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# Recent problems solved by 'rapaljer'

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 Linear-equations/6397: what do they mean by find the LCM of 2 certain numbers1 solutions Answer 3427 by rapaljer(4667)   on 2005-08-01 23:37:02 (Show Source): You can put this solution on YOUR website!The LCM of two numbers is the smallest number that is a multiple of both of these numbers. For example, given the numbers 6 and 12, the smallest (least) number that both 6 and 12 divide into would be 12. In addition to 12, you can see that 24, 36, 48, etc. would all be multiples of both 6 and 12 since both 6 and 12 divide evenly into all of these numbers. However, the SMALLEST number that you can find that is evenly divisible by both 6 and 12 is 12. As a second example, given 3 and 8, the LCM would be 24, since 24 is a multiple of both 3 and 8, and there is no smaller number that does this. Sometimes the LCM is the larger of the numbers like for 6 and 12. Sometimes the LCM is the product of the numbers. Sometimes you have to take multiples of the larger number until you find the number that works. For example, given the numbers 9 and 12, to find the LCM, take multiples of 12 (like 12, 24, 36, etc.) until you find one that is divisible by 9. The first one in this list is 36 so the LCM is 36. One of the main reasons for finding the LCM is because the LCM is the Least Common Denominator that you need when adding two fractions. I have a section in my book Basic Algebra: One Step at a Time that might be helpful. You can find it on my website by clicking on this URL. Someday I might make it a lesson for this website. Until then, at least you can have it here: http://www2.scc-fl.edu/rrapalje/BasicAlgebra/Samples%20from%20Basic%20One%20Step%20Ch%203/3.03%20LCD/3.03%20LCD.htm R^2 at SCC
 Linear-equations/6398: what does LCM stand for1 solutions Answer 3426 by rapaljer(4667)   on 2005-08-01 23:24:05 (Show Source): You can put this solution on YOUR website!Least Common Multiple
 Numeric_Fractions/6170: I have a problem with this problem i keep on getting a wrong answer 31/2 + 42/3 please show how u do this problem ANS=177/61 solutions Answer 3348 by rapaljer(4667)   on 2005-07-31 00:12:36 (Show Source): You can put this solution on YOUR website!You have to get a common denominator for the denominators of 2 and 3. The least common denominator for these numbers is 6. To convert the first denominator to 6ths, you must multiply the numerator and denominator of the first fraction by 3, and to get the second denominator to 6ths, you must multiply numerator and denominator by 2: Add numerators together: R^2 at SCC
 Quadratic_Equations/6253: I need help with this problem, I am evidently missing a step. Here is the problem: 3x^2(r + 3s) -6y^2(r + 3s) The answer in the book is: 3(r + 3s)(x^2 - 2y^2) I can not figure out how this is the answer, will you please show each step. Thanks. tsj 1 solutions Answer 3347 by rapaljer(4667)   on 2005-07-30 23:34:58 (Show Source): You can put this solution on YOUR website!Do you see that you have TWO common factors here? There is a common factor of 3 and also a common factor of (r+3s). Take out ALL common factors: 3(r+3x)(____+____) , where what is left in the first position is , and in the second R^2 at SCC
 Linear-equations/6260: how do i simplify this expression? 5cd minus 6d?1 solutions Answer 3345 by rapaljer(4667)   on 2005-07-30 23:29:11 (Show Source): You can put this solution on YOUR website!You can't combine these terms because they are not like-terms. The only thing you can do is to factor it by taking out the common factor of d, d(5c-6), but this is not considered simplifying an expression. Basically, the expression you have given cannot be simplified. R^2 at SCC
