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 Functions/527336: find the domain of the given function f(y)= 1/(y+1)1 solutions Answer 348859 by jim_thompson5910(28595)   on 2011-11-06 22:56:17 (Show Source): You can put this solution on YOUR website!You cannot divide by zero So y+1 cannot be zero If it were, then y + 1 = 0, which would mean that y = -1 So if y = -1, then y + 1 = 0, which would cause a division by zero error. To avoid this, we exclude this value from the domain. So the domain is the set of all real numbers, but y cannot equal -1. 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/527334: find the domain of the given function f(x)=3x^3-4x^2+x-11 solutions Answer 348857 by jim_thompson5910(28595)   on 2011-11-06 22:50:28 (Show Source): You can put this solution on YOUR website!The domain of ANY polynomial is the set of all real numbers. So the domain is the set of all real numbers (since f(x) is a polynomial function). 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
 Human-and-algebraic-language/527301: the product of a number and 501 solutions Answer 348848 by jim_thompson5910(28595)   on 2011-11-06 21:51:15 (Show Source): You can put this solution on YOUR website!"the product of a number and 50" translates to 50x where x is the unknown number. 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/527243: Find an equation of the line that satisfies the given conditions. Through (−1, −2) and (6, 5) 1 solutions Answer 348830 by jim_thompson5910(28595)   on 2011-11-06 20:43:07 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Rewrite as Distribute Multiply Subtract 2 from both sides. Combine like terms. Simplify So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and 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
 Rational-functions/527124: Hey, I've been looking all over the internet for a way to convert (y=(m)x+b) into point-slope form. I can't remember though whether this only applies to quadratic equations. If you consider this two questions, my apologies, I'm new to this. Thanks.1 solutions Answer 348818 by jim_thompson5910(28595)   on 2011-11-06 19:53:17 (Show Source): You can put this solution on YOUR website!Point slope form is y - y1 = m(x - x1) where (x1, y1) is a point that lies on the graph and m is the slope From y = mx+b, the slope will be given. It'll be up to you find a point that lies on the graph. The easiest point is the y-intercept, which is (0, b). So x1 = 0 and y1 = b This means that y = mx+b converts to y - b = m(x - 0) where y1 = 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
Complex_Numbers/527181: factor the trinomial by grouping : 15x^3+47x^2+28x
1 solutions

Answer 348815 by jim_thompson5910(28595)   on 2011-11-06 19:48:18 (Show Source):
You can put this solution on YOUR website!

Factor out the GCF .

Now let's try to factor the inner expression

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

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 :
1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
-1,-2,-3,-4,-5,-6,-7,-10,-12,-14,-15,-20,-21,-28,-30,-35,-42,-60,-70,-84,-105,-140,-210,-420

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

These factors pair up and multiply to .
1*420 = 420
2*210 = 420
3*140 = 420
4*105 = 420
5*84 = 420
6*70 = 420
7*60 = 420
10*42 = 420
12*35 = 420
14*30 = 420
15*28 = 420
20*21 = 420
(-1)*(-420) = 420
(-2)*(-210) = 420
(-3)*(-140) = 420
(-4)*(-105) = 420
(-5)*(-84) = 420
(-6)*(-70) = 420
(-7)*(-60) = 420
(-10)*(-42) = 420
(-12)*(-35) = 420
(-14)*(-30) = 420
(-15)*(-28) = 420
(-20)*(-21) = 420

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

First NumberSecond NumberSum
14201+420=421
22102+210=212
31403+140=143
41054+105=109
5845+84=89
6706+70=76
7607+60=67
104210+42=52
123512+35=47
143014+30=44
152815+28=43
202120+21=41
-1-420-1+(-420)=-421
-2-210-2+(-210)=-212
-3-140-3+(-140)=-143
-4-105-4+(-105)=-109
-5-84-5+(-84)=-89
-6-70-6+(-70)=-76
-7-60-7+(-60)=-67
-10-42-10+(-42)=-52
-12-35-12+(-35)=-47
-14-30-14+(-30)=-44
-15-28-15+(-28)=-43
-20-21-20+(-21)=-41

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 then factors further to

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

So completely 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).

