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# Recent problems solved by 'fractalier'

fractalier answered: 2101 problems
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 Systems-of-equations/38085: Solve the system of equations by graphing. y-2x=0 y=4x-1 What is the solution of the system of equations? 1 solutions Answer 23686 by fractalier(2101)   on 2006-05-17 10:55:38 (Show Source): You can put this solution on YOUR website!From y - 2x = 0 y = 4x - 1 I can show you the solution but graphing it here is impossible... Normally you can set up an x-and-y chart and plug in values to get the points you plot...or you can put each line in slope-intercept form and graph... In either case, the place where the lines intersect is your solution... In this case, this is x = 1/2 and y = 1 or (1/2, 1)
 Linear_Equations_And_Systems_Word_Problems/37665: This question is from textbook Safety Rent-a-Car rents an intermediate-size car at a daily rate of \$21.95 plus .19 per mile. City Rentals rent an intermediate-size car for \$18.95 plus .21 per mile. For what milage is the cost the same?1 solutions Answer 23685 by fractalier(2101)   on 2006-05-17 10:51:04 (Show Source): You can put this solution on YOUR website!Let x be the number of miles. Then we convert the facts of the problem into algebra and get: 21.95 + .19x = 18.95 + .21x Let us multiply everything by 100 to get rid of decimals... 2195 + 19x = 1895 + 21x Now subtract 19 x from both sides 2195 = 1895 + 2x Now subtract 1895 from both sides and then divide by two... 300 = 2x x = 150 miles
 Graphs/38105: MATCH EACH SYSTEM WITH IT'S CORRECT SOLUTION. 2Y-8=X 2Y+2X=2 A. (3,2) B.(3,3) C. (-2,3) D. (2,3)1 solutions Answer 23684 by fractalier(2101)   on 2006-05-17 10:46:43 (Show Source): You can put this solution on YOUR website!From 2Y - 8 = X 2Y + 2X = 2 let us substitute 2y - 8 for x in the second equation and get 2y + 2(2y - 8) = 2 2y + 4y - 16 = 2 6y - 16 = 2 6y = 18 y = 3 and then x = 2y - 8 x = 2(3) - 8 x = -2 Choice C.
 Graphs/38108: MATCH EACH SYSTEM WITH IT'S SOLUTION 2Y=X+3 X=Y A. (3,2) B. (3,3) C. (-2,3) D. (2,3)1 solutions Answer 23683 by fractalier(2101)   on 2006-05-17 10:44:04 (Show Source): You can put this solution on YOUR website!From 2Y=X+3 X=Y we can substitute x for y in the first equation and get 2x = x + 3 x = 3 then y = 3 Choice B.
 Graphs/38172: Could you please help me with this one? The equation of a line that contains the point (-2,4) and is parellel to y=2x-3.1 solutions Answer 23682 by fractalier(2101)   on 2006-05-17 10:42:14 (Show Source): You can put this solution on YOUR website!Answered this already...see below...y = 2x + 8
 Square-cubic-other-roots/38140: What is 3 (square root 5) - 5 (square root 3)1 solutions Answer 23681 by fractalier(2101)   on 2006-05-17 10:39:56 (Show Source): You can put this solution on YOUR website!3sqrt(5) - 5sqrt(3) cannot be combined. It is its own answer. If you want an approximate number, well 3*2.236 - 5*1.732 = -1.952
 Linear-equations/38149: Question: Find the equation of a line that contains the point(-2,4) and is parellel to the y=2x-3. Please show the steps.1 solutions Answer 23680 by fractalier(2101)   on 2006-05-17 10:36:41 (Show Source): You can put this solution on YOUR website!Please scroll down and find my earlier solution...y = 2x + 8
 Numeric_Fractions/38169: Need help solving: -3x +3/4=1/8 Thanks1 solutions Answer 23679 by fractalier(2101)   on 2006-05-17 10:35:46 (Show Source): You can put this solution on YOUR website!From -3x + 3/4 = 1/8 we need to to subtract 3/4 from both sides -3x = 1/8 - 3/4 -3x = -5/8 then divide both sides by -3 x = 5/24
 Radicals/38176: 2{3x-1}=4 OR 2 square root of 3x-1 equals 41 solutions Answer 23678 by fractalier(2101)   on 2006-05-17 10:33:54 (Show Source): You can put this solution on YOUR website!Okay from 2sqrt(3x - 1) = 4 we divide both sides by two first sqrt(3x - 1) = 2 then square both sides 3x - 1 = 4 then solve and check 3x = 5 x = 5/3 It checks.
