# See tutors' answers!

Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'longjonsilver'

longjonsilver answered: 2272 problems
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 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279, >>Next

 Polynomials-and-rational-expressions/40709: Please write in standard notation. 2.5 * 10^5 Thanks!1 solutions Answer 26107 by longjonsilver(2297)   on 2006-06-04 17:56:40 (Show Source): You can put this solution on YOUR website!this already is in standard notation Jon
 Polynomials-and-rational-expressions/40710: Please evaluate. 4^0 Thanks!1 solutions Answer 26104 by longjonsilver(2297)   on 2006-06-04 17:54:30 (Show Source): You can put this solution on YOUR website!anything to power of zero is 1. jon
 Trigonometry-basics/40533: This question is from textbook Can you please check my answer? Our professor has shown us how to get these answers in decimal, and the book shows how to get them with radicals. Question: A child pulls a wagon with a force of 40 lbs. The handle of the wagon makes a angle of 30° with the ground. Express the force vector F in terms i and j. Answer: 17.32i+10j Thank You1 solutions Answer 25992 by longjonsilver(2297)   on 2006-06-03 19:37:33 (Show Source): You can put this solution on YOUR website!draw a simple line diagram...basically a right angled triangle. I assume that i is in the horizontal and j is in the vertical directions. Assuming this to be the case, we have the angle 30 degrees and the hypotenuse is 40. What we are basically doing is "resolving" this into 2 component parts, at right angles to each other: Horizontally, let this portion/projection of the 40 lb force be called H say, so that using trig: cos30 = adj/hyp Vertically, we get an equivalent for the projection, V: sin30 = opp/hyp So, the vector of the force pulling the handle can be thought of as and 20j. Force is Your answer is not correct - from a directional point of view it is fine, but the magnitude of 17.32i + 10j is not 400, it is --> which is 20. jon.
 Polynomials-and-rational-expressions/40564: Write in scientific notation. 75,000,0001 solutions Answer 25990 by longjonsilver(2297)   on 2006-06-03 19:24:15 (Show Source): You can put this solution on YOUR website!75,000,000 in standard notation is Jon
 Miscellaneous_Word_Problems/40565: If m varies directly as n and inversly as o, and m=20 when n=50 and o=10, find m when n=96 and o=16. m=____ Thank You.1 solutions Answer 25988 by longjonsilver(2297)   on 2006-06-03 19:23:04 (Show Source): You can put this solution on YOUR website!m is proportional to , so that , where k is a constant, to be found. Given that m=20, n=50, o=10 then we have --> k = 20/5 --> k = 4 So, Hence, when n=96 and o=16 we get: jon.
 Polynomials-and-rational-expressions/40573: A viedo game has three villans which appear on screen at different intervals. One villan appears every 3 seconds, a second villan appears every 5 seconds, and a third villan appears every 12 seconds. When will all three villans appear at the same time? List all the possibilites ihn an organized way. A)in 120 seconds B)in 150 seconds C)in 60 seconds D)in 30 seconds1 solutions Answer 25986 by longjonsilver(2297)   on 2006-06-03 19:15:18 (Show Source): You can put this solution on YOUR website!the answers have to be multiples of all 3 numbers: 3, 5 and 12. Looking at 5 and 12, we have 60, 120, 180, 240, etc. 3 also goes into each of these, so this set of numbers is the answer. Jon.
 Trigonometry-basics/40539: This question is from textbook The vector V has initial point P and terminal point Q. Write V in the form ai+bj; that is find its positive vector. P=(0,0);Q=(3,4)1 solutions Answer 25985 by longjonsilver(2297)   on 2006-06-03 19:12:22 (Show Source): You can put this solution on YOUR website!V=3i+4j Jon
 Polynomials-and-rational-expressions/40568: Write in Standard notation. 2.5 * 10^51 solutions Answer 25983 by longjonsilver(2297)   on 2006-06-03 19:11:06 (Show Source): You can put this solution on YOUR website!for me, from England, this is in Standard Notation already. Jon.
