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# Recent problems solved by 'fractalier'

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 Polynomials-and-rational-expressions/38402: find the slope of the line 10x-2y=601 solutions Answer 23893 by fractalier(2101)   on 2006-05-18 12:55:57 (Show Source): You can put this solution on YOUR website!If we can get it into y = mx + b form, we can read the slope m... so from 10x - 2y = 60, we solve for y -2y = -10x + 60 y = 5x - 30 so the slope is 5. Another way is to merely look at -a/b from the original equation...that gives 5 also...
 Polynomials-and-rational-expressions/38401: classify the polynomial 4x to the second power +31 solutions Answer 23890 by fractalier(2101)   on 2006-05-18 12:51:08 (Show Source): You can put this solution on YOUR website!4x^2 + 3 is a second order binomial
 logarithm/38399: If a bank compounds continuous, then the formula becomes simpler, that is A=Pe^rt where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Use 20,000 at for 3 years at a rate of 8 percent. This is what I have so far: A= 20,000e^.08*2 A= 20,000e^.16 = ? I am lost as to finding the answer, I don't understand what to do with e. Could you please help me? Thanks, Christine1 solutions Answer 23889 by fractalier(2101)   on 2006-05-18 12:49:55 (Show Source): You can put this solution on YOUR website!Okay from A=Pe^rt we plug in what we know (using three years) A = 20000(e^(.08*3)) A = 20000e^.24 Now use your calculator to evaluate e^.24 as 1.271, then multiply it by 20000 to get the final answer A = \$25424.98
 Equations/38398: x SQUARED(2) + 7 = 21 CAN YOU HELP ME SOLVE THIS EQUATION? ALSO COULD YOU EXPLAIN HOW YOU WOULD KNOW IF YOU SUBTRACT, DIVIDE OR ADD TO THE OTHER SIDE?1 solutions Answer 23887 by fractalier(2101)   on 2006-05-18 12:43:43 (Show Source): You can put this solution on YOUR website!The general idea is to isolate x on one side of the equation and put everything else on the other side...to do that, you normally try to UNDO what is being done to x...so in this problem x^2 + 7 = 21 you want to undo the +7 by subtracting 7 from both sides first, giving us x^2 = 14 now you want to take the square root of both sides. This undoes the squaring of x, and we get x = ± sqrt(14) Two answers, a plus and a minus square root of 14.
 Polynomials-and-rational-expressions/38392: I have a test tomorrow and these questions will be dominant on the test (12x to the exponent of 3 + 15x to the exponenet of 3)(+4x +5) I know the answer because my teacher gave it to me but I dont know how to get the answer. Is there anyway you can walk me through the steps?1 solutions Answer 23885 by fractalier(2101)   on 2006-05-18 12:40:33 (Show Source): You can put this solution on YOUR website!If what you mean is (12x^3 + 15x^3)(4x + 5), you can add the first two terms together before multiplying, and get 27x^3(4x + 5) = 108x^4 + 135x^3 Remember that when you multiply like bases, you add the exponents...
 Divisibility_and_Prime_Numbers/38391: What is the product of 126 and 6041 solutions Answer 23883 by fractalier(2101)   on 2006-05-18 12:37:31 (Show Source): You can put this solution on YOUR website!126 x 604 = 76104
 Divisibility_and_Prime_Numbers/38396: How do you change 28/9 to a mixed or whole number.1 solutions Answer 23882 by fractalier(2101)   on 2006-05-18 12:35:59 (Show Source): You can put this solution on YOUR website!28/9 = 3 1/9 Every fraction is really a division problem in disguise...so you divide 28 by 9 and get 3 remainder 1, or 3 1/9.
 Divisibility_and_Prime_Numbers/38395: How do you change 3 2/5 to an improper fraction?1 solutions Answer 23881 by fractalier(2101)   on 2006-05-18 12:34:25 (Show Source): You can put this solution on YOUR website!3 2/5 becomes 17/5 this way... You say 3 times 5 plus 2, all over the 5...
