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Recent problems solved by 'rapaljer'
rapaljer answered: 4664 problems
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Will someone please help me with this fraction? I do not no how to make the tiny to the power numbers so I made them regular size. so each 2 after each w is a to the power 2. And the 2 after the w is also a to the power 2. I hope I am making sense here. Help me figure this out please.
1 solutions
Answer 168996 by rapaljer(4667)   on 2009-10-15 21:41:53 (Show Source):
You can put this solution on YOUR website!
Factor everything that can be factored:
Now, divide out the (w-1) factors in the numerator and denominator:
Next, divide out one of the (w+1) factors:
For additional explanation on this section, please see my own website. Do a "Bing" or "Google" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of these searches. Then near the top of my Homepage, look for "Basic, Intermediate and College Algebra". Choose "Basic Algebra", "Chapter 3", "Section 3.02 Multiplying and Dividing Fractions". See also the "MATH IN LIVING COLOR" pages that go with this section.
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Polynomials-and-rational-expressions/227394: they want this factored completely
98a^4-72b^2
im not understanding
1 solutions
Answer 168990 by rapaljer(4667) on 2009-10-15 21:23:20 (Show Source):
You can put this solution on YOUR website!The first step in factoring is ALWAYS to factor the COMMON FACTOR, which in this problem is 2.
98a^4-72b^2
2(49a^4-36b^2)
Notice that you have PERFECT SQUARES inside the parentheses.
2(_______)(_______)
The First times First has to come out to 49a^4. So, try this combination 7a^2*7a^2.
2(7a^2____)(7a^2____)
Now, the Last times Last has to come out to 36b^2. Try 6b*6b.
2(7a^2__6b)(7a^2__6b)
In order to get this to come out to -36b^2, you need OPPOSITE signs:
2(7a^2-6b)(7a^2+6b)
For additional explanation on FACTORING, please see my own website. Do a "Bing" or "Google" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of these searches. Then near the top of my Homepage, look for "Basic, Intermediate and College Algebra". Choose "Basic Algebra", "Chapter 2". There are several topics on Factoring, especially "Factoring the Common Factor", "Factoring Trinomials", and "Factoring the Difference of Squares." See also the "MATH IN LIVING COLOR" pages that go with these sections.
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Numbers_Word_Problems/227386: The sum of three consecutive even numbers is 150. Find the numbers.
What does it mean consecutive even numbers? How do I do this?
Thank you
1 solutions
Answer 168987 by rapaljer(4667) on 2009-10-15 21:12:57 (Show Source):
You can put this solution on YOUR website!Consecutive even numbers means like 2,4, and 6.
Or 18, 20, 22.
Or 74, 76, 78.
In general the second number is always 2 more than the first one, and the third one is always 4 more than the first one.
So, let x= first even number
x+2= second even number
x+4= third even number.
If three consecutive even numbers is 150, then
x+ x+2+x+4= 150
3x+6=150
3x=144
x= 48
x+2=50
x+4=52
Check: The sum of the numbers 48+50+52=150. It checks!
For additional explanation on Word Problems, in particular "Consecutive Integer" problems, please see my own website. Do a "Bing" or "Google" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of these searches. Then near the top of my Homepage, look for "Basic, Intermediate and College Algebra". Choose "Basic Algebra", "Chapter 1", "Section 1.10 Word Problems Part I". See also the "MATH IN LIVING COLOR" pages that go with this section.
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
Number-Line/226314: whats 11 solutions
Answer 168984 by rapaljer(4667) on 2009-10-15 21:05:34 (Show Source):
You can put this solution on YOUR website! means the same as  . x represents ANY number that is GREATER than 1. For example 2, 3, 4, etc. Draw a numberline and locate the number 1 on this numberline. Shade everything to the RIGHT of 1. You do NOT want to include the number 1, so you can either use an open circle, or a parentheses opening to the right, whichever notation your teacher tells you to use.
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
Problems-with-consecutive-odd-even-integers/227367: Three times the greater of two consecutive odd integers is five less than four times the smaller. Find the two numbers.
1 solutions
Answer 168979 by rapaljer(4667) on 2009-10-15 20:48:07 (Show Source):
You can put this solution on YOUR website!Let x = first odd integer (smaller)
x+2 = second odd integer (larger)
3(x+2) = 4x-5
3x+ 6 = 4x -5
Subtract 3x from each side:
3x-3x + 6 = 4x-3x -5
6=x-5
Add +5 to each side:
6+5= x-5+5
11=x
x+2= 13.