 Divisibility_and_Prime_Numbers/40263: I couldn't figure out how to type a straight line on my computer so I used [ instead. [ 4] + [ - 3 ]1 solutions Answer 25620 by longjonsilver(2297)   on 2006-06-01 06:08:59 (Show Source): You can put this solution on YOUR website!|4| + |-3| is 4+3 7 | on my keyboard is the \ key shifted: the one to the left of the Z key. Jon
 Polynomials-and-rational-expressions/40186: Joe's Dairy Farm has 100 gallons of milk that is 4.6% butterfat. How much skimmilk (no butterfat) should be mixed with it to make milk that is 3.2% fat? ________gallons of milk should be added. -------------------------------------------------------------------------------- A chemist has one solution that is 80% acid and another soulution that is 30% acid. How much of the first (80%) solution is needed to make a 400L solution that is 62% acid? __________liters of the 80% solution is required. Thanx1 solutions Answer 25619 by longjonsilver(2297)   on 2006-06-01 06:01:09 (Show Source): You can put this solution on YOUR website!read my Lesson on Mixtures. That should help you understand this type of question. Anyway: 1. We cannot think about "amounts of butterfat, since the skimmed has none: its percentage is zero. So i have turned it around and considered the percentage of non-fat milk in the milk: the skimmed will be 100%. 100*0.954 + x*1.00 = (100+x)*0.968 95.4 + x = 96.8 + 0.968x x - 0.968x = 96.8 - 95.4 0.032x = 1.4 x = (1.4)/(0.032) x = 43.75 gallons 2. Start with 80% acid and a 30% acid. --> Let there be x litres of the 80% solution acid. So, how much of the 30%? Answer is "the rest of the 400 litres ie (400-x). This is the tricky bit you need to "see". So, 0.80x + 0.30(400-x) = 0.62*400 0.80x + 120 - 0.30x = 256 0.80x - 0.30x = 256 - 120 0.50x = 136 x = 272 So we need 272 litres of the 80% acid and we need 128 litres of the 30% acid jon.
 Equations/40244: please help me solve 2x=5y=9x1 solutions Answer 25618 by longjonsilver(2297)   on 2006-06-01 03:55:33 (Show Source): You can put this solution on YOUR website!please re-submit the question, as it does not make sense as it stands Jon.
 Polynomials-and-rational-expressions/40097: Find values of a and k for a parabola containing the points given: y-k = a(x+3)^2 (-5,1)and (1,7) I've been working on this problem for a while, but I could use a little help. Thanks (:1 solutions Answer 25552 by longjonsilver(2297)   on 2006-05-31 17:38:25 (Show Source): You can put this solution on YOUR website! OK, put in the values (-5,1) or and put in the values (1,7) or So simultaneous equations 4a + k = 1 16a + k = 7 Subtract these to find a and then find k. jon.
 Geometric_formulas/40114: This question is from textbook geometry, measuring, reasoning, applying The endpoints of a diameter of a circle are (-2,1) and (6, -5). Write the standard equationof the circle?1 solutions Answer 25550 by longjonsilver(2297)   on 2006-05-31 17:33:10 (Show Source): You can put this solution on YOUR website!1. find the origin of the circle by finding the midpoint between the 2 quoted points. 2. Calculate the length of the diameter using the standard formula for length of a line. Find the radius from this length by dividing by 2. 3. Find the standard equation of a circle and put in the values of the coordinates of the centre and the length of the radius. Done. Jon.
 decimal-numbers/40023: Cany someone help me solve this problem? Find the least common multiple of 24 and 48. Thanks, Sher1 solutions Answer 25430 by longjonsilver(2297)   on 2006-05-31 09:11:30 (Show Source): You can put this solution on YOUR website!multiples of 5 are 5,10,15,20,25,30,...etc so we need to work out a few for both 24 and 48. When we reach a number that is in both the list for 24 and 48, then we stop...this is the lowest common multiple. OK, 24 first. 24,48,... here we have 48 which is the other number. So straight away we have the lowest common multiple of 24 and 48 is 48. jon.
 Numeric_Fractions/40025: Can someone help me with this problem? Subtract: 6 4/5 - 2 1/5 Thanks, Sher1 solutions Answer 25429 by longjonsilver(2297)   on 2006-05-31 09:08:49 (Show Source): You can put this solution on YOUR website!just like the addition one: 6 4/5 is 30/5 and 4/5 --> 34/5 and 2 1/5 is 10/5 and 1/5 --> 11/5 So, 34/5 - 11/5 is 23/5 and this is equivalent to 4 and 3/5 jon.
