You can put this solution on YOUR website!Let us clear fractions by multiplying all by z^2, so from 6 - 17/z - 3/z^2 = 0 we get 6z^2 - 17z - 3 = 0 which we can factor into (6z + 1)(z - 3) = 0 and solve, giving us z = -1/6 and z = 3
 absolute-value/39535: One of our sample problems is.. and i'm lost: Identify the property that is used 5 (6+7)=5+ (7+6)1 solutions Answer 24973 by fractalier(2101)   on 2006-05-26 10:10:44 (Show Source): You can put this solution on YOUR website!I imagine that you meant to write 5 + (6 + 7) = 5 + (7 + 6) If that is the case, then we are demonstrating the commutative property of addition, a property which states that order doesn't matter when we add numbers...
 Average/39534: Question: 6.(5+4) = What I'm thinking: I'm thinking it is 6 times 9 = 54 1 solutions Answer 24972 by fractalier(2101)   on 2006-05-26 10:08:16 (Show Source): You can put this solution on YOUR website!Yes. If the period after the six represents multiplication, as in 6*(5+4) = 6*9 = 54
 Geometric_formulas/39514: The quotient when 3 more than a number is divided by less than that same number Write each of the following geometric expressions using the given symbols If you can please help me.I got this problem wrong,and I would like to know how to do it correct. Thank you1 solutions Answer 24971 by fractalier(2101)   on 2006-05-26 10:06:35 (Show Source): You can put this solution on YOUR website!Just posted this solution...
 Travel_Word_Problems/39532: The quotient when 3 more than a number is dived by 3 less than that same number. Write each of the following geometric expressions using the given symbols1 solutions Answer 24970 by fractalier(2101)   on 2006-05-26 10:05:41 (Show Source): You can put this solution on YOUR website!Just posted this solution...
 Length-and-distance/39533: The quotient when 3 more than a number is divided by 3 less than that same number. Write each of the following geometric expressions using the given symbols1 solutions Answer 24969 by fractalier(2101)   on 2006-05-26 10:03:41 (Show Source): You can put this solution on YOUR website!Let the unknown number be x. Then we have (x + 3) / (x - 3)
 absolute-value/39530: The sum m & n ,divided by the difference m & n1 solutions Answer 24968 by fractalier(2101)   on 2006-05-26 10:02:22 (Show Source): You can put this solution on YOUR website!Just posted this solution...
 absolute-value/39531: The sum m & n ,divided by the difference of m & n1 solutions Answer 24967 by fractalier(2101)   on 2006-05-26 10:01:30 (Show Source): You can put this solution on YOUR website!You would express this as (m + n) / (m - n)
 Equations/39515: It is estimated that the Earth is losing 4000 species of plants and animals per year. If S represents the number of species living last year year, how many species are on Earth this year.. 1 solutions Answer 24966 by fractalier(2101)   on 2006-05-26 10:00:49 (Show Source): You can put this solution on YOUR website!Just posted this solution...
 Functions/39517: It is estimated that the Earth is losing 4000 species of plants and animals per year. If S represents the number of species living last year year, how many species are on Earth this year.. 1 solutions Answer 24965 by fractalier(2101)   on 2006-05-26 09:57:57 (Show Source): You can put this solution on YOUR website!Look at it this way... No matter how many species there were last year, you would be subtracting 4000 to get this year's number...if there were 90,000 last year, you'd have 86,000 this year... Thus if there were S species last year, there would be S - 4000 this year...
 Inequalities/39518: This question is from textbook . Fill in the chart given this linear equation: 2x + y = 42. x y -2 -1 0 1 21 solutions Answer 24964 by fractalier(2101)   on 2006-05-26 09:55:47 (Show Source): You can put this solution on YOUR website!Just posted this solution...
