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# Recent problems solved by 'rapaljer'

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 Polynomials-and-rational-expressions/23009: I need help because i am doing this w/o my book. Please and thank you. the question says Find the zero's of the polynomial function. f(x)=2(x-5)(x-6)^3 I have two more questions and that is it.The next one says use the correct compound interest formula A=P[1+r/n]^nt or A=Pe^rt to solve I don't know what they mean can u tell me please. Using that it says Find the accumulated value of an investment of \$10,000 at 4% compounded annually for 17yrs.1 solutions Answer 11413 by rapaljer(4667)   on 2005-12-20 01:12:33 (Show Source): You can put this solution on YOUR website!Zeros of the polynomial function are the points where f(x) = 0. What values of x will zero out the equation? Answer: x= 5 and x= 6. These are also the x-intercepts. The graph looks like this: For your second question, A=P[1 +r/n]^nt is for interest compounded for periods such as annually, semiannually, quarterly, daily, etc. The formula A=Pe^rt is for interest compounded continuously. Find the accumulated value of an investment of \$10,000 at 4% compounded annually for 17yrs. Use the first formula above, where P=\$10,000, r=.04, n=1 time per year, and t= 17 years. I get this with this formula and a calculator: A= 10000[1+.04)^17 =\$19479.00496 Final answer: \$19,479.00 What did you get?? R^2 at SCC
 Quadratic_Equations/23005: When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD, and why can you not do the same operation when simplifying a rational expression?1 solutions Answer 11412 by rapaljer(4667)   on 2005-12-20 00:21:31 (Show Source): You can put this solution on YOUR website!This is an EXCELLENT question!! When solving a rational equation, you are actually multiplying both sides of the EQUATION by the LCD. It is a property of equations that allows you to multiply both sides of the equation by the same non-zero number or expression. However, when you are simplifying rational expressions--did you get that key word there?? EXPRESSIONS!! Now you are NOT dealing with an equation, but only an expression. So with an EXPRESSION, you don't have the properties of EQUATIONS!! One of my favorite questions! Thanks for asking it!! R^2 at SCC
 Equations/22969: Please Help Me Solve This Problem: Simplify Each: y^-7 Thank you for your time and help !1 solutions Answer 11409 by rapaljer(4667)   on 2005-12-19 23:55:16 (Show Source): You can put this solution on YOUR website!Have you done anything with the laws of exponents? For example, when you divide with the same base number, you subtract exponents: If it had been can you see that if you subtract exponents you would have which could be written ? This same problem could also be simplified as a fraction to be reduced by dividing out the five x factors in the numerator with five of the x factors in the denominator. In this method, all the x factors in the numerator divide out, and you would be left with a 1 in the numerator since they all divided out and seven factors of x left in the denominator: What you have just done is derived the formula In summary, any time you have a negative exponent, you get a fraction whose numerator is 1, and whose denominator is the same as the original problem but with a positive exponent. For examples: R^2 at SCC
 Travel_Word_Problems/23013: After leaving Moose Jaw, Hanson drove 200 kilometers at x km/hr and then decreased his speed by 20 km/ and drove 240 additional kilomethers. Write a rational expression for his total traveling time. Evaluate the expression for x = 100. 1 solutions Answer 11407 by rapaljer(4667)   on 2005-12-19 23:18:03 (Show Source): You can put this solution on YOUR website!D=RT T=D/R T(x) = D/R + D/R T(x) = 200/x + 240/(x-20) When x= 100, T(100) = 200/100 + 240/(100-20) T(100) = 200/100 + 240/80 T(100) = 2 + 3 = 5 hours R^2 at SCC
 Linear_Algebra/23018: -4-square root of -20 ------------------------ 51 solutions Answer 11406 by rapaljer(4667)   on 2005-12-19 23:12:43 (Show Source): You can put this solution on YOUR website! Does not reduce. You can factor it if you like, but factoring is not usually necessary since the fraction does not reduce. R^2 at SCC
