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 Rational-functions/412149: what does it mean when a questions say "what value should be excluded from the domain of the function"?1 solutions Answer 289551 by jim_thompson5910(28715)   on 2011-02-21 17:33:53 (Show Source): You can put this solution on YOUR website!You can NEVER divide by zero. Ever. So we CANNOT do something like because it is undefined. So if you have the rational expression , then we must exclude x=0 from the domain because we CANNOT divide by zero. If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Equations/412012: 7x+8x-12=591 solutions Answer 289467 by jim_thompson5910(28715)   on 2011-02-21 13:08:43 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the answer is which approximates to . If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
Polynomials-and-rational-expressions/412024: I am trying to factor this but I can't factor it?? Can you please help this is my problem 64c^2-80cx+25x^2 is this nonfactorable? THANK YOU!
1 solutions

Answer 289466 by jim_thompson5910(28715)   on 2011-02-21 13:06:27 (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 64 and 25 respectively.

Now multiply the first coefficient 64 and the last coefficient 25 to get 1600. Now what two numbers multiply to 1600 and add to the middle coefficient -80? Let's list all of the factors of 1600:

Factors of 1600:
1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,160,200,320,400,800

-1,-2,-4,-5,-8,-10,-16,-20,-25,-32,-40,-50,-64,-80,-100,-160,-200,-320,-400,-800 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 1600
1*1600
2*800
4*400
5*320
8*200
10*160
16*100
20*80
25*64
32*50
40*40
(-1)*(-1600)
(-2)*(-800)
(-4)*(-400)
(-5)*(-320)
(-8)*(-200)
(-10)*(-160)
(-16)*(-100)
(-20)*(-80)
(-25)*(-64)
(-32)*(-50)
(-40)*(-40)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -80? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -80

First NumberSecond NumberSum
116001+1600=1601
28002+800=802
44004+400=404
53205+320=325
82008+200=208
1016010+160=170
1610016+100=116
208020+80=100
256425+64=89
325032+50=82
404040+40=80
-1-1600-1+(-1600)=-1601
-2-800-2+(-800)=-802
-4-400-4+(-400)=-404
-5-320-5+(-320)=-325
-8-200-8+(-200)=-208
-10-160-10+(-160)=-170
-16-100-16+(-100)=-116
-20-80-20+(-80)=-100
-25-64-25+(-64)=-89
-32-50-32+(-50)=-82
-40-40-40+(-40)=-80

From this list we can see that -40 and -40 add up to -80 and multiply to 1600

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

note: is equivalent to since the term occurs twice. So also factors to

------------------------------------------------------------

So factors to

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

 Equations/410763: I am totally lost please help. Solving by substitution or elimination 2x+y=6 x-y=31 solutions Answer 288776 by jim_thompson5910(28715)   on 2011-02-17 17:36:54 (Show Source): You can put this solution on YOUR website!Basic outline: Add the two equations to get: 2x+y=6 x-y=3 ------ 3x+0y=9 which gives us the new equation 3x=9 Next solve for x. Once you have the solution for x, use it to find y. You do this by plugging that value of x into either equation and solving for y.
 test/410756: If f(x)= 6sinx + 4cosx What is the derivative of f(x)? What is the derivative of f(5)?1 solutions Answer 288774 by jim_thompson5910(28715)   on 2011-02-17 17:35:14 (Show Source): You can put this solution on YOUR website!Hint: the derivative of sine is cosine and the derivative of cosine is -sine. Also, the derivative of a constant is 0.
 Functions/409605: Find the domain and range of {(-3,-7), (-1,-3), (0,-1), (2,3), (4,7)} I don't understand this at all.1 solutions Answer 288275 by jim_thompson5910(28715)   on 2011-02-15 17:37:56 (Show Source): You can put this solution on YOUR website!The domain is the set of all inputs. In this case, this means that the domain is the set of all x coordinates. So the domain is {-3, -1, 0, 2, 4} Notice how these values are all x coordinates. In a similar fashion, the range is the set of all the y coordinates (since the range is the set of all outputs). So the range is {-7, -3, -1, 3, 7} If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Inequalities/409500: 32 - 8y > -4 (y - 10)1 solutions Answer 288246 by jim_thompson5910(28715)   on 2011-02-15 14:22:30 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Subtract from both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the answer is If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Probability-and-statistics/409514: Compute P9,91 solutions Answer 288243 by jim_thompson5910(28715)   on 2011-02-15 14:15:20 (Show Source): You can put this solution on YOUR website!Use the formula P(n,r) = (n!)/((n-r)!) to get P(9,9) = (9!)/((9-9)!) P(9,9) = (9!)/(0!) P(9,9) = (9!)/1 P(9,9) = 9! P(9,9) = 9*8*7*6*5*4*3*2*1 P(9,9) = 362880 Note: P(x,x) = x! for all nonnegative integers x If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
Polynomials-and-rational-expressions/409296: how do you factor y2+2xy+x2
1 solutions