 Quadratic_Equations/6256: I am totally lost on this problem, please explain and show the steps. Here is the problem: 2m^2n^2 - 32mn^2 + 8m^2 - 128 I thought the factor of this expression would be "2", but I lost and I do not understand how this is the answer: 2(m + 4)(m - 4)(mn^2 + 4) Confused tsj1 solutions Answer 3344 by rapaljer(4667)   on 2005-07-30 23:26:35 (Show Source): You can put this solution on YOUR website!You did the first step right--you factored out the common factor of 2: However what remains is something with 4 terms that factors by "grouping." From the first two terms, take out an , and from the last two terms, take out a 4. At this point, I suspect that you copied the problem right. In order to factor by grouping, you MUST have a common factor after you do the grouping and factor as we did here. As you can see, this is NOT the case, because of the extra m in the first grouping. Let me suggest what I think the problem should have been: Now you can take out the common factor, which is Last, factor the which is the difference of two squares: R^2 at SCC
 Radicals/6000: radical sign 44 - radical sign 111 solutions Answer 3163 by rapaljer(4667)   on 2005-07-27 23:38:56 (Show Source): You can put this solution on YOUR website! First look for a factor of 44 that is a perfect square. That would be 4. So break this down into You know that the , so write this: These are like terms, so you can combine them: or For additional examples and explanations IN LIVING COLOR, see also my webpage that will soon be a lesson plan in Algebra.com in the next few days, time permitting, at http://www2.scc-fl.edu/rrapalje/Math%20in%20Living%20Color/radical_expressions.htm. You can also find it by double clicking on my tutor name, rapaljer, and go to Math in Living Color, and then look under Basic Algebra. I hope you can find it if you need additional examples and explanations--IN COLOR!! R^2 at SCC
 Inverses/5991: If two numbers have opposite signs, their quotient is,... 1 solutions Answer 3162 by rapaljer(4667)   on 2005-07-27 23:26:17 (Show Source): You can put this solution on YOUR website!NEGATIVE!! And I'm POSITIVE about that one too!!! R^2 at SCC
 Inverses/5992: The sign of the sum of two negative numbers is,...1 solutions Answer 3161 by rapaljer(4667)   on 2005-07-27 23:24:29 (Show Source): You can put this solution on YOUR website!NEGATIVE!! And I'm absolutely POSITIVE about this. Yes, that's my final answer. NEGATIVE!! R^2 at SCC
 Mixture_Word_Problems/6004: find the slope of a line that is parallel to and slope that is perpendicular to the following line: y=-3x Thanks Caroline1 solutions Answer 3160 by rapaljer(4667)   on 2005-07-27 23:22:14 (Show Source): You can put this solution on YOUR website!In the equation of a line in the form y=mx+b, the coefficient of x is the slope of the line. The slope of this line is therefore the coefficient of x, which is -3. A line parallel to this line is going in the same direction, so it also has a slope of m= -3. A line that is perpendicular to a given line has a slope that is the NEGATIVE RECIPROCAL of the slope of the given line. Therefore, the slope of a line perpendicular to must have a slope that is the opposite sign AND the reciprocal of m = -3, which is . R^2 at SCC
 Mixture_Word_Problems/6007: find the slope of a line that is parallel to and slope of a line that is perpendicular to : y=8 Thanks a Ton!!1 solutions Answer 3159 by rapaljer(4667)   on 2005-07-27 23:16:23 (Show Source): You can put this solution on YOUR website!The line y = 8 is a horizontal line, and the slope of ANY horizontal line is 0. Any line parallel to a horizontal line is going in the same direction, so it has the same slope, ZERO. Any line perpendicular to any horizontal line must be a vertical line, and the slope of a vertical line is undefined. So the slope of any line perpendicular to y = 8 is UNDEFINED. R^2 at SCC
 Problems-with-consecutive-odd-even-integers/5517: The product of two consecutive odd integers is 195. i tried x(x+2)=195 1 solutions Answer 2813 by rapaljer(4667)   on 2005-07-22 09:45:50 (Show Source): You can put this solution on YOUR website!You are right. x(x+2) = 195 It's quadratic, and it factors. Basically you need two numbers whose product is 195 and whose difference is only 2, so the numbers will be numerically very close together. Try a number that is near the square root of 195. It would be somewhere between 13 and 15. In fact that is IT: 13 and 15!! (x+15)(x-13)= 0 There are two solutions: In the first case: x= -15 x+2= -13 In the second case: x= 13 x+2 = 15. R^2 at SCC