 Divisibility_and_Prime_Numbers/38394: Can 89/13, 151/11 or 223/23 be simplivied?1 solutions Answer 23880 by fractalier(2101)   on 2006-05-18 12:32:56 (Show Source): You can put this solution on YOUR website!Well they are all reduced to lowest terms, but improper fractions...if mixed numbers are required, they become 6 11/13, 13 8/11, and 9 16/23 respectively.
 Divisibility_and_Prime_Numbers/38393: Can you list the factors of the number 8?1 solutions Answer 23879 by fractalier(2101)   on 2006-05-18 12:30:53 (Show Source): You can put this solution on YOUR website!Sure...what numbers go into 8 evenly? 1, 2, 4, and 8
 Exponential-and-logarithmic-functions/38390: This question is from textbook Please help me with these four questions in the review section. Find the value of v in each equation. 18. log(27) 3=v 20. log(4) 1/16=v Write each expression as a single logarithm. Then simplify, if possible 24. log(5) 3 + log(5) 6 + log(5) 25. log 6 - log 3 + 2 log 7 Note: (number in para is the base)1 solutions Answer 23878 by fractalier(2101)   on 2006-05-18 12:29:56 (Show Source): You can put this solution on YOUR website!For log(27) 3 = v, it becomes 27^v = 3 and v = 1/3 For log(4) 1/16 = v, it becomes 4^v = 1/16 and v = -2 Cannot do log(5) 3 + log(5) 6 + log(5) ??? because of the missing piece, but log 6 - log 3 + 2 log 7 = log (6/3 * 7^2) = log 98
 Divisibility_and_Prime_Numbers/38223: Divide. Write result in simplest form: 3/4 divide by 9 5 1/3 divided by 2 2/5 2 problems to resolve Thanks1 solutions Answer 23876 by fractalier(2101)   on 2006-05-18 12:25:32 (Show Source): You can put this solution on YOUR website!3/4 divided by 9 is equal to 3/4 times 1/9 = 3/36 = 1/12 and 5 1/3 divided by 2 2/5 = 16/3 divided by 12/5 = 16/3 * 5/12 = 80/36 = 20/9 = 2 2/9
 Quadratic_Equations/38389: What is the largest rectangular area that can be enclosed with 30 feet of fencing? I need the dimensions.1 solutions Answer 23875 by fractalier(2101)   on 2006-05-18 12:22:52 (Show Source): You can put this solution on YOUR website!Turns out that the rectangle is a square, 7.5 feet on a side, with an area of 56.25 square feet.
 Rectangles/38388: Is the formula used to figure out the cube of a carton - length x width x height divided by 1726?1 solutions Answer 23873 by fractalier(2101)   on 2006-05-18 12:17:43 (Show Source): You can put this solution on YOUR website!If you mean finding the volume of a carton and changing cubic inches into cubic feet, you would divide L x W x H by 1728, not 1726.
 Rectangles/38371: The area of a rectangle is 64 in. sq. If the area is increased by 25% what is the dimension of the new rectangle?1 solutions Answer 23872 by fractalier(2101)   on 2006-05-18 12:15:33 (Show Source): You can put this solution on YOUR website!This cannot be answered as asked. We know the new area is 80. We can say that if the proportion of the new rectangle is the same as the old rectangle, then the length and width have both been increased by a factor of sqrt(5)/2... We need more information. Is this a square?
