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1 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
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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=177/6
1 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:
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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 
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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.
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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
tsj
1 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:
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Radicals/6000: radical sign 44 - radical sign 11
1 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!!
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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 Caroline
1 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  .
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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.
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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.
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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):
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Graphs/5446: what are the x and y coordinates of
y=2x-1
thanks
1 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
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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.
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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):
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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, ).
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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!
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Human-and-algebraic-language/5483: my questions is
solve for x. ax-b=c
thanks for the help
1 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 
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