 Numeric_Fractions/40024: Can someone help me with this problem? Add: 4 2/7 + 1 5/7 Thanks, Sher1 solutions Answer 25428 by longjonsilver(2297)   on 2006-05-31 09:05:50 (Show Source): You can put this solution on YOUR website!strictly, you do not need to do this method with this fractional sum, but practice it anyway: 4 and 2/7 is how many 7ths in total? 4 complete "pies" each divided into 7ths is a total of 28 7ths. Plus the other 2 gives a total of 30/7. Similarly, 1 and 5/7 is 7/7 and 5/7 --> 12/7 in total So, we have 30/7 + 12/7 which is 42/7 which happens to be 6. jon.
 Graphs/39986: This question is from textbook algebra 1 can anybody tell me how to graph a function out of an equation for example like f(x)= -2x^2 + 4x + 11 solutions Answer 25427 by longjonsilver(2297)   on 2006-05-31 09:00:27 (Show Source): You can put this solution on YOUR website!when you say graph, you mean plot, on graph paper? If so, pick values of x...your choice. Pick some easy ones like 0,1,2,3,4. Possibly -1,-2,-3 -4 too. For each, put it into the equation and find the value of f(x) ie "y". Hopefully you will have picked enough x-values that your graph will cover the "interesting" part of the curve, namely the place it turns. So...give it a go :-) jon
 Polynomials-and-rational-expressions/40005: Find 4 consecutive odd integers if the product of the two smaller integers is 112 less than the product of the two larger integers. thanx1 solutions Answer 25425 by longjonsilver(2297)   on 2006-05-31 08:56:43 (Show Source): You can put this solution on YOUR website!let smallest number be x. Then we have x+2, x+4 and x+6 successively. So, x(x+2) = (x+4)(x+6) - 112 x = (-88)/(-8) x = 11 so, we have 11,13,15 and 17 CHECK: 11*13 is 143 15*17 is 255 and 255-143 is 112: correct jon.
 Polynomials-and-rational-expressions/40011: Markita bought a roll of carpeting 8.5 ft wide. The maximum area the carpet will cover is at most 136sq ft. What is the largest possible length of the carpet? thanx1 solutions Answer 25424 by longjonsilver(2297)   on 2006-05-31 08:49:45 (Show Source): You can put this solution on YOUR website!length*width = area length*8.5 = 136 length = 136/8.5 length = 16 ft at the most. jon.
 Polynomials-and-rational-expressions/40014: The 4 children were born 1 yr apart. the oldest is 12. how old are the other 3 children from oldest to youngest? thanx1 solutions Answer 25423 by longjonsilver(2297)   on 2006-05-31 08:48:02 (Show Source): You can put this solution on YOUR website!12, 11, 10, 9 these have 1 year between them, in theory. It is a rubbish question, as ages are so variable over a year. Jon
 Polynomials-and-rational-expressions/40013: If a number is subtracted from its square, the result is 2. Find the number. The length of a rectangle is 4 cm longer than the width. If the perimeter of the rectangle is 20 cm what is the area? Area=___cm^2 thanx1 solutions Answer 25422 by longjonsilver(2297)   on 2006-05-31 08:44:30 (Show Source): You can put this solution on YOUR website!Let number be x. Its square is therefore So: a number is subtracted from its square: and this equals 2 --> so, is a quadratic to solve. (x-2)(x+1) = 0 (x-2) = 0 or (x+1) = 0 x=2 or x=-1 these are your 2 possible answers jon.
 Polynomials-and-rational-expressions/40016: The sum of the digets of a two digit number is 10. if the digets were reversed, the new number would be 54 less than the original number. find the original number. thanx1 solutions Answer 25421 by longjonsilver(2297)   on 2006-05-31 08:37:54 (Show Source): You can put this solution on YOUR website!Well, from just thinking about it: 19 and 91 --> difference is 72 28 and 82 --> difference is 54 37 and 73 --> difference is 46 46 and 64 --> difference is 18 so you have your answer there: 28 and 82 OK, algebraically: Let the number be written as xy where x+y=10 xy means the number is (10x+y) like 28 is (10*2 + 8) and yx is the reversed version: (10y+x) and we are told that new number = old number - 54 --> 10y+x = 10x+y - 54 9y-9x = -54 or 9x-9y = 54 (just swapping all the signs over --> like moving the lefthand terms to the right hand side and vice versa) So, we have: 9x-9y = 54 x+y = 10 9x-9y = 54 9x+9y = 90 Now, add the 2 equations together: 18x = 144 x = 144/18 x = 8 and so y must be 2. So answer is: original number, xy, is 82 jon.