 Miscellaneous_Word_Problems/38384: The decibel level of sound is given by D= 10log ( I/10^−12), where I is the sound intensity measured in watts per square meter. Find the decibel level of a whisper at an intensity of 5.4 × 10-10 watts per1 solutions Answer 23871 by fractalier(2101)   on 2006-05-18 12:11:44 (Show Source): You can put this solution on YOUR website!Okay from D = 10log (I/10^-12) we plug in the intensity I we are given to find D... D = 10 * log(5.4 × 10^-10 / 10^-12) D = 10 * log(5.4 x 10^2) D = 10 * 2.732 D = 27.32 decibels
 logarithm/38387: Use this formula logb a= loga/ logb, find log2 1000. I don't understand how you do this equation. I tried many different things and nothing works. Thanks, Christine1 solutions Answer 23870 by fractalier(2101)   on 2006-05-18 12:07:02 (Show Source): You can put this solution on YOUR website!This is what is called "the change of base" formula...logb a= loga/ logb...the logs on the right side are to the base 10 (but could really be any base we choose) In this case, log2 1000, our b = 2 and our a = 1000, so that log2 1000 = log 1000 / log 2 log2 1000 = 3 / .30103 = 9.97 or almost 10 and that makes sense since 2^10 = 1024 and just about 1000
 Numbers_Word_Problems/38386: find a number such that 25 more than half the number is 60.1 solutions Answer 23869 by fractalier(2101)   on 2006-05-18 12:02:45 (Show Source): You can put this solution on YOUR website!If x is the number, we have 25 + (1/2)x = 60 Now subtract 25 and then multiply by 2, giving us (1/2)x = 35 x = 70
 Rational-functions/38383: This question is on our homework and I have no idea how to do it: If a fraction has the value of 2/3 and the numerator is increased by 10, and the denomonator is increased by 20, the new fraction has the value of 3/5. Find the original fraction. I don't even understand the question. 1 solutions Answer 23868 by fractalier(2101)   on 2006-05-18 12:00:29 (Show Source): You can put this solution on YOUR website!I hate when that happens...but seriously folks... Let x be the original numerator. Let y be the original denominator. Then we can say that x/y = 2/3 Now look at the second set of facts... (x + 10) / (y + 20) = 3/5 If we cross-multiply both equations we can solve them...like this... 2y = 3x 5(x + 10) = 3(y + 20) Now y = 3/2 x and we can substitute that into the second equation... 5(x + 10) = 3(3/2 x + 20) 5x + 50 = 9/2 x + 60 Now subtract 9/2 x from both sides and then subtract 50 from both sides... 1/2 x + 50 = 60 1/2 x = 10 and thus x = 20 Looking at the very first equation, if x = 20, y = 30 and the original fraction is 20/30
 percentage/38378: A canary diamond sells for \$49,000 and is marked up 55% on the selling price. What is the markup amount and cost?1 solutions Answer 23865 by fractalier(2101)   on 2006-05-18 11:34:46 (Show Source): You can put this solution on YOUR website!Selling price = cost + markup, but markup = markup rate * cost, Selling price = cost + markup rate * cost...now plug in 49000 = c + .55c = 1.55c c = \$49000 / 1.55 c = \$31612.90 markup = \$49000 - c = \$49000 - \$31612.90 = \$17387.10
 Radicals/38242: Find the following product and express answer in simplest radical form. All variables represent non negative real numbers. ((SQRT of 17a) + (SQRT of 7y))((SQRT of 17a)-(SQRT of 7y))1 solutions Answer 23864 by fractalier(2101)   on 2006-05-18 11:26:40 (Show Source): You can put this solution on YOUR website!The problem [sqrt(17a) + sqrt(7y)] * [sqrt(17a) - sqrt(7y)] is merely a complicated sum times a difference problem...which is of the form (a+b)(a-b) = a^2 - b^2 Same thing here... [sqrt(17a) + sqrt(7y)] * [sqrt(17a) - sqrt(7y)] = 17a - 7y
 percentage/38375: A bottle of perfume sells for \$84.97 and costs the merchant \$25. What is the markup rate?1 solutions Answer 23863 by fractalier(2101)   on 2006-05-18 11:18:55 (Show Source): You can put this solution on YOUR website!Selling price = cost + markup But markup = markup rate * cost, thus Selling price = cost + (markup rate * cost) Now plug in 84.97 = 25 + 25r 59.97 = 25r r = 59.97 / 25 or almost 2.4, which is 240%
 percentage/38376: A coconut costs the merchant .15 and is marked up 75%. Find the selling price. 1 solutions Answer 23862 by fractalier(2101)   on 2006-05-18 11:13:29 (Show Source): You can put this solution on YOUR website!If it is marked up 75%, it is marked up 75% of the original cost, thus the final selling price is the cost plus the markup... Selling price = Cost + markup Selling price = .15 + (.75)(.15) Selling price = .15 + .1125 Selling price = .2625
 Permutations/38372: I have two bags of marbles. One bag has a green, yellow and blue marble. The other bag has a blue,yellow,white and red marble. What is the probability of picking a blue marble from both bags?1 solutions Answer 23861 by fractalier(2101)   on 2006-05-18 11:09:50 (Show Source): You can put this solution on YOUR website!Since you must pick a blue from both bags to be "successful," you must multiply the individual probabilities...so 1/3 * 1/4 = 1/12, your answer.