Answer 288151 by jim_thompson5910(28715)   on 2011-02-15 01:11:45 (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 1 respectively.

Now multiply the first coefficient 1 and the last coefficient 1 to get 1. Now what two numbers multiply to 1 and add to the middle coefficient 2? Let's list all of the factors of 1:

Factors of 1:
1

-1 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 1
1*1
(-1)*(-1)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2

First NumberSecond NumberSum
111+1=2
-1-1-1+(-1)=-2

From this list we can see that 1 and 1 add up to 2 and multiply to 1

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

note: is equivalent to since the term occurs twice. So also factors to

------------------------------------------------------------

So factors to

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

 Polynomials-and-rational-expressions/409257: Hi, I am solving with the quadraic formula and would like you to check my work and answer please. 3n^2-2n+5=0 -2 sqrt ((-2)^2-4(3)(5))/(2(3)) -2 sqrt (4-60)/(2) -2 sqrt (60)/(2) -2 sqrt ((4)(15))/(2) -2 +- 2 sqrt (15)/(2) is this final answer? 1 solutions Answer 288148 by jim_thompson5910(28715)   on 2011-02-15 01:02:52 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for n Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) or Break up the expression. or Reduce So the answers are or If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Radicals/409283: How do i find the root -sqrt ( 25 )1 solutions Answer 288147 by jim_thompson5910(28715)   on 2011-02-15 00:58:44 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Inequalities/409260: how to solve 4k-4-3k>13-7k-1+81 solutions Answer 288140 by jim_thompson5910(28715)   on 2011-02-14 22:48:52 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Combine like terms on the left side. Combine like terms on the right side. Add to both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Equations/409262: 16-2(8w-7)=3w-18(2-w)1 solutions Answer 288139 by jim_thompson5910(28715)   on 2011-02-14 22:47:34 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is which approximates to . If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Probability-and-statistics/409103: I have the the first part to this problem, I think. The tree diagram I have drawn but have no idea if it is correct. I am completely stumped on the last 2 parts. I have read and reread the material and even looked at how some of the problems are done on here. But I am still lost on this one. PLEASE HELP! I have to turn it in this evening! Thanks... Problem: A mini license plate for a toy car must consist of a two letters followed by a one digit odd number. Each letter must be a P, Q or a R. Repetition of letters is not permitted. • Use the counting principle to determine the number of points in the sample space. • Construct a tree diagram to represent this situation. • List the sample space. • Determine the exact probability of creating a mini license plate with a Q. Give solution exactly in reduced fraction form. A) P,Q, and R = 3 ways 1 digit odd # = 5 ways 3*5 = 15 B) tree diagram 1st column P, Q, R 2nd column 1,3,5,7,9 beside each letter c) HELP! D) Help! 1 solutions Answer 288063 by jim_thompson5910(28715)   on 2011-02-14 19:17:07 (Show Source): You can put this solution on YOUR website!A) # of letters possible * # of letters possible * # of odd digits = 3 * 2 * 5 = 6 * 5 = 30 So there are 30 different license plates (you're missing half of them) -------------------------------------- B) I can't draw here. -------------------------------------- C) Sample Space {PQ1, PQ3, PQ5, PQ7, PQ9, PR1, PR3, PR5, PR7, PR9, QP1, QP3, QP5, QP7, QP9, QR1, QR3, QR5, QR7, QR9, RP1, RP3, RP5, RP7, RP9, RQ1, RQ3, RQ5, RQ7, RQ9} -------------------------------------- D) There are 20 license plates that have a Q in them, and they are {PQ1, PQ3, PQ5, PQ7, PQ9, QP1, QP3, QP5, QP7, QP9, QR1, QR3, QR5, QR7, QR9, RQ1, RQ3, RQ5, RQ7, RQ9} There are 30 plates total. So the probability is If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Quadratic_Equations/408793: Can you help me with this problem? 