Smaller = 11, Larger = 13.
Check:
Three times the larger is five less than 4 times the smaller.
3(13)= 4(11) -5
39= 44-5
It checks!!
For additional explanation on Word Problems, in particular "Consecutive Integer" problems, please see my own website. Do a "Bing" or "Google" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of these searches. Then near the top of my Homepage, look for "Basic, Intermediate and College Algebra". Choose "Basic Algebra", "Chapter 1", "Section 1.10 Word Problems Part I". See also the "MATH IN LIVING COLOR" pages that go with this section.
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
Geometric_formulas/227360: solve the formula for the variable indicated
A = 1/2 bh for b
1 solutions
Answer 168977 by rapaljer(4667) on 2009-10-15 20:38:36 (Show Source):
You can put this solution on YOUR website!
Clear the fraction by multiplying both sides by the denominator which is 2.
To solve for b, divide both sides by h:
For additional explanation on this topic of "Literal Equations", see my own website. Do a "Bing" or "Google" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of these searches. Then near the top of my Homepage, look for "Basic, Intermediate and College Algebra". Choose "Basic Algebra", "Chapter 3", "Section 3.07".
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
Equations/227346: solve for r S = a / (a - r) I know the answer but don't know how to get it
1 solutions
Answer 168975 by rapaljer(4667) on 2009-10-15 20:28:40 (Show Source):
You can put this solution on YOUR website! Solve for r.
Multiply both sides of the equation by the denominator (a-r).
Get the r term alone on the left side by subtracting Sa from each side:
Divide both sides by -S:
Multiply numerator and denominator by -1:
 or  or 
You may want to take a look at my own website for my non-traditional explanation of the topic that I call "Literal Equations". Do a "Bing" or "Google" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of these searches. Then near the top of my Homepage, look for "Basic, Intermediate and College Algebra". Choose either Basic Algebra" Chapter 3", "Section 3.07". For a slightly more advanced explanation, see "Intermediate Algebra", "Chapter 2", "Section 2.07".
As to your specific problem that you posted, I don't think you gave enough information to solve it.
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Graphs/227348: What is -2/3t = 16?
1 solutions
Answer 168973 by rapaljer(4667) on 2009-10-15 20:14:46 (Show Source):
You can put this solution on YOUR website!
In order to "undo" multiplying by -2/3, multiply both sides of the equation by the reciprocal of -2/3, which is -3/2.
Divide out the 2 into 16, which leaves 8 in the numerator.
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
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Miscellaneous_Word_Problems/227335: How would you write an equation for a direct variation with a graph that passes through each point?
(-1.5,9)
My teacher didn't explain this very good. Thank you
1 solutions
Answer 168971 by rapaljer(4667) on 2009-10-15 20:10:33 (Show Source):
You can put this solution on YOUR website!If your teacher didn't explain this topic very well, then why don't you take a look at my own website. Do a "Bing" or "Google" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of these searches. Then near the top of my Homepage, look for "Basic, Intermediate and College Algebra". Choose "Intermediate Algebra", "Chapter 2", "Section 2.09".
As to your specific problem that you posted, I don't think you gave enough information to solve it.
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
Rational-functions/227329: what is 3 over 8 equal to 6 over x?
1 solutions
Answer 168964 by rapaljer(4667) on 2009-10-15 19:40:09 (Show Source):
You can put this solution on YOUR website! so 
However, the easy way to do this particular problem is to notice that if you start with "3 over 8 equal to 6 over what", the 6 is double the 3, so you have to double the 8 to get 16.
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
Equations/227322: 9b=7b-70
1 solutions
Answer 168959 by rapaljer(4667) on 2009-10-15 19:29:25 (Show Source):
You can put this solution on YOUR website!9b=7b-70
Get all the b terms on the left side by subtracting 7b from each side:
9b-7b=-70
2b=-70
Divide both sides by 2:
b=-70/2=-35
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
logarithm/227316: 1.1(2.6)^2x = 6(4.4)^x
I have to solve for x and I need the exact solution, not a decimal.
I am getting really frustrated because everytime I try something, it leads me to a dead end. Please help?
1 solutions
Answer 168957 by rapaljer(4667) on 2009-10-15 19:25:01 (Show Source):
You can put this solution on YOUR website!