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

 Complex_Numbers/527144: simplify the square root of 1251 solutions Answer 348814 by jim_thompson5910(28595)   on 2011-11-06 19:40:39 (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
 Linear-systems/527123: 46-(2x+1)<3(x+5)+x1 solutions Answer 348802 by jim_thompson5910(28595)   on 2011-11-06 18:52:47 (Show Source): You can put this solution on YOUR website! Start with the given inequality. 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 . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: 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
 Graphs/527116: Find the slope of each line from the given equation. y + 5=01 solutions Answer 348792 by jim_thompson5910(28595)   on 2011-11-06 18:40:51 (Show Source): You can put this solution on YOUR website!y + 5 = 0 y = -5 y = 0x-5 The equation is now in y = mx+b form where m is the slope. Since m = 0, the slope is 0. 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
 Graphs/527113: Find the slope of each line from the given equation. 4x-7y=11 1 solutions Answer 348789 by jim_thompson5910(28595)   on 2011-11-06 18:38:34 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. So the equation is now in slope intercept form where the slope 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
 absolute-value/527080: can u solve this equation? i got 1/3 and 7/5 but the computer says their is no solution: i will use parenthesis as absolute value because i can not find the symbols for it 2(3x-4)+15=91 solutions Answer 348773 by jim_thompson5910(28595)   on 2011-11-06 17:56:22 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract 15 from both sides. Divide both sides by 2 Since the equation is NEVER true (note: remember, the absolute value of any number is ALWAYS positive), there are no solutions to So there are no solutions to the original equation. 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
 Polygons/527065: Each base angle of an isosceles triangle measures 70 degrees. Find the vertex angle.1 solutions Answer 348769 by jim_thompson5910(28595)   on 2011-11-06 17:40:16 (Show Source): You can put this solution on YOUR website!Let x = vertex angle Since all angles in a triangle add to 180 degrees, we know that 70+70+x = 180 140+x = 180 x = 180-140 x = 40 So the vertex angle is 40 degrees. 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/527063: how do you solve this question? 2x^2 + 18x + 28 = 01 solutions Answer 348768 by jim_thompson5910(28595)   on 2011-11-06 17:37:00 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Square to get . Multiply to get Subtract from 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 solutions 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
 Square-cubic-other-roots/527059: 2x+y=31 solutions Answer 348767 by jim_thompson5910(28595)   on 2011-11-06 17:31:40 (Show Source): You can put this solution on YOUR website!2x+y=3 y=3-2x y = -2x+3
 Equations/527052: is x=1 a solution to 4x-3=7,yes or no 1 solutions Answer 348766 by jim_thompson5910(28595)   on 2011-11-06 17:24:43 (Show Source): You can put this solution on YOUR website! 4x-3=7 4(1)-3=7 4-3=7 1=7 Since the last equation is NOT true, this means that x = 1 is NOT a solution. 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
 Rational-functions/527050: simplify 6(b-4) this is a 5th grade problem 1 solutions Answer 348764 by jim_thompson5910(28595)   on 2011-11-06 17:18:22 (Show Source): You can put this solution on YOUR website! 6(b-4) 6(b)+6(-4) 6b-24 So 6(b-4) = 6b-24 for all values of 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
 Polygons/527040: How many sides does a regular polygon have if each exterior angle equals 30 degrees1 solutions Answer 348763 by jim_thompson5910(28595)   on 2011-11-06 17:01:43 (Show Source): You can put this solution on YOUR website!The sum of all the exterior angles is 360 degrees So this means that if there are n sides, then 30n = 360 Solve for n to get 30n = 360 n = 360/30 n = 12 So there are 12 sides 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/527038: show the equation, show all work,final answer must be in simplest form b+ 1/9= 91 solutions Answer 348762 by jim_thompson5910(28595)   on 2011-11-06 17:00:01 (Show Source): You can put this solution on YOUR website! 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/527037: solve the equation. If it is an identity(all real numbers) or a contradiction(no solution), so state. 6x+2+3x= 10x +2-x 1 solutions Answer 348760 by jim_thompson5910(28595)   on 2011-11-06 16:56:32 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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. Simplify. Since this equation is ALWAYS true for any x value, this means x can equal any number. So there are an infinite number of solutions. This means that this equation is an identity. 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/527025: Area is to square inches As volume is to 1 solutions Answer 348754 by jim_thompson5910(28595)   on 2011-11-06 16:36:01 (Show Source): You can put this solution on YOUR website!Cubic inches