2(a-6)^2-45=53 1 solutions Answer 287908 by jim_thompson5910(28715)   on 2011-02-14 00:00:21 (Show Source): You can put this solution on YOUR website! Start with the given equation. FOIL Distribute. Subtract 53 from both sides. Combine like terms. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for a Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the answers are or If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Exponents/408791: 4^x -6 = 41 solutions Answer 287906 by jim_thompson5910(28715)   on 2011-02-13 23:57:06 (Show Source): You can put this solution on YOUR website! Note: since the bases are equal, the exponents are equal. So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Exponential-and-logarithmic-functions/408778: Is there a faster way to simplify (x-y)^8 than distributing it? I'm having a hard time figuring it out. 1 solutions Answer 287904 by jim_thompson5910(28715)   on 2011-02-13 23:08:43 (Show Source): You can put this solution on YOUR website!Yes it involves the Binomial Theorem and Pascals Triangle. Check out this page for more info.
 Inequalities/408765: can you please show me how to solve this problem? -2|3x-4|<16 thank you1 solutions Answer 287891 by jim_thompson5910(28715)   on 2011-02-13 22:22:38 (Show Source): You can put this solution on YOUR website!If you divide both sides of the inequality by -2 you'll get |3x-4| > -8 Note: remember that the sign will flip when you divide both sides by a negative number. Now remember that the absolute value of ANY number is ALWAYS nonnegative. In other words, it will NEVER be negative. Since 0 and every positive number is greater than any negative number, this means that the inequality |3x-4| > -8 is true for ALL values of x. So there are an infinite number of solutions. Basically, any real number will work for x. If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Linear_Algebra/408760: Evaluate the function f(x) = -x^2 + 5 for x = 41 solutions Answer 287886 by jim_thompson5910(28715)   on 2011-02-13 22:15:07 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in . Square to get . Multiply and to get . Combine like terms. So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 logarithm/408682: Solve the following exponential equations using logarithms: 2^(x) = 3^(x+1) Feeling pretty lost on this one... I've tried to google for similar examples, but when I do find a similar problem it's solves using a form like this: "xln(2)=(xln(3)+ln(3))" I think this is a little beyond where I am now :( Looking for a more basic algebra solution! Appreciate any help!! Thanks :)1 solutions Answer 287853 by jim_thompson5910(28715)   on 2011-02-13 21:15:55 (Show Source): You can put this solution on YOUR website!If something like "xln(2)=(xln(3)+ln(3))" scares you, then just replace each "ln" with "log" and you'll get xlog(2)=xlog(3)+log(3) Why can I replace "ln" with "log"? Because "ln" is actually a log that has base 'e' (2.718...). However you can use any log of any base. So you can use the default log of base 10 if you want. If you need more help, email me at jim_thompson5910@hotmail.com