 Linear-equations/5513: I do not understand how the book came up with this answer here is the two equations they are similar however they have different numbers. #(1) 3/(2x+1)-1/x = 2x/x(2x+1) this is what I am doing I am multilplying each side by the lcd which is [x(2x+1)]. I understand that there is some canceling out that's why the rightside of the equation is 2x, but how did they get the ans. 3x-(2x+1) for the leftside of the equation. what happens to the 1/X? I can't see how this answer came to be. Please help me. :) Mrs. Shavette Wiggins1 solutions Answer 2812 by rapaljer(4667)   on 2005-07-22 09:39:29 (Show Source): You can put this solution on YOUR website! I'm not sure exactly what you did, but this is the way it looked for me: It should look like this, when you multiply both sides by the LCD: Which boils down to this when you clear all the fractions: Check to make sure none of the denoninators are zero, and it looks okay. It does check if you substitute x= -1 for x. R^2 at SCC
 Linear-equations/5449: is 3x+y^2=7 a linear equation? yes or no? and why? thanks a lot for your help!1 solutions Answer 2810 by rapaljer(4667)   on 2005-07-22 01:17:31 (Show Source): You can put this solution on YOUR website!Linear means that you have only variables raised to the first power. Since you have a y^2 it is NOT linear! R^2 at SCC
 Human-and-algebraic-language/5445: my question is: solve 6m-5n=-14 for m thanks 1 solutions Answer 2809 by rapaljer(4667)   on 2005-07-22 01:15:53 (Show Source): You can put this solution on YOUR website! Add + 5n to each side of the equation: Divide both sides by 6: R^2 at SCC
 Human-and-algebraic-language/5448: if a rocket is launched with an initial velocity of 64 feet per second, its height h(t),in feet, after t second is given by the formula h(t)=64t-16t^2. what is the height of this rocket after 2 seconds? thanks for your help!1 solutions Answer 2808 by rapaljer(4667)   on 2005-07-22 01:12:27 (Show Source): You can put this solution on YOUR website! feet R^2 at SCC
 Graphs/5446: what are the x and y coordinates of y=2x-1 thanks1 solutions Answer 2807 by rapaljer(4667)   on 2005-07-22 01:09:31 (Show Source): You can put this solution on YOUR website!I think you mean to find the x and y intercepts of the line y= 2x-1. The y-intercept is where x=0: y = -1 The x-intercept is where y = 0: 0= 2x- 1 1= 2x x= 1/2 R^2 at SCC
 Graphs/5447: what are the x and y coordinates of y=-1 thanks!1 solutions Answer 2806 by rapaljer(4667)   on 2005-07-22 01:04:04 (Show Source): You can put this solution on YOUR website!The equation y=-1 represents a horizontal line that is one unit below the x-axis. Every point on the line has y coordinate -1. The x-coordinate could be any value of x. Then again, maybe you mean to find the x and y-INTERCEPTS!! If this is the case, then the y intercept is -1, and there is NO x-intercept, since the graph never crosses the x-axis. R^2 at SCC
 Polynomials-and-rational-expressions/5451: i need to write y+4=-2/3(x-9) in standard form. thanks a lot for helping me!1 solutions Answer 2805 by rapaljer(4667)   on 2005-07-22 01:01:11 (Show Source): You can put this solution on YOUR website!Start by multiplying both sides by the denominator which is 3: Add +2x and - 12 to each side: R^2 at SCC
 Systems-of-equations/5454: my question is: write the equation in slipe-intercept form of a line having a y-intercept of -8 and a slipe of 3. when i did the problem i came out with y=3x-8 but i'm not sure if thats right could you help me? thanks!1 solutions Answer 2804 by rapaljer(4667)   on 2005-07-22 00:55:34 (Show Source): You can put this solution on YOUR website!Correct again! R^2 at SCC
 Mixture_Word_Problems/5457: True or False??? The union of the negative integers and the counting numbers is the set of integers?? Thanks Caroline1 solutions Answer 2803 by rapaljer(4667)   on 2005-07-22 00:54:16 (Show Source): You can put this solution on YOUR website!That is correct! R^2 at SCC
 Polynomials-and-rational-expressions/5458: my question is: write the equation of a line passing through the points (-3,7) and (2,4). when i did the problem i got y=3x+30/4 is that right? thanks for helping me!1 solutions Answer 2802 by rapaljer(4667)   on 2005-07-22 00:53:10 (Show Source): You can put this solution on YOUR website!I think you missed this one. First find the slope, which is m= m = Check by substituting x = 2, and see if you get y = 4! It works!! R^2 at SCC