 Equations/527021: 8= 3y-5 solve equation1 solutions Answer 348746 by jim_thompson5910(28595)   on 2011-11-06 16:28:25 (Show Source): You can put this solution on YOUR website!8= 3y-5 8+5= 3y 13= 3y 13/3=y y=13/3 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/527018: -8r + 8 < -2(3r – 9) 1 solutions Answer 348745 by jim_thompson5910(28595)   on 2011-11-06 16:27:03 (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 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
 Equations/527016: 7 – 10z > 5 1 solutions Answer 348744 by jim_thompson5910(28595)   on 2011-11-06 16:26:00 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. 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 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
 expressions/527003: Simplify -2[9 - (x + 7)].1 solutions Answer 348743 by jim_thompson5910(28595)   on 2011-11-06 16:09:39 (Show Source): You can put this solution on YOUR website! -2[9 - (x + 7)] -2[9 - x - 7] -2[2 - x] -4 + 2x 2x - 4 So -2[9 - (x + 7)] = 2x - 4 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-equations/526995: Which of the following is the equation of a line that passes through (-2, -1) and (-4, -3)? A step-by-step solved answer would be very helpful, as well as side notes as to what is happening in each step. Thank you! -Laura DiPietro1 solutions Answer 348739 by jim_thompson5910(28595)   on 2011-11-06 15:52:00 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Rewrite as Distribute Multiply Subtract 1 from both sides. Combine like terms. Simplify So the equation that goes through the points and 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
 Inverses/526992: what is the additive or inverse of -991 solutions Answer 348738 by jim_thompson5910(28595)   on 2011-11-06 15:45:13 (Show Source): You can put this solution on YOUR website!The additive inverse of x is -x In this case, x = -99, so the additive inverse of x = -99 is -x = -(-99) = 99 This means that the additive inverse of -99 is 99 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/526991: 5 1/2 x 3=?1 solutions Answer 348737 by jim_thompson5910(28595)   on 2011-11-06 15:42:29 (Show Source): You can put this solution on YOUR website!5 1/2 = 5+1/2 = 10/2+1/2 = 11/2 So 5 1/2 x 3 = 11/2 x 3 = 11/2 x 3/1 = 33/2 This means that 5 1/2 x 3 = 33/2 which is 16 1/2 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/526926: what is the speed if a car traveled 400km in 5hr1 solutions Answer 348731 by jim_thompson5910(28595)   on 2011-11-06 15:02:20 (Show Source): You can put this solution on YOUR website!d = rt 400 = r(5) 400/5 = r 80 = r r = 80 So the speed is 80 km/hr 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/526927: Simplify by removing factors of 1 6y^11/7y^8 Please assist. I have tried to find an example, but I am stuck.1 solutions Answer 348729 by jim_thompson5910(28595)   on 2011-11-06 14:34:36 (Show Source): You can put this solution on YOUR website!To divide monomials, we simply subtract corresponding exponents. 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
 test/526941: (1,9); slope 41 solutions Answer 348728 by jim_thompson5910(28595)   on 2011-11-06 14:31:31 (Show Source): You can put this solution on YOUR website! y = mx+b 9 = 4(1)+b 9 = 4+b 9-4 = b 5 = b b = 5 So the equation is y = 4x+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
 Complex_Numbers/526946: Find the absolute value of the complex number. |-10-5i| <---how do i do this?!1 solutions Answer 348727 by jim_thompson5910(28595)   on 2011-11-06 14:27:37 (Show Source): You can put this solution on YOUR website!Since is in standard form , we can see that and Start with the absolute value of a complex number formula. Plug in and . Square to get . Square to get . Add. Simplify the square root. 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