 Trigonometry-basics/408715: sin(a+b)-sin(a-b)=2cosasinb How do I solve this problem? I am so close to a break down over this. Help!! 1 solutions Answer 287850 by jim_thompson5910(28715)   on 2011-02-13 21:11:02 (Show Source): You can put this solution on YOUR website!sin(a+b)-sin(a-b)=2cos(a)sin(b) sin(a)cos(b)+cos(a)sin(b)-(sin(a)cos(b)-cos(a)sin(b))=2cos(a)sin(b) sin(a)cos(b)+cos(a)sin(b)-sin(a)cos(b)+cos(a)sin(b)=2cos(a)sin(b) (sin(a)cos(b)-sin(a)cos(b))+(cos(a)sin(b)+cos(a)sin(b))=2cos(a)sin(b) 0+2cos(a)sin(b)=2cos(a)sin(b) 2cos(a)sin(b)=2cos(a)sin(b) So the original equation is an identity (ie it's true for ALL values of 'a' and 'b') If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Expressions-with-variables/407911: x/3+x/3+x1 solutions Answer 287424 by jim_thompson5910(28715)   on 2011-02-11 13:48:32 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Numeric_Fractions/407905: could someone please help me divide -15/-31 solutions Answer 287421 by jim_thompson5910(28715)   on 2011-02-11 13:31:41 (Show Source): You can put this solution on YOUR website!since 3*5 = 15, this means that 15/3 = 5 So -15/(-3) = 5 If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Equations/407898: -x/6=-2 1 solutions Answer 287419 by jim_thompson5910(28715)   on 2011-02-11 13:08:24 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by 6. Multiply. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Square-cubic-other-roots/407893: How do you find the square root of a negative number, such as -81 solutions Answer 287418 by jim_thompson5910(28715)   on 2011-02-11 12:56:25 (Show Source): You can put this solution on YOUR website!Hint: Use the idea that
 Linear-equations/407845: 3x-7>=81 solutions Answer 287412 by jim_thompson5910(28715)   on 2011-02-11 12:20:54 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Polynomials-and-rational-expressions/407820: I am needing help please. Completly factor the expression and show all work: 18x^2-32y^21 solutions Answer 287410 by jim_thompson5910(28715)   on 2011-02-11 12:18:53 (Show Source): You can put this solution on YOUR website! Note: I used the difference of squares formula on the last step. So If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Probability-and-statistics/407809: In how many ways can 10 instructors be assigned to eight sections of a course in mathematics?1 solutions Answer 287409 by jim_thompson5910(28715)   on 2011-02-11 12:16:34 (Show Source): You can put this solution on YOUR website!Assuming that order matters, there are 10 P 8 = (10!)/(10-8)! = 10!/2! = 3628800/2 = 1814400 different ways to assign 8 sections to 10 teachers. If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Distributive-associative-commutative-properties/407804: Distributive Property 1 solutions Answer 287408 by jim_thompson5910(28715)   on 2011-02-11 12:14:40 (Show Source): You can put this solution on YOUR website!What about the distributive property? Is there more to the problem?
 Expressions-with-variables/407817: what is the variable in 5n+11=-2+11 solutions Answer 287407 by jim_thompson5910(28715)   on 2011-02-11 12:14:07 (Show Source): You can put this solution on YOUR website!The variable is the unknown number. Since we (usually) don't know the value of the variable, we assign that variable to be a letter (or some other symbol) other than an actual number. So in this case, the unknown number is 'n'. So the variable is 'n' (without quotes) If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Functions/407808: how do i find the domain of (3,4) (-5,4) (2,1) (8,4)1 solutions Answer 287405 by jim_thompson5910(28715)   on 2011-02-11 12:12:43 (Show Source): You can put this solution on YOUR website!The domain is the set of allowable inputs, which in this case means the set of x coordinates. So the domain is {-5,2,3,8} since these are all x coordinates of the given points. If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim