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can you please help to get answers on these 2 questions?
1.Select the option for “?” that continues the pattern in each question
2, 7, 26, 101, 400, ?
2.Select the option for “?” that continues the pattern in each question
7, 21, 8, 72, 9, ?
1 solutions
Answer 490754 by rapaljer(4670) on 20131128 09:10:15 (Show Source):
You can put this solution on YOUR website! I see a pattern for the first set in which you take the given number and multiply by 4 and subtract 1, then multiply by 4 subtract 2, multiply by 4 subtract 3, mult by 4 and subtract 4, etc. Starting with 2, multiply by 4 subtract 1 giving you 7. Take 7, multiply by 4 and subtract 2 giving you 26. Mult 26 times 4 and subtract 3 giving you 101. Multi by 4 subtract 4 giving you 400. Next would be multiply by 4 and subtract 5 giving 1595.
For the second pattern, I'm not sure. You might try starting with 7 *3 = 21. Next, take 8*3^2= 72. Next, take 9*3^3=243. This might be a stretch, but it's all I can think of.
Happy Thanksgiving!! Please see my website for FREE math explanations, and practice tests. See www.mathinlivingcolor.com.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

Quadratic_Equations/799755: Im having trouble on factoring. The problem is 20a^3+37a^2+8a. I pulled out an a as the greatest common factor and now have a(20a^2+37a+8). But now im stuck. is this where I do the product and some? I just don't know where to go from her.
1 solutions
Answer 482826 by rapaljer(4670) on 20131016 14:48:41 (Show Source):
You can put this solution on YOUR website! You are correct to take out the common factor of a. This gives you
a(20a^2+37a+8), which you have. The next step is to factor the trinomial. I call this "Advanced Trinomial Factoring," and I have a detailed explanation on my website that you may want to see. First however, I'll try to explain your problem for you. You need to "undo" the trinomial by "unFOILing" it, if you know what I mean. You need to break down the 20a^2 into a product that will be the "First" times "First":
( a+___ )(20a+___ )
(2a+___ )(10a+___ ) or
(5a+___ )(4a+___ )
Meanwhile the Last times Last has to end up with a product of 8:
(___+ 8)(___+ 1)
(___+ 1)(___+ 8)
(___+ 2)( ___+4)
(___+ 4)(___+ 2)
Most importantly, the middle term has to add up to 37a. There are often a LOT of different combinations to try to see which one works. However, there are usually some short cuts too!! In this case, a really GOOD shortcut is that the middle term 37a is an ODD number, so you CANNOT use any EVENEVEN combinations. This means that it HAS to be 5a*4 or 20a*a. Also, it HAS to be 1*8 or 8*1 for the last times last.
It turns out that the winning combination is (5a+8)(4a+1), since the middle term 5a + 32a adds up to 37a. Final answer is a(5a+8)(4a+1).
Please see also my website by using the easytospell and easytoremember link www.mathinlivingcolor.com. Click the link at the bottom of the page which takes you to my Homepage. On the Homepage, look for the link near the top of the page "Basic Algebra: One Step at a Time." Look in "Chapter 2" for the section called "Advanced Trinomial Factoring". There you will find a much more detailed explanation of the topic, with lots of examples and exercises, with many of the exercises solved IN COLOR on the corresponding "Math in Living Color" pages. The website has detailed explanation for most topics in algebra, explained especially for students who have trouble understanding their traditional textbooks! If you like the website, please recommend it to your friends and family who have trouble with math!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

Radicals/741628: I need to solve the equation of
1 2 2y
   = 
y+2 y3 y^2y6
I get an answer of y=7 is this answer correct?
also i have another answer that am not too sure about
1 a 2
   = 
a+3 a^29 3a
my answer is 3=2 not so sure about this one either..
Could someone please check if my answers are correct, and could guide me on how to do them if they are wrong.
Thank you!
1 solutions
Answer 452097 by rapaljer(4670) on 20130425 02:55:36 (Show Source):

Travel_Word_Problems/741643: Please Help Me solve this problem.
It took 32 liters of gas to travel 450 km. How many liters would it take to drive 800 km (round it to the nearest tenth).
I figured if I took the 450 km times 2 would give 900 km and 64 liters to do this. I guessed it would be between 55 to 60 Liters to do this; but that is my guess and do not know how to work the problem out.
Please Help Me!
1 solutions
Answer 452091 by rapaljer(4670) on 20130425 02:20:15 (Show Source):

Circles/718623: find the center radius form of the equation of a circle with the center(2,8) and tangent to the x axis
1 solutions
Answer 440995 by rapaljer(4670) on 20130225 12:03:14 (Show Source):
You can put this solution on YOUR website! If the center is at (2,8), and it is tangent to the x axis, this means that it just barely touches the x axis from a center that is 8 units above the xaxis. So, the radius of the circle is 8.
(xh)^2 + (yk)^2 = r^2
(x2)^2 + (y8)^2 = 64
For additional help with circles, you may want to see my nontraditional explanation of this and other topics on my own website: www.mathinlivingcolor.com.
Click on the link at the very bottom of the page which will take you to my Homepage, and look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "College Algebra" and look in Chapter 2 for the section on Circles. Then, I solved many of my problems IN COLOR, which makes all the difference in the world, to understanding math concepts. Try it for this topic as well as others, and let me know what YOU think.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

Polynomialsandrationalexpressions/718666: what is the answer to: 2x3(x5)1
Directions say to simplify. I first thought you would combine like terms but i cannot figure this out.
1 solutions
Answer 440992 by rapaljer(4670) on 20130225 11:37:50 (Show Source):
You can put this solution on YOUR website! The first step, if there are parentheses in the problem, is to remove the parentheses by distributive property.
2x 3(x5) 1
2x3x+151
Now, combine like terms:
5x + 14
For additional explanations on this type of problem that may be easier to understand than the traditional explanations, please see my own website at www.mathinlivingcolor.com. Then click on the link at the very bottom of the page, which will take you to my Homepage, and look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in Chapter 1 for topics about Signed Numbers, Order of Operations, and especially Distributive Property. You may also really like my explanation of Equation Solving. Also, look for solutions to many of the problems you will find there IN COLOR!! Color really makes a difference in being able to understand what was done in the problem.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

Expressionswithvariables/684006: What is 3p + 2 (2p  4)
1 solutions
Answer 423874 by rapaljer(4670) on 20121122 22:40:18 (Show Source):
You can put this solution on YOUR website! This one is called the Distributive Property. It might help to think of it as
3p + 2 1(2p  4)
3p + 2 2p + 4
3p  2p + 2 + 4
p + 6
I have a LOT of explanations, examples, and FULL COLOR solutions to problems like this on my own website.
To see my website go to www.mathinlivingcolor.com, named after my theme "Math in Living Color." Look for a single link near the bottom of this page that will take you to my Homepage. Once on my Homepage, look for "Basic, Intermediate and College Algebra: One Step at a Time", and select "Basic Algebra". Look in "Chapter 1" for "Section 1.06".
If you have questions on other topics, just send me an Email! I'll be glad to help you find the right page on my website. I hope you like my website and that you will recommend it to family and friends! Remember, my goal is to make math EASIER than your own textbook is making it, and it's ALL FREE!!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
www.mathinlivingcolor.com.

Polynomialsandrationalexpressions/684000: Factor the Polynomial:
x^3+7x^2+15x+9
I don't even know where to start, however I made an attempt, by trying to use the factor by grouping method which all I got is:
(x^3+7x^2)+(15x+9)
x^2(x+7)+3(5x+3)
and that's were I stopped because I know that two of them should be the same
thank you in advance :D
1 solutions
Answer 423864 by rapaljer(4670) on 20121122 21:37:53 (Show Source):
You can put this solution on YOUR website! This one does NOT work by grouping! You need to use Synthetic Division. Start by looking at the LAST term, which is 9. You need to find a number that is a factor of 9, and do synthetic division by that number until you get a remainder of 0. I can see that one that works here is 1, maybe others as well.
I don't know exactly how to lay out a synthetic division problem on this website, but I have quite a few examples on my website in Intermediate Algebra or College Algebra.
To see my website go to www.mathinlivingcolor.com, named after my theme "Math in Living Color." Look for a single link near the bottom of this page that will take you to my Homepage. Once on my Homepage, for explanation of Sythetic Division, look for "Basic, Intermediate and College Algebra: One Step at a Time", and select "Intermediate Algebra". Look in "Chapter 2" for "Section 2.10" page 232! College Algebra Chapter 3 has additional explanation about using Synthetic Division in order to factor polynomials. Send me an email if you need additional help with this one.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
www.mathinlivingcolor.com.

percentage/684001: A student took a test composed of 10 questions, with correct answers worth 5 points. If the student received 30 points for his grade, how many questions were correct?
I know the answer is 6 but how do I put it in an exquation
1 solutions
Answer 423863 by rapaljer(4670) on 20121122 21:24:53 (Show Source):

logarithm/682562: solve for x
log16(2x + 1) = 0.5
1 solutions
Answer 423243 by rapaljer(4670) on 20121119 00:44:57 (Show Source):
You can put this solution on YOUR website! means that
I have a LOT of explanations, examples, and FULL COLOR solutions to problems like this on my own website. I even have VIDEOS of me teaching logarithms in my younger days before I retired and my hair was still dark!! Logarithms are probably not nearly as hard as your textbook is making it.
My website is all FREE with NO ADVERTISING, and I'm not selling anything! I just want to make this as easy as I can for you.
To see my website go to www.mathinlivingcolor.com, named after my theme "Math in Living Color." Look for a single link near the bottom of this page that will take you to my Homepage. Once on my Homepage, look for "Basic, Intermediate and College Algebra: One Step at a Time", and select "College Algebra". Look in "Chapter 4" for Logarithms!
As for the videos, look for the link on my Homepage called "Rapalje Videos in Living Color", and choose College Algebra. Choose the videos on Logarithms, Part II. Regretfully, the videos are from 20 years ago, and any mention of calculators in the videos is horribly outdated. Sorry about that!
If you have questions on other topics, just send me an Email! I'll be glad to help you find the right page on my website. I hope you like my website and that you will recommend it to family and friends! Remember, my goal is to make math EASIER than your own textbook is making it, and it's ALL FREE!!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
www.mathinlivingcolor.com.