 Age_Word_Problems/38373: Bob's father is 3 times old as Bob. 4 years ago, he was 4 times older. How old is Bob?1 solutions Answer 23860 by fractalier(2101)   on 2006-05-18 11:04:39 (Show Source): You can put this solution on YOUR website!Just answered this one, see below...
 Age_Word_Problems/38374: Bob's father is 3 times old as Bob. 4 years ago, he was 4 times older. How old is Bob?1 solutions Answer 23859 by fractalier(2101)   on 2006-05-18 11:02:32 (Show Source): You can put this solution on YOUR website!Always assign variables in age problems in the NOW. Let B be Bob's age NOW. Let F be the father's age NOW. From the problem, F = 3B F - 4 = 4(B - 4) Substituting, we get 3B - 4 = 4B - 16 -B = -12 and B = 12
 Trigonometry-basics/38366: Can someone please help: Solve the equations: x-2y+z =7 2x-5y+2z =17 -3x+7y+5z =-32 Thanks,1 solutions Answer 23858 by fractalier(2101)   on 2006-05-18 10:59:13 (Show Source): You can put this solution on YOUR website!It is a bit difficult to explain the entire procedure, but in essence what you do is to eliminate the same variable from pairs of equations, via the linear combination method. You want to "boil" three equations and three unknowns down to two equations and two unknowns...for example, from x-2y+z =7 2x-5y+2z =17 -3x+7y+5z =-32 we can double the first equation and subtract it from the second one, eliminating x...repeat that procedure with the first and third equation, etc... You will find the solution x = 2, y = -3, and z = -1
 Exponential-and-logarithmic-functions/38293: Could you help me solve this problem the directions is multiply then simplify each expression The Expression is: (3x+2)(x^-5x+2)1 solutions Answer 23857 by fractalier(2101)   on 2006-05-18 10:52:59 (Show Source): You can put this solution on YOUR website!What we do is multiply each term in the first expression times each term in the second expression...so we have (3x + 2)(x^2 - 5x + 2) = 3x^3 - 15x^2 + 6x + 2x^2 - 10x + 4 Now collect like terms... = 3x^3 - 13x^2 - 4x + 4 and we're done...
 Angles/38259: if one angle measures 140 degrees, what is the probability that if you draw a line inbetween that both angles will be acute? My first answer was 89:140, but i'm not sure if i worked it correctly.1 solutions Answer 23856 by fractalier(2101)   on 2006-05-18 10:38:39 (Show Source): You can put this solution on YOUR website!The way I looked at is this... The random line can be drawn in the middle 39.999999 degrees of the large angle and still split the 140 degree angle into two acute angles, so the odds are roughly 40 out of 140, or 2/7.
 Linear_Algebra/38307: What is a linear relationship?1 solutions Answer 23855 by fractalier(2101)   on 2006-05-18 10:27:48 (Show Source): You can put this solution on YOUR website!The word linear means line. A linear relationship between two variables, when graphed, is a straight line. It also means that both variables are expressed to the first power only, no roots, no higher exponents.
 Polynomials-and-rational-expressions/38364: Not sure if I'm right, please help! n^2-n-20/2n^2 * n^2+5n/n^2-25 I keep coming up with -n^2+n Am I doing this right?1 solutions Answer 23854 by fractalier(2101)   on 2006-05-18 10:21:31 (Show Source): You can put this solution on YOUR website!Let's see if you're right...from n^2-n-20/2n^2 * n^2+5n/n^2-25 we factor and cancel where possible, so (n - 5)(n + 4) / 2(n + 1) * n(n + 5) / (n + 5)(n - 5) All the n+5's and n-5's cancel, so we have n(n + 4) / 2(n + 1) I guess you weren't right...