 Travel_Word_Problems/39529: Suppose that the tempature outside is dropping at a constant rate.At noon, the tempature is 70 F,and it drops to 58F at 5pm ..How much did the tempature change each hour? I thought it was half hour ,but i was wrong.Sorry the 5 did not come up in my other post. 1 solutions Answer 24963 by fractalier(2101)   on 2006-05-26 09:55:13 (Show Source): You can put this solution on YOUR website!Well, we can logic it out... If the temperature drops from 70 to 58, it dropped 12 degrees. If it took 5 hours, then we divide 12 degress by 5 hours, and get 12 / 5 = 2.4 degrees per hour We can look at it another way too... (70 - 58) / (5 - 0) = 2.4
 Inequalities/39527: This question is from textbook Fill in the chart given this linear equation: 2x + y = 42. x y -2 -1 0 1 21 solutions Answer 24962 by fractalier(2101)   on 2006-05-26 09:51:53 (Show Source): You can put this solution on YOUR website!To fill in these values, merely substitute the various x's into the equation and determine the y's... 2x + y = 42 x_____y -2____46 -1____44 0_____42 1_____40 2_____38 See the pattern? Linear equations are always like this...
 Inequalities/39528: This question is from textbook 1. Solve for x: 2(x + 3) > 201 solutions Answer 24961 by fractalier(2101)   on 2006-05-26 09:49:31 (Show Source): You can put this solution on YOUR website!We wish to isolate x by "undoing" that which is being done to it...so from 2(x + 3) > 20 divide by 2 and get x + 3 > 10 and subtract 3 x > 7 and we're done.
 Numbers_Word_Problems/39408: The sum of two numbers is 100. One number is 5 less than twice the other. Find the numbers.1 solutions Answer 24884 by fractalier(2101)   on 2006-05-25 18:10:11 (Show Source): You can put this solution on YOUR website!Let the two numbers be x and y. Thus x + y = 100 and x = 2y - 5 Now substitute for x in the first equation and get 2y - 5 + y = 100 3y - 5 = 100 3y = 105 y = 35 and since they add to 100, x = 65
 Rational-functions/39438: what's the answer to this problem? 10y2+15y divded by 35y2-5y (the 2's beside the y's mean the y's are squared)1 solutions Answer 24881 by fractalier(2101)   on 2006-05-25 17:59:42 (Show Source): You can put this solution on YOUR website!(10y^2 + 15y) / (35y^2 - 5y) we can factor both and get (10y^2 + 15y) / (35y^2 - 5y) = 5y(2y + 3) / 5y(7y - 1) now notice the 5y's cancel, leaving us (2y + 3) / (7y - 1)
 Polynomials-and-rational-expressions/39451: how do you rationalize(sqrt x+5)-3/ x-4?1 solutions Answer 24880 by fractalier(2101)   on 2006-05-25 17:57:36 (Show Source): You can put this solution on YOUR website!Normally when we use the term rationalize, it usually refers to a denominator that is irrational or complex, but the way you have given the expression, (sqrt x+5)-3/ x-4 it appears that the numerator is irrational. This is acceptable the way it is. If we try to rationalize it, the denominator will become irrational and unacceptable.
 logarithm/39441: Solve e^2x = 5.1 solutions Answer 24878 by fractalier(2101)   on 2006-05-25 17:52:35 (Show Source): You can put this solution on YOUR website!From e^2x = 5 take the ln of both sides ln e^2x = ln 5 2x = ln 5 x = (1/2)ln 5
 logarithm/39443: Solve -4e^2x + 3 = -51 solutions Answer 24875 by fractalier(2101)   on 2006-05-25 17:09:11 (Show Source): You can put this solution on YOUR website!From -4e^2x + 3 = -5 subtract three, then divide by minus four... -4e^2x = -8 e^2x = 2 take ln 2x = ln 2 x = (1/2)*ln 2
 Travel_Word_Problems/39410: A cyclist rode 1 mile in 3 minutes with the wind and returned in 4 minutes against the wind. Find his speed without the wind.1 solutions Answer 24867 by fractalier(2101)   on 2006-05-25 13:39:59 (Show Source): You can put this solution on YOUR website!The equation we use in these problems is D = RT, distance = rate times time. With the wind, D = 1, T = 3 and his rate is R + w, w being the wind. Against it, D = 1, T = 4, and his rate is R - w. So we have 3(R + w) = 1 4(R - w) = 1 from which we get (R + w) = 1/3 (R - w) = 1/4 adding equations we get 2R = 7/12 and R = 7/24 miles per minute = 60(7/24) = 17.5 miles per hour