Take the ln of each side:
Get the x terms on the right side, and the NON-x terms on the left side:
Factor out the x on the left side:
Divide both sides by  :
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
Probability-and-statistics/224528: When two cards are drawn from a standard 52-card deck, what is the probability that they are of different suits?
1 solutions
Answer 167720 by rapaljer(4667) on 2009-10-10 09:16:28 (Show Source):
You can put this solution on YOUR website!The question is really what is the probability that the second card is NOT the same suit as the first card. There are four suits possible, and of these 1 suit matches and three do NOT. Therefore, the probability it does NOT match is 3 out of 4.
Prob = 3/4
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Percentage-and-ratio-word-problems/224531: It takes 40 days for a pond to get filled with rain water. If the level of water doubles each day, then how long would it take to fill 1/4 of the pond?
(A) 10 days (B) 20 days (C) 30 days (D) 35 days (E) 38 days
1 solutions
Answer 167719 by rapaljer(4667) on 2009-10-10 09:12:16 (Show Source):
You can put this solution on YOUR website!This is a NEAT problem. I'm going to say 38 days, because if the pond is 1/4 filled on day 38, then it doubles and becomes half full on day 39, then it doubles again and becomes full on day 40.
Again, congratulation on a REALLY neat problem!!
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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logarithm/224524: How to solve:
e^sinx = 4^cosx
1 solutions
Answer 167717 by rapaljer(4667) on 2009-10-10 09:06:29 (Show Source):
You can put this solution on YOUR website!e^sinx = 4^cosx
Take the ln of each side:
By the law of logarithms,
Divide both sides by cosx
Undo the tan function by taking the arctan of each side:
My calculator gives me 54.2 degrees or .95 radians.
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Travel_Word_Problems/224525: If I drive 80 kilometers in 2 hours and then 60 kilometers in 5 hours, what was my average speed in kilometers per hour over the two trips?
1 solutions
Answer 167716 by rapaljer(4667) on 2009-10-10 08:57:03 (Show Source):
You can put this solution on YOUR website!Your total distance was 140 km and the total time was 7 hrs.
Therefore, the average speed for the total trip was r=D/t=140 km/7 hr= 20 km/hr.
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logarithm/224522: How can I solve: ln(cosx)=-1
the answer I think is 1371.58
1 solutions
Answer 167715 by rapaljer(4667) on 2009-10-10 08:53:04 (Show Source):
You can put this solution on YOUR website!ln(cosx)=-1
First "undo" the ln by raising both sides as a power of e.
Next, undo the cos function by using the arccos function:
Using a calculator, I got 68.42 degrees. If the calculator is in radian mode, I got 1.19 radians.
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Equations/224521: Here is the problem. Directions are to solve and check.
3m-(m+1)=6m+1
My work:
1st. 3m-1m-1=6m+1
2nd. 2m-1=6m+1
3rd. 2m-2m-1=-2m+1
4th. -1=4m+1
That is as far as I can get. I dont understand what else to do.
1 solutions
Answer 167714 by rapaljer(4667) on 2009-10-10 08:42:30 (Show Source):
You can put this solution on YOUR website!You have all the m terms on the right side, so get all the number terms to the left side by subtracting 1 from each side.
-1=4m+1
-1-1=4m+1-1
-2=4m
Divide by 4:
-2/4=4m/4
-1/2=m
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Rational-functions/224515: given f(x)=sqrt x+3 and g(x)=6x find f(g(x)) i.e.(fog)(x) and find (fog)(1)
I know that you need to replace the x in sqrt of x +3 so it would read sqrt 6x+3
then would I change that to (6x+3)^2 =36x^2+36x+9.
1 solutions
Answer 167713 by rapaljer(4667) on 2009-10-10 08:22:58 (Show Source):
You can put this solution on YOUR website!Your first part is correct. f(g(x)) means to substitute g(x) = 6x into the formula for f, so  . However, what you did next was NOT correct. You have a SQUARE ROOT, NOT a SQUARE! Do NOT square it!!!
f(g(1)) means to substitute 1 in place of the x.
This would be 
f(g(1)) = 3
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Travel_Word_Problems/224505: calculate the distance you will travel if u miantain an average speed of 10 m/s for 40 s?
i think 400 .. i really need the questions for today and thanks
1 solutions
Answer 167712 by rapaljer(4667) on 2009-10-10 08:14:00 (Show Source):
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