 Radicals/38173: Please help!! x=1+6 sqrt x-9 Thank you!1 solutions Answer 23677 by fractalier(2101)   on 2006-05-17 10:30:59 (Show Source): You can put this solution on YOUR website!Okay, from x = 1 + 6sqrt(x-9), move the one over first and get x - 1 = 6sqrt(x-9) Now square both sides x^2 - 2x + 1 = 36(x - 9) Now expand, combine, factor, solve and check... x^2 - 2x + 1 = 36x - 324 x^2 - 38x + 325 = 0 (x - 13)(x - 25) = 0 x = 13 or x = 25 Both check out, so we have two solutions...
 Exponential-and-logarithmic-functions/38177: This question is from textbook Heath Algebra 2 An Integrated Approach Please help me with this problem: 1 solutions Answer 23676 by fractalier(2101)   on 2006-05-17 10:26:48 (Show Source): You can put this solution on YOUR website!Okay, from 6e^(-x) = 3 we'll divide by 6 first and get e^(-x) = 1/2 then take the ln of both sides ln[e^(-x)] = ln(1/2) -x = ln(1/2) x = -ln(1/2) x = ln 2
 Divisibility_and_Prime_Numbers/38198: Evaluate the following. Be sure to use the proper units. 5 lb/ft X 3 ft1 solutions Answer 23675 by fractalier(2101)   on 2006-05-17 10:24:49 (Show Source): You can put this solution on YOUR website!5 lb/ft X 3 ft = 15 lb You can cancel units like feet just like you cancel x's or y's...
 Radicals/38202: Express the following expression in simplest radical form. All variables represent positive real numbers. SQRT of (8y^3)/49x1 solutions Answer 23674 by fractalier(2101)   on 2006-05-17 10:23:36 (Show Source): You can put this solution on YOUR website!From sqrt(8y^3 / 49x), we will need to rationalize the denominator by multiplying by sqrt(x) / sqrt(x)...this will give us a perfect square in the denominator... sqrt(8y^3 / 49x) = sqrt(8y^3 / 49x) * [sqrt(x) / sqrt(x)] = sqrt(8xy^3 / 49x^2) We can pull perfect squares out of the radical from the numerator and denominator, giving us the answer... sqrt(8xy^3 / 49x^2) = (2y / 7x) * sqrt(2xy)
 Equations/38183: i dont get an you explain in detail and give the steps -4=-4(f-7)1 solutions Answer 23672 by fractalier(2101)   on 2006-05-17 10:19:53 (Show Source): You can put this solution on YOUR website!Okay, from -4 = -4(f - 7) we can divide both sides by -4 first... 1 = f - 7 then add seven to both sides, and f = 8
 Quadratic_Equations/38209: Solve the radical equation. 6 SQRT of x = x+51 solutions Answer 23671 by fractalier(2101)   on 2006-05-17 10:18:22 (Show Source): You can put this solution on YOUR website!Okay from 6sqrt(x) = x + 5, let us square both sides... 36x = x^2 + 10x + 25 Subtract the 36x, factor, solve and check... x^2 - 26x + 25 = 0 (x - 25)(x - 1) = 0 x = 25 or x = 1 They both check out okay...two solutions here...
