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 expressions/621977: what is the answer of 4x-4ay1 solutions Answer 393152 by jim_thompson5910(28598)   on 2012-06-30 12:54:52 (Show Source): You can put this solution on YOUR website!You can factor out the GCF 4 to go from 4x-4ay to 4(x-ay)
 sets-and-operations/624814: 1) Determine the following A′ ∪ (A ∩ B) 2) express this set in set-builder notation D = {5, 10, 15, 20,... }1 solutions Answer 393151 by jim_thompson5910(28598)   on 2012-06-30 12:52:27 (Show Source): You can put this solution on YOUR website!1) We would need to know the sets A and B ------------------------------------------------------- 2) D = {5k| k is a natural number)
 Linear-equations/624844: 10cm1 solutions Answer 393148 by jim_thompson5910(28598)   on 2012-06-30 12:50:16 (Show Source): You can put this solution on YOUR website!Was there more to the problem?
 Polynomials-and-rational-expressions/624889: (x^2+y^4)(x^2-y^4)1 solutions Answer 393145 by jim_thompson5910(28598)   on 2012-06-30 12:39:21 (Show Source): You can put this solution on YOUR website!(x^2+y^4)(x^2-y^4) x^2(x^2-y^4)+y^4(x^2-y^4) x^4-x^2y^4+x^2y^4-y^8 x^4-y^8 So (x^2+y^4)(x^2-y^4) = x^4-y^8 -------------------------------------------------------------------------------------------------------------- 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/624089: 3c^2=10c solve for C C=?1 solutions Answer 393142 by jim_thompson5910(28598)   on 2012-06-30 12:36:19 (Show Source): You can put this solution on YOUR website!3c^2=10c 3c^2-10c=0 c(3c-10)=0 c=0 or 3c-10=0 c=0 or 3c=10 c=0 or c=10/3 So the solutions are c=0 or c=10/3 -------------------------------------------------------------------------------------------------------------- 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/624249: factor 3x^2 +13x -10
1 solutions

Answer 393141 by jim_thompson5910(28598)   on 2012-06-30 12:34:26 (Show Source):
You can put this solution on YOUR website!
I'm assuming you meant to write 3x^2+13x-10

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-30) = -30
2*(-15) = -30
3*(-10) = -30
5*(-6) = -30
(-1)*(30) = -30
(-2)*(15) = -30
(-3)*(10) = -30
(-5)*(6) = -30

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1-301+(-30)=-29
2-152+(-15)=-13
3-103+(-10)=-7
5-65+(-6)=-1
-130-1+30=29
-215-2+15=13
-310-3+10=7
-56-5+6=1

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

===============================================================

So factors to .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

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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
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 Equations/624892: true or false. ___1 Two sixths is a whole number1 solutions Answer 393140 by jim_thompson5910(28598)   on 2012-06-30 12:32:37 (Show Source): You can put this solution on YOUR website!This is false since 2/6 = 1/3 = 0.3333 which has a decimal part.
 Geometry_proofs/624775: Given: Angle 1 is congruent to angle 3. Prove: Angle 2 is congruent to angle 4. *Angle 1 and 2 are vertical angles. Angle 3 and 4 are vertical angles.1 solutions Answer 393042 by jim_thompson5910(28598)   on 2012-06-29 17:55:56 (Show Source): You can put this solution on YOUR website!Angles 1 and 2 are vertical angles. So angle 1 = angle 2 because vertical angles are congruent. Angles 3 and 4 are vertical as well. So angle 3 = angle 4 by the same reason. ------------------------------------------------------- Since it's given that "Angle 1 is congruent to angle 3. ", this also means that angle 1 = angle 3 Now we can use substitution to get angle 1 = angle 3 angle 2 = angle 3 << -- replace "angle 1" with "angle 2" (since the two are congruent) angle 2 = angle 4 << -- replace "angle 3" with "angle 4" (since the two are congruent) So because we've shown that angle 2 = angle 4 , this proves Angle 2 is congruent to angle 4
 Exponents-negative-and-fractional/624778: Scientific Notation problem: Short Answer: Convert this number to scientific notation. SHOW ALL WORK! 76,485 Seemed simple when I started, but it wasn't. Help.1 solutions Answer 393040 by jim_thompson5910(28598)   on 2012-06-29 17:49:06 (Show Source): You can put this solution on YOUR website!Place the decimal point between the first two digits to get 7.6485 Now move the decimal 4 places to the right (to get back to the original number). So the base is 7.6485 and the exponent is 4 This means that 76,485 = 7.6485 x 10^4
 Linear_Algebra/624750: Assume that all matrices are invertible and solve for the matrix X in: (A^-1 X)^-1 =A (B^-1 A)^-11 solutions Answer 393006 by jim_thompson5910(28598)   on 2012-06-29 15:17:10 (Show Source): You can put this solution on YOUR website!(A^-1 X)^-1 =A (B^-1 A)^-1 (A^-1 X)^-1(A^-1 X) =(A (B^-1 A)^-1)(A^-1 X) I =(A (B^-1 A)^-1)(A^-1 X) A^-1 * I =(A^-1 A (B^-1 A)^-1)(A^-1 X) A^-1 = ((B^-1 A)^-1)(A^-1 X) (B^-1 A)A^-1 = ((B^-1 A)(B^-1 A)^-1)(A^-1 X) (B^-1 A)A^-1 = A^-1 X A(B^-1 A)A^-1 = A*A^-1 X A(B^-1 A)A^-1 = X X = A(B^-1 A)A^-1 So the solution is X = A(B^-1 A)A^-1
 Subset/624747: what is the subset of {2,5,7}1 solutions Answer 393004 by jim_thompson5910(28598)   on 2012-06-29 15:09:16 (Show Source): You can put this solution on YOUR website!Any set that draws elements from the given set (and ONLY elements from that set) Eg: {2,5} is a subset but {2,5,6} is NOT a subset (since 6 is NOT in the original set) -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Age_Word_Problems/624743: Ina church the ratio of adults to children is 7 to 5. there are 85 people. How many of them are children?1 solutions Answer 393003 by jim_thompson5910(28598)   on 2012-06-29 15:02:05 (Show Source): You can put this solution on YOUR website!7/5 = a/c 7/5 = (85-c)/c 7c = 5(85-c) 7c = 425-5c 7c+5c = 425 12c = 425 c = 425/12 c = 35.41666 Round to the nearest integer to get 35 children ***Note: because I'm getting a decimal answer, there might be a typo somewhere in the original problem***
 Radicals/624740: how do you write the 4th root of x multiplied by the 5th root of 3x as a single radical expression?1 solutions Answer 392999 by jim_thompson5910(28598)   on 2012-06-29 14:30:55 (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/624741: 3/8 +(-1/6)71 solutions Answer 392998 by jim_thompson5910(28598)   on 2012-06-29 14:28:13 (Show Source): You can put this solution on YOUR website!3/8+(-1/6)7 3/8-7/6 9/24-7/6 9/24-28/24 (9-28)/24 -19/24 So 3/8+(-1/6)7 = -19/24 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Money_Word_Problems/624683: So I have tried to work this out, I have no idea where to start and I'm stuck. Could someone please help me figure this out and tell me how you got the answer do I can try to so the second part of the problem. The price of a certain stock at the beginning of the week was \$61. Here are the changes in price during the week: +3,+2,-1,-4,-5. What is the price of the stock at the end of the week? Thank you very much.1 solutions Answer 392991 by jim_thompson5910(28598)   on 2012-06-29 14:07:07 (Show Source): You can put this solution on YOUR website!Add up the changes: +3+2+(-1)+(-4)+(-5) = -5 So the final change is -5 This means that the stock lost \$5 at the end of the week. So the stock price at the end of the week is 61 + (-5) = 56 dollars -------------------------------------------------------------------------------------------------------------- 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/624721: I need help trying to solve this. Well I know the answer, I just need a deeper explanation. x^2-x-6/x^2-4 The answer they gave was x-3/x-21 solutions Answer 392967 by jim_thompson5910(28598)   on 2012-06-29 11:43:29 (Show Source): You can put this solution on YOUR website!The idea is to factor each piece and cancel any common factors So fully simplifies to
 Functions/624715: f(x) = x + 2 and asked to evaluate for f(-2) and f(0)1 solutions Answer 392966 by jim_thompson5910(28598)   on 2012-06-29 11:34:13 (Show Source): You can put this solution on YOUR website!f(x) = x + 2 f(-2) = -2 + 2 f(-2) = 0 ======================================================= f(x) = x + 2 f(0) = 0 + 2 f(0) = 2
 Graphs/624608: Solve these equations using the addition property. x + y = k x - y = k The lines intersect at1 solutions Answer 392902 by jim_thompson5910(28598)   on 2012-06-28 19:49:19 (Show Source): You can put this solution on YOUR website!x + y = k x - y = k --------- 2x + 0y = 2k 2x = 2k x = 2k/2 x = k ---------------------------------------------------------------- x+y = k k+y = k y = k-k y = 0 So the solutions are x = k and y = 0 So the lines intersect at (k, 0)
 Divisibility_and_Prime_Numbers/624603: Solve a+8b=31 solutions Answer 392898 by jim_thompson5910(28598)   on 2012-06-28 19:45:14 (Show Source): You can put this solution on YOUR website!Solve for a? or solve for b? Please clarify. Thank you.
 Square-cubic-other-roots/624592: please help solve by factoring y^2 + 3y = 81 solutions Answer 392887 by jim_thompson5910(28598)   on 2012-06-28 18:41:21 (Show Source): You can put this solution on YOUR website!You can't factor this (since no two whole numbers multiply to -8 and add to 3). So please make sure that you copied/typed it correctly. Thank you.
 test/624578: 1 solutions Answer 392870 by jim_thompson5910(28598)   on 2012-06-28 17:17:20 (Show Source): You can put this solution on YOUR website!Problem missing. Please repost. Thank you.
 Percentage-and-ratio-word-problems/624577: How do u find 3.2% of 5001 solutions Answer 392864 by jim_thompson5910(28598)   on 2012-06-28 16:53:38 (Show Source): You can put this solution on YOUR website!3.2% converts to 0.032 in decimal form (move that decimal over 2 spots to the left) Now multiply 0.032 by 500 to get the answer of 0.032*500 = 16 So 3.2% of 500 is 16 -------------------------------------------------------------------------------------------------------------- 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/624554: I need to factor the polynomials and solve the equation 32xy^3 +4x= I factored out 4x to get 4x(8y^3+1) but I am unsure if I should do that. Thanks in advance for your help. Also can you please show me the steps.1 solutions Answer 392841 by jim_thompson5910(28598)   on 2012-06-28 15:21:00 (Show Source): You can put this solution on YOUR website!Now let's factor Start with the given expression. Rewrite as . Rewrite as . Now factor by using the sum of cubes formula. Remember the sum of cubes formula is Multiply So factors to . In other words, ==================================================================================== Answer: So in the end, completely 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 --------------------------------------------------------------------------------------------------------------
 Travel_Word_Problems/624557: Supply the missing operation symbols to make each number statement true. 1. 56__ 8 __ 14 = 21 2. 10__ 6 __5 = 11 3. 50 = 6___7___8 4. (6___39)___15 = 3 5. 4 = 16___ 7 ___ 81 solutions Answer 392836 by jim_thompson5910(28598)   on 2012-06-28 15:11:55 (Show Source): You can put this solution on YOUR website!I'll do the first two to get you started 1. 56 _/_ 8 _+_ 14 = 21 2. 10 _+_ 6 _-_ 5 = 11 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Evaluation_Word_Problems/624558: Seven times what number is 1596?1 solutions Answer 392835 by jim_thompson5910(28598)   on 2012-06-28 15:09:28 (Show Source): You can put this solution on YOUR website!"Seven times what number is 1596" --> 7x = 1596 7x = 1596 7x/7 = 1596/7 x = 228 So "Seven times what number is 1596" turns into "Seven times 228 is 1596" -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Geometry_Word_Problems/624552: It's laundry time again, and you have a roll of \$10 worth of quarters to take to the Wash-'n-Whirl. Each US quarter has width of 1.75 mm and a radius of 12 mm. What is the volume of the roll of quarters? 1 solutions Answer 392834 by jim_thompson5910(28598)   on 2012-06-28 14:57:25 (Show Source): You can put this solution on YOUR website!There are 10/0.25 = 40 quarters total. The total height of the stack of quarters is h = 40*1.75 = 70 mm The volume is then... V = pi*r^2*h V = pi*12^2*70 V = 10080pi << ------- Exact Volume V = 10080(3.14159) V = 31667.2272 << ------- Approximate Volume -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Mixture_Word_Problems/624549: What is the first ten terms of a sequence whose first term is -10 and whose common difference is -2. 1 solutions Answer 392831 by jim_thompson5910(28598)   on 2012-06-28 14:42:06 (Show Source): You can put this solution on YOUR website!Start with the first term of -10 and subtract off 2 each time to get the next term, so the first ten terms are... -10,-12,-14,-16,-18,-20,-22,-24,-26,-28 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------