 Travel_Word_Problems/23019: I know there's a similar problem, but got very confused by the way the set-up was formatted in the response. Can someone pllleeeeease help? All I need is to see which numbers & variables go where, then I should be able to solve it. Thanks in advance! In still water a boat can travel 15 mph. It travels 36 miles upstream & 36 miles downstream in a total time of 5 hours. Find the speed of the current. (The book says the answer is 3 mph)1 solutions Answer 11404 by rapaljer(4667)   on 2005-12-19 22:49:32 (Show Source): You can put this solution on YOUR website!Let x = speed of the current 15 +x = speed of the boat downstream (with the current) 15-x = speed of the boat upstream (against the current) Distance upstream = Distance downstream = 36 miles D=RT T= D/R Total Time = D/R + D/R = 5 hours Multiply both sides of the equation by the LCD which is (15+x)(15-x): x= 3 or x= -3 Reject the negative answer. x=3 mph = speed of the current. R^2 at SCC
 Polynomials-and-rational-expressions/23015: Please help. I need to factor the following: 6x^5 + 4x^3 - 8x. I got as far as 2x(3x^4 + 2x^2 - 4). I'm not sure this is right. Is this problem a prime polynomial? Thanks.1 solutions Answer 11399 by rapaljer(4667)   on 2005-12-19 20:55:05 (Show Source): You can put this solution on YOUR website!You are correct! And the trinomial does NOT refactor. R^2 at SCC
 Exponential-and-logarithmic-functions/23014: log 5+log (n+1)=log 6n 9 9 9 1 solutions Answer 11396 by rapaljer(4667)   on 2005-12-19 20:51:16 (Show Source): You can put this solution on YOUR website! , so If , then 5(n+1) = 6n 5n+5 = 6n Subtract 5n from each side: 5= n Remember to check the value of n to make sure you don't have a log of a negative number. You do not, so the answer n=5 is acceptable. R^2 at SCC
 Mixture_Word_Problems/23012: Karen spends one-fourth of her weekly allowance on sodas each week. if she spends \$1 each day on sodas, what is her weekly allowance.(1 week = 7 days 1 solutions Answer 11395 by rapaljer(4667)   on 2005-12-19 20:33:18 (Show Source): You can put this solution on YOUR website!She spends \$7 per week on sodas, which equals 1/4 of the total allowance. Let x = total allowance Here is the equation: One fourth of total allowance equals \$7. Multiply both sides by 4: R^2 at SCC
 Linear-equations/23002: can you please help me on origin. How do you write an equation for the line containing the origin and the points (2,1) Please help me im clueless I know that origin has something to do with slop and the slope formula is Y2-Y1 over X2- X1. I have no idea what to do and i have a teacher that does not clearly explain things and this is my last resort. 1 solutions Answer 11392 by rapaljer(4667)   on 2005-12-19 19:38:00 (Show Source): You can put this solution on YOUR website!If the line contains the origin, that means that in the equation of a line y=mx+b the value of b = 0. All you need is the slope, which is rise over run, up 1 and over 2 to get from (0,0) to (2,1). The slope m is rise over run = 1/2, so the equation is or R^2 at SCC
 Exponential-and-logarithmic-functions/23001: __________________2 log (3x-1)=log (2x ) ___8__________8 im sorry i dont really know how to type those on the computer but the to is for 2x squared and the 8s are supposed to be log and then the little 8 thing I dont really know how to do this stuff so if you could show me one i would know how to do it Thank you1 solutions Answer 11391 by rapaljer(4667)   on 2005-12-19 19:34:14 (Show Source): You can put this solution on YOUR website!Let me take a shot at it anyway. Is this what you mean: ??? If that is the question, then you can say that if , then . Likewise, means that , which is a quadratic equation. Get this equal to zero by adding -3x +1 to each side of the equation: This does not factors so you'll have to solve by quadratic formula. Before I go to a lot of trouble to do that, let's check to see if I copied the problem correctly. You can repost this or send me an Email to finish the problem. R^2 at SCC
 Travel_Word_Problems/23000: I have tried very hard to come up with the equation for this problem. I figured that the answer is 8 miles but I am lost trying to write the equation Thank you. Ronald rode away from home in a car at ther rate of 32mph. He walked back at the rate of 4mph. The round trip required 2 1/4 hours. How far did Ronald ride.1 solutions Answer 11390 by rapaljer(4667)   on 2005-12-19 19:01:00 (Show Source): You can put this solution on YOUR website!Let D = distance home. D=RT Time = time riding + time walking = 2.25 hours Multiply both sides by the LCD which is 32: miles Does that look right?? R^2 at SCC
 logarithm/22993: help! log10^(square root of 100, then a little 5 on the right of the sign)1 solutions Answer 11388 by rapaljer(4667)   on 2005-12-19 18:54:14 (Show Source): You can put this solution on YOUR website!I'm not sure I understand your question, but I'll try to answer it anyway. When you write log with no base number, then it is assumed that you mean log base 10. Let's do a beginners lesson in logarithms. log 10 means , which means "what power would you raise 10 to in order to get 10?" The answer is the power which is . log 100 means , which means "what power would you raise 10 to in order to get 100?" The answer is the power which is . log 1000 means , which means "what power would you raise 10 to in order to get 1000?" The answer is the power which is . It so happens that if you have , then the answer is ! In your problem, I'm not sure what the power of 10 was, but whatever it was, I'll bet that power is the answer to the problem. R^2 at SCC
 Travel_Word_Problems/22994: Jim is able to sell a hand-carved statue for \$670 which was a 35% profit over his cost. How much did the statue originally cost him? I saw the solution for this question, but I didnot get it.1 solutions Answer 11387 by rapaljer(4667)   on 2005-12-19 18:38:13 (Show Source): You can put this solution on YOUR website!Let x = cost. .35x = profit Cost + Profit = Selling price x + .35x = 670 1.00 + .35x = 670 1.35x = 670 Divide both sides by 1.35: x= 670/1.35= \$496.30 approximately It usually comes out more even than this, but such is life sometimes. I still think it is correct. R^2 at SCC
 Graphs/22998: i need help with appropriate susbtitution please.the question says solve by making the appropriate substitution ex. x to the 4 power -9x squared-112+01 solutions Answer 11386 by rapaljer(4667)   on 2005-12-19 18:31:22 (Show Source): You can put this solution on YOUR website!Do you mean: You need to factor this by finding two numbers whose product is 112 and whose difference is 9. If you can't think of the combination, start at the beginning with 1: 1*112 2* 56 3 does not go into 112 4* 28 7* 16 That's it! There is the difference of 9! or or There are no real numbers that you can square to get a negative number, so has no real solutions. If you wanted complex solutions also, then the solutions of the last part would be R^2 at SCC
 Complex_Numbers/22997: Directions: Write an expression to answer each question. What is the product of 12 and a? Is the answer 12a?1 solutions Answer 11384 by rapaljer(4667)   on 2005-12-19 18:16:19 (Show Source): You can put this solution on YOUR website!Yes it is! R^2 at SCC P.S. I seem to have missed posting a lesson plan that might be helpful related to this question. I have it on my website if you care to look at it. Go to my website by clicking on my tutor name "rapaljer" anywhere in algebra.com, then click on "Basic Algebra", then "Samples from Basic Algebra One Step", then go to "Chapter 1", and look for "Like Terms and Distibutive Property". That section addresses a lot of terminology questions and a lot of small issues that we who know math take for granted. Here is the URL for this, in case you can click on the following and go there directly: http://www2.scc-fl.edu/rrapalje/BasicAlgebra/Samples%20from%20Basic%20One%20Step%20Ch%201/1106%20Like%20Terms%20and%20Distrib%20Prop.htm. I'll try to get it posted also to algebra.com as a lesson plan when I get a chance.
 Polynomials-and-rational-expressions/22996: I REALLY need help for the following problem. 1.5m^6(-2m^2)^4. The solution to this is hidden in a multiple choice problem and none of the answers I've calculated ad up to the possible answers I need to pick from. Help would be appreciated and thank you in advance!1 solutions Answer 11383 by rapaljer(4667)   on 2005-12-19 18:07:26 (Show Source): You can put this solution on YOUR website!PLEASE NOTE: I made a TERRIBLE error in this problem, now corrected thanks to the CORRECT solution by AnyltcPhil. Thanks Phil. Notice that Does that match up to any of your multiple choice answers? R^2 at SCC
 Travel_Word_Problems/22995: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? I did not get the answer to this problem, so if you could please give me some solutions.1 solutions Answer 11381 by rapaljer(4667)   on 2005-12-19 18:02:31 (Show Source): You can put this solution on YOUR website!If Sally can paint the house in 4 hours, then in 1 hour she can paint 1/4 of the house. If John can paint the house in 6 hours, then in 1 hour he can paint 1/6 of the house. Let x = number of hours it would take them together to paint the house, then working together, in 1 hour they can paint 1/x of the house. The equation is this: Multiply both sides by the LCD which is 12x: = 2.4 hours R^2 at SCC
 logarithm/22964: HELP =) ! resolving the Question 2570 (p200 - 250) : log of 9 to the base square root of x - log of 3 to the base x = 9 + 6 log of x to the base square root of 3 a tutor found x = 3^(1/4) or x = 1/3 I only found one answer x = 3^(1/4) Who is right ? And where is the (my?) flaw ? Thanks a lot !!! Here is my answer : logV""x(9) - logx(3) = 9 + 6logV""3(x) (logx 9) / (logx V""x) - logx 3 = 9 + 6( (logx x) / (logx V""3) ) (logx 9) / ( (logx x) / 2 ) - logx 3 = 9 + 6( 1 / ( (logx 3) / 2 ) ) (logx 9) / ( (logx x) / 2 ) - logx 3 = 9 + 6 / ( (logx 3) / 2 ) 2logx 9 - logx 3 = 9 + 6 ( 2 / logx 3 ) 2logx 9 - logx 3 = 9 + 12 / logx 3 logx 3 ( 2logx 9 - logx 3 - 9 ) = 12 logx 3 ( 4logx 3 - logx 3 - 9 ) = 12 logx 3 ( 3logx 3 - 9 ) = 12 3(logx 3)^2 - 9logx 3 = 12 (logx 3)^2 - 3logx 3 = 4 logx 3 - 3 = 4 / (logx 3) logx 3 - 3 = 1/4 logx 3 logx 3 - 3 = logx 3^(1/4) logx 3 - logx 3^(1/4) = 3 logx (3/3^(1/4) ) = 3 x^3 = 3/3^(1/4) x^3 = 3^(3/4) x^3 = 3^( (1/4) * 3 ) x^3 = ( 3^(1/4) )^3 x = 3^(1/4) 1 solutions Answer 11335 by rapaljer(4667)   on 2005-12-19 10:25:14 (Show Source): You can put this solution on YOUR website!I would have to agree with the tutor, since I found two solutions when I solved it myself. I don't entirely understand your notation, but I think you may have lost a solution when you went from a quadratic equation to a linear equation: (logx 3)^2 - 3logx 3 = 4 logx 3 - 3 = 4 / (logx 3) It might have been safer if you had set it equal to zero, and factored it. [ logx 3 - 4] [logx 3 + 1] = 0 This way, you too will get two solutions. R^2 at SCC
 Mixture_Word_Problems/22957: Please help me, i had a hard time to answer these questions. Thank you! Here it goes, how much water must be evaporated from 18 kilograms of a 20% salt solution to produce a 50% solution?1 solutions Answer 11323 by rapaljer(4667)   on 2005-12-19 07:42:21 (Show Source): You can put this solution on YOUR website!Let x = amount of water evaporated 18 = amount of liquid before 18-x = amount of liquid after Amount of salt before = Amount of salt after .20*18= .50(18-x) 3.6 = 9.0 - .5x Subtract 9.0 from each side 3.6 - 9.0 = 9.0 - 9.0 - .5x -5.4 = -.5x Divide by -.5: x= 10.8 liters Check: .2* 18 = 3.6 before .5*(18-10.8)= .5(7.2)= 3.6 after R^2 at SCC
 Equations/22887: Please Help me solve this equation: factor each: x^2-x-30 Thanks !1 solutions Answer 11318 by rapaljer(4667)   on 2005-12-18 23:52:12 (Show Source): You can put this solution on YOUR website!This is NOT an equation, so you can't solve it! However, if you meant x^2 -x - 30 = 0 (x-6)(x+5) = 0 x=6 or x= -5 R^2 at SCC
 Expressions-with-variables/22947: -7n+3p-4n+p1 solutions Answer 11317 by rapaljer(4667)   on 2005-12-18 22:25:49 (Show Source): You can put this solution on YOUR website!Just get the like terms together and combine like terms (remember that p means 1p): -7n+3p -4n+p -7n-4n +3p +1p -11n + 4p R^2 at SCC
 Polynomials-and-rational-expressions/22923: What is a shortcut of finding a trinomial squared...For Example like: (x^2-3x+5)^21 solutions Answer 11316 by rapaljer(4667)   on 2005-12-18 22:23:24 (Show Source): You can put this solution on YOUR website! I'd never thought of it before, but I suppose you could square each of the terms, then take twice the product of each combination of terms. I guess that would do it, right? Try it out: = = I don't know! It probably is easier (and safer!) to just multiply it out the regular way. Maybe that's why I never heard of this "shortcut"!! R^2 at SCC
 Polynomials-and-rational-expressions/22932: 56 x to the third power plus 64 x to the second power take away 20 x divided 8 x to the second power take away 2 x take away 15 times 2 x to the second power plus 5 x take away 21 divided 63 x to the third power plus 129 x to the second power take away 421 solutions Answer 11315 by rapaljer(4667)   on 2005-12-18 22:11:59 (Show Source): You can put this solution on YOUR website!You went to a lot of trouble to write this out. In the form of fractions is this what you meant? Is that what you meant, or perhaps either you or I mis-copied something. At least I hope we mis-copied something, because I've looked at this, and it doesn't simplify. I see a couple of places it would factor (the first numerator and both denominators factor), but I don't see how it will simplify!! R^2 at SCC
 Linear-equations/22946: HOW DO YOU WRITE A PROBLEM IN SLOPE FORMAT 1 solutions Answer 11314 by rapaljer(4667)   on 2005-12-18 21:54:30 (Show Source): You can put this solution on YOUR website!If the equation of a line is given in "standard form", such as Ax+By=C, then you must solve for y. For example, given 3x+2y = -12, you begin by subtracting 3x from both sides: 3x+2y=-12 2y = -3x - 12 Next, divide both sides by the coefficient of y, which is 2: This is called slope-intercept form of the equation since the coefficient of x is the slope (in this case ), and the y intercept is the number term (in this case the y intercept is -6). I'm assuming that this is what you meant by "slope format" R^2 at SCC