 Exponential-and-logarithmic-functions/40021: y=a^x I forget how to even start this. Let alone complete this.1 solutions Answer 25420 by longjonsilver(2297)   on 2006-05-31 08:29:49 (Show Source): You can put this solution on YOUR website!and what precisely do you want to do with it? You neglected to say Jon
 Polynomials-and-rational-expressions/39505: how do u do sythetic division (i know nothing about this topic whatsoever)Please explain for a beginner like me1 solutions Answer 24981 by longjonsilver(2297)   on 2006-05-26 10:50:58 (Show Source): You can put this solution on YOUR website!this URL is an excellent start for you: http://www.purplemath.com/modules/synthdiv.htm jon
 Surface-area/39540: A Traingle has sides 3x + 7 , 4x - 9, and 5x + 6. Find the expression that represents its perimeter. 1 solutions Answer 24980 by longjonsilver(2297)   on 2006-05-26 10:48:32 (Show Source): You can put this solution on YOUR website!perimeter = (3x+7) + (4x-9) + (5x+6) perimeter = 3x+7+4x-9+5x+6 perimeter = 12x+4 perimeter = 4(3x+1) jon.
 Distributive-associative-commutative-properties/39539: Use the distributive property to remove the parentheses in each express. then simply by combining like term. 7 (4w -3) -25w 1 solutions Answer 24979 by longjonsilver(2297)   on 2006-05-26 10:46:50 (Show Source): You can put this solution on YOUR website!7(4w - 3) - 25w 28w - 21 - 25w 3w - 21 3(w-7) jon.
 Expressions-with-variables/39434: In a parallel circuit, the joint resistance is 8 ohms. If one resistor is 12 ohms less than the second resistor, find both resistors.1 solutions Answer 24885 by longjonsilver(2297)   on 2006-05-25 18:10:53 (Show Source): You can put this solution on YOUR website!parallel circuit with resistors A and B, then the total resistance is given by R where so, given our info of one resistor being x and the other being (x-12), we get: (x-4)(x-24) = 0 so x-4=0 or x-24=0 x=4 or x=24 Now x is not 4 for our resistor problem, since the other resistor would then be 4-12 --> -8. This is physically impossible. So, the only answer we have is that the resistors are 24 and (24-12) --> 12. jon.
 Matrices-and-determiminant/39448: Use Cramer's Rule to solve this equation. 7x-2y=4 3x+y=-61 solutions Answer 24883 by longjonsilver(2297)   on 2006-05-25 18:03:05 (Show Source): You can put this solution on YOUR website!check the other one i did and have a go yourself Jon.
 Matrices-and-determiminant/39449: Use Cramer's Rule to solve this equation. 2x-5y=18 -x+3y=101 solutions Answer 24882 by longjonsilver(2297)   on 2006-05-25 18:02:21 (Show Source): You can put this solution on YOUR website!M = Its determinant, D is: D = (2)(3)-(-1)(-5) D = 6-5 D = 1 Now repeat on Dx = (18)(3)-(10)(-5) Dx = 54+50 Dx = 104 and also on Dy = (2)(10)-(-1)(18) Dy = 20+18 Dy = 38 So, x = Dx/D --> x = 104/1 --> x = 104 So, y = Dy/D --> y = 38/1 --> y = 38 CHECK: 2x-5y 2(104)-5(38) 208-190 18... CORRECT and -x+3y -(104)+3(38) -104+114 10... CORRECT jon.
 Exponential-and-logarithmic-functions/39439: I need this for work ASAP. What is the derivative I need this for work ASAP. What is the derivative d/dx( f(x) ^ g(x) ) where ^ is the sign of EXPONENTIATION and f and g are function of x. Please NOTE AGAIN that I am not talking about a compound function, I am talking about one function taken TO THE DEGREE of another. thanks1 solutions Answer 24879 by longjonsilver(2297)   on 2006-05-25 17:54:10 (Show Source): You can put this solution on YOUR website!have a read of this i found on google: http://www.physicsforums.com/showthread.php?t=87992 basically... take natural logs first then differentiate the whole thing. Good luck :-) Jon.
 logarithm/39440: What is the answer to 5^2x = 8?1 solutions Answer 24877 by longjonsilver(2297)   on 2006-05-25 17:15:22 (Show Source): You can put this solution on YOUR website! Take logs - to base 5 of both sides: --> this log is base5 and now convert this to a base10 calculation, so that you can use your calculator: --> this is base10 --> this is base10 jon.