 Systems-of-equations/5459: my question is: find the coordinates of the midpoint of the line segment with endpoints (-3,6) amd (-1,9). when i did this problem i got (-2,-3/2) is that right? thanks for the help!1 solutions Answer 2801 by rapaljer(4667)   on 2005-07-22 00:43:58 (Show Source): You can put this solution on YOUR website!OOPS!! I think you missed one here. The x coordinate is right, but when you do the y coordinate, remember, you add the y components together and divide by 2. So the y value = or . The midpoint is (-2,). R^2 at SCC
 Systems-of-equations/5462: my question is: write the equation of a line that has a slope of 2/3 and passes through point (6,-3). my answer was y+3=2/3(x-6) is that right? thanks for the help!1 solutions Answer 2800 by rapaljer(4667)   on 2005-07-22 00:38:54 (Show Source): You can put this solution on YOUR website!This is correct. You might want to write it in either standard form or slope-intercept form. I like slope-intercept form, because of graphing calculators today. Subtract 3 from each side: A good way to check this is to substitute the value of x in the equation, and see if you get the y value. , which checks! R^2 at SCC
 Polynomials-and-rational-expressions/5460: if line a has a slope of -3/8 then what is the slope of a line perpendicular to a? i got 8/3 is that right? thanks!1 solutions Answer 2799 by rapaljer(4667)   on 2005-07-22 00:32:35 (Show Source): You can put this solution on YOUR website!Correctomondo again!! R^2 at SCC
 Polynomials-and-rational-expressions/5461: if line b has a slope of -5/3, then what is the slope of a line parallel to b? i got -5/3 is that right? thanks for the help!1 solutions Answer 2798 by rapaljer(4667)   on 2005-07-22 00:31:31 (Show Source): You can put this solution on YOUR website!Correctomondo!! R^2 at SCC
 Human-and-algebraic-language/5464: If the graph of a system of equations is interecting lines, the system has how many solution(s). thanks for your help!1 solutions Answer 2797 by rapaljer(4667)   on 2005-07-22 00:30:02 (Show Source): You can put this solution on YOUR website!If two straight lines intersect, then there must be ONE and ONLY ONE point of intersection. R^2 at SCC
 Human-and-algebraic-language/5465: If the graph of a systme of equations is two parallel lines, the system has how many solution(s). thanks for your help!1 solutions Answer 2796 by rapaljer(4667)   on 2005-07-22 00:27:53 (Show Source): You can put this solution on YOUR website!If two lines are parallel, then they NEVER intersect. There will be NO SOLUTIONS!! R^2 at SCC
 Human-and-algebraic-language/5466: If the graph of a system of equations is one line, then the system has how many solution(s). thanks for your help!1 solutions Answer 2795 by rapaljer(4667)   on 2005-07-22 00:26:29 (Show Source): You can put this solution on YOUR website!If the two equations actually represent the same line, then the entire line is the solution. The entire line represents infinitely many points. R^2 at SCC
 Human-and-algebraic-language/5483: my questions is solve for x. ax-b=c thanks for the help1 solutions Answer 2794 by rapaljer(4667)   on 2005-07-22 00:23:44 (Show Source): You can put this solution on YOUR website!This is a problem that looks quite intimidating but it is really quite simple, as long as you are not intimidated by the ugly answer that you get. In order to "undo" the subtraction of b, you should start by adding "+b" to each side of the equation: or (either way is acceptable!) Next, since you have "ax", which means "a times x," you must undo this by dividing both sides by a. The result looks like this: or R^2 at SCC
 Human-and-algebraic-language/5485: my questions is what number increased by 40% equals 14? thanks for the help1 solutions Answer 2793 by rapaljer(4667)   on 2005-07-22 00:17:14 (Show Source): You can put this solution on YOUR website!Let x = the number .40 x = 40% of the number x + .40x = 14 Commbine like terms: 1.00x + .40x = 14 1.40x = 14 1.4x = 14 Divide both sides of the equation by 1.4 R^2 at SCC