 Linear-equations/38179: Need some help Find the equation of a line that contains the point (-2,4)and is parallel to y=2x-3 thank you for your time.1 solutions Answer 23670 by fractalier(2101)   on 2006-05-17 10:16:04 (Show Source): You can put this solution on YOUR website!Parallel means same slope...so we need a line going thru (-2, 4) with a slope of 2...we use the point-slope formula... y - y1 = m(x - x1) y - 4 = 2(x -(-2)) y - 4 = 2(x + 2) y - 4 = 2x + 4 y = 2x + 8
 Sequences-and-series/38187: Calculate the sum of all even positive integers from 2 to 4000.1 solutions Answer 23669 by fractalier(2101)   on 2006-05-17 10:14:10 (Show Source): You can put this solution on YOUR website!Gauss showed the shortcut for this hundreds of years ago, when he was but a child... Notice that if you add the first and last terms you get 4002. If you add the second and second-to-last terms you get 4002. If you add the third and third-to-last terms you get 4002. And so on, and so on... Now how many pairs making 4002's are there? Well, half the number of numbers present. There are 2000 even numbers from 2 to 4000. That means 1000 pairs, each adding to 4002. So the sum is 1000 * 4002 = 4002000. Cool!
 Polynomials-and-rational-expressions/38200: 5x^2-20y^21 solutions Answer 23668 by fractalier(2101)   on 2006-05-17 10:09:49 (Show Source): You can put this solution on YOUR website!From 5x^2 - 20y^2, we first factor out the 5 and get 5(x^2 - 4y^2) But x^2 - 4y^2 is the difference of squares, and can be factored again... 5(x^2 - 4y^2) = 5(x + 2y)(x - 2y)
 Radicals/38208: Express the following expression in simplest radical form. All variables represent positive real numbers. SQRT of 27(a^2)b / SQRT of 7(a^3)(b^3)1 solutions Answer 23667 by fractalier(2101)   on 2006-05-17 10:07:38 (Show Source): You can put this solution on YOUR website!From sqrt27(a^2)b / sqrt7(a^3)(b^3) we can make it all one root and then cancel as possible, thus we get sqrt[27(a^2)b / 7(a^3)(b^3)] = sqrt[27 / 7ab^2] From here, we need to rationalize the denominator by multiplying top and bottom by sqrt(7a)/sqrt(7a)...so we have sqrt[27 / 7ab^2] * sqrt(7a)/sqrt(7a) = sqrt[189a / 49(a^2)(b^2)] Now 49(a^2)(b^2) is a perfect square so we can remove it from the root...our final answer is sqrt(189a) / 7ab
 Quadratic_Equations/38203: Solve the quadratic equation by factoring and applying the property "ab=0 if and only if a=0 or b=0" (x^2)-4x-21=01 solutions Answer 23665 by fractalier(2101)   on 2006-05-17 10:02:10 (Show Source): You can put this solution on YOUR website!First we factor the trinomial x^2 - 4x - 21 = 0 into its binomial factors: (x - 7)(x + 3) = 0 Now if two quantities multiply together to make zero, one (or both) has to be zero... Thus x - 7 = 0 and x + 3 = 0 which leads to x = 7 or x = -3
 Money_Word_Problems/38110: Use the compound interest equation to find how long, to the nearest tenth of a year, it will take a \$5000 investment to double if it is invested at 7% interest compounded quarterly. The answer is 10.0 years, I just can't figure out how to get it.1 solutions Answer 23611 by fractalier(2101)   on 2006-05-16 16:53:11 (Show Source): You can put this solution on YOUR website!Okay, from the equation A = P(1 + r/n)^nt we plug in what we know and solve for what we don't know... 10000 = 5000(1 + (.07/4))^4t now divide by 5000 2 = (1 + (.07/4))^4t take the log of both sides log 2 = 4t*log(1 + (.07/4)) now solve for t... t = log 2 / 4(log 1.0175) t = 9.988 years or roughly 10 years
 Graphs/38082: Solve the system by addition 5x + 9y = -12 x - 2y = 101 solutions Answer 23610 by fractalier(2101)   on 2006-05-16 16:47:12 (Show Source): You can put this solution on YOUR website!From 5x + 9y = -12 x - 2y = 10 let us multiply the bottom equation by (-5) and add it to the top one... 5x + 9y = -12 -5x + 10y = -50 which yields 19y = -62 and the not-so-nice y = -62/19 Now plug that into the second equation to find x... x - 2(-62/19) = 10 x + 124/19 = 10 x + 124/19 = 190/19 x = 66/19
 Radicals/38080: Change the radical to simplest radical form: 3 SQRT of 25 / 3 SQRT of 51 solutions Answer 23609 by fractalier(2101)   on 2006-05-16 16:43:12 (Show Source): You can put this solution on YOUR website!3*sqrt(25) / 3*sqrt(5) can be figured by direct division. The 3's cancel and sqrt(25) / sqrt(5) = sqrt(5).
 Divisibility_and_Prime_Numbers/38090: which of the following numbers are composit? 0, 1, 15, 19, 23, 31, 49, 55, 59, 87, 91, 97, 103, 1051 solutions Answer 23608 by fractalier(2101)   on 2006-05-16 16:41:16 (Show Source): You can put this solution on YOUR website!Those nmbers which can be factored into numbers other than itself and one are composite. Thus, 15, 49, 55, 87, 91 and 105 are composite. Aside from 0 and 1, the rest are prime.
 Graphs/38111: WHICH EQUATION IS PERPENDICULAR TO Y=4X+3? A. Y=-4X-1 B. Y=-1/4X+2 C. Y=1/4X-6 D. Y=3X+91 solutions Answer 23606 by fractalier(2101)   on 2006-05-16 16:39:29 (Show Source): You can put this solution on YOUR website!Perpendicular lines have slopes which are negative reciprocals of each other. thus we need a line with a slope of -1/4. Choice B is correct.
 test/38112: __________ LINES ARE LINES THAT FORM RIGHT ANGLES1 solutions Answer 23605 by fractalier(2101)   on 2006-05-16 16:38:10 (Show Source): You can put this solution on YOUR website!Perpendicular
 Rational-functions/38114: when a postive is multiplied by a negative is the solution a postive or a negative? i think it is postive but im not sure...1 solutions Answer 23604 by fractalier(2101)   on 2006-05-16 16:37:36 (Show Source): You can put this solution on YOUR website!A positive quantity multiplied by a negative quantity equals ==> a negative quantity. Remember ==> same sign is positive, different sign is negative.
 Parallelograms/38097: if a rhombus is inscribed in a circle, does that mean the diagonals would be congruent?1 solutions Answer 23603 by fractalier(2101)   on 2006-05-16 16:35:57 (Show Source): You can put this solution on YOUR website!Yes. Because the opposite angles would have to be equal to 90 degrees. Since you are given it is a rhombus, and not merely an arbitrary rectangle, it would have to be a square. Of course both squares and rectangles have congruent diagonals.
 Graphs/38109: MATCH EACH SYSTEM WITH THE CORRECT SOLUTION X-Y=1 X=1/2Y+2 A. (3,2) B. (3,3) C.(-2,3) D.(2,3)1 solutions Answer 23602 by fractalier(2101)   on 2006-05-16 16:32:00 (Show Source): You can put this solution on YOUR website!From x - y = 1 and x = (1/2)y + 2 Let us subtract 1/2y in the second one and then subtract equations.. x - y = 1 x - (1/2)y = 2 which leads to -(1/2)y = -1 and y = 2 plug that in the first eqn and get x = 3
 Equations/38098: WHICH EQUATION IS PARALLEL TO Y=0.5X+1? A. Y= 0.5X+1 B. Y=-0.5X+2 C. Y=0.5X-4 D. Y=X+11 solutions Answer 23601 by fractalier(2101)   on 2006-05-16 16:29:02 (Show Source): You can put this solution on YOUR website!Parallel lines have equal slopes. Thus which of the choices has a slope of .5? Choice C is best. Choice is the exact same line and not technically parallel.
 Miscellaneous_Word_Problems/38106: A fish was caught whose tail weighed 9 pounds. His head weighed as much as his tail and half his body, and his body weighed as much as his head and tail. How much did the fish weigh?1 solutions Answer 23600 by fractalier(2101)   on 2006-05-16 16:26:48 (Show Source): You can put this solution on YOUR website!If the tail was 9 lbs, the head was 9 lbs too. If that was half the body, the body must have been 18 lbs, and the sum of head and tail, as stated... Thus the entire fish, head, body and tail was 36 pounds. That's some fish!