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 Equations/542043: what is the answer to g+3/10=2/5 1 solutions Answer 354443 by jim_thompson5910(28598)   on 2011-12-05 18:34:59 (Show Source): You can put this solution on YOUR website! Start with the given equation. Cross multiply Multiply Distribute. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . 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
 Rational-functions/542129: How do I do this? Find: f(3) f(x)=2x-11 solutions Answer 354442 by jim_thompson5910(28598)   on 2011-12-05 18:32:26 (Show Source): You can put this solution on YOUR website!f(x)=2x-1 f(3)=2(3)-1 ... Replace x with 3 (since x = 3 when evaluating f(3)) f(3)=6-1 f(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
Numeric_Fractions/540613: I need help solving this problem really bad factor: b^2+8ab-20c^2
1 solutions

Answer 354440 by jim_thompson5910(28598)   on 2011-12-05 18:31:09 (Show Source):
You can put this solution on YOUR website!

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

Now multiply the first coefficient by the last coefficient 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 :
1,2,4,5,10,20
-1,-2,-4,-5,-10,-20

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

These factors pair up and multiply to .
1*(-20) = -20
2*(-10) = -20
4*(-5) = -20
(-1)*(20) = -20
(-2)*(10) = -20
(-4)*(5) = -20

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

First NumberSecond NumberSum
1-201+(-20)=-19
2-102+(-10)=-8
4-54+(-5)=-1
-120-1+20=19
-210-2+10=8
-45-4+5=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.

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

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).

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/542085: what is 4(y-4) > 2(5y+4) ?1 solutions Answer 354439 by jim_thompson5910(28598)   on 2011-12-05 18:30:44 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Add to 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
 Numeric_Fractions/542094: what is 6(2a-6) is greater or equal to 4(4a+4)?1 solutions Answer 354438 by jim_thompson5910(28598)   on 2011-12-05 18:30:22 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Add to 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
 Numeric_Fractions/542107: what is 3x+7=>2x?1 solutions Answer 354437 by jim_thompson5910(28598)   on 2011-12-05 18:29:53 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. ---------------------------------------------------------------------- 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
 Numeric_Fractions/542109: what is 3y-5 < 5y +71 solutions Answer 354436 by jim_thompson5910(28598)   on 2011-12-05 18:29:18 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Add to 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
 Linear-equations/542112: What is the slope of the line that contains the points (2,13) and (6,33)?1 solutions Answer 354435 by jim_thompson5910(28598)   on 2011-12-05 18:28:42 (Show Source): You can put this solution on YOUR website! 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 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
 Numbers_Word_Problems/542128: Is 16y^2-49 is s trinomial square, difference of square, or neither?1 solutions Answer 354434 by jim_thompson5910(28598)   on 2011-12-05 18:27:56 (Show Source): You can put this solution on YOUR website!16y^2-49 is a difference of squares since 16y^2 = (4y)^2 and 49 = 7^2
 Numeric_Fractions/542113: 5/6+5/61 solutions Answer 354433 by jim_thompson5910(28598)   on 2011-12-05 18:27:23 (Show Source): You can put this solution on YOUR website!5/6+5/6 = (5+5)/6 = 10/6 = 5/3 So 5/6+5/6 = 5/3 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
 test/542115: What is x+4y=10 in slope intercept form? 1 solutions Answer 354432 by jim_thompson5910(28598)   on 2011-12-05 18:26:35 (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 and the y-intercept is note: the y-intercept is the point 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/542123: I need help finding the answer of a/2 - a/12 = -5a/41 solutions Answer 354430 by jim_thompson5910(28598)   on 2011-12-05 18:25:56 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Combine like terms on the left side. Add to both sides. Combine like terms on the left side. Divide both sides by to isolate . 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/541584: What Are The Steps To The Equation Here: a + 5 = -5a + 51 solutions Answer 354215 by jim_thompson5910(28598)   on 2011-12-04 20:18:19 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 . 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/541570: solve for x. Express your answer in interval notation. 8-2(3-x)< 12 I really appreciate help from you guys,! Thanks to you I still might be able to pass my math class! - 1 solutions Answer 354210 by jim_thompson5910(28598)   on 2011-12-04 19:51:54 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . 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/541394: 2/3x = -81 solutions Answer 354171 by jim_thompson5910(28598)   on 2011-12-04 15:27:20 (Show Source): You can put this solution on YOUR website!2/3x = -8 2x = -8*3 2x = -24 x = -24/2 x = -12 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/541350: 76 < 4x -6 (Hint: Solve just like a regular equation.)1 solutions Answer 354159 by jim_thompson5910(28598)   on 2011-12-04 14:23:08 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. 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
 Linear-equations/541348: Find the slope and y-intercept of the graph of the equation Ax+By=C where B is not equal to 0. Use your results to find the slope and y-intercept of the graph of 3x+2y=181 solutions Answer 354157 by jim_thompson5910(28598)   on 2011-12-04 14:16:40 (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 and the y-intercept is note: the y-intercept is the point 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/541321: You are trying your luck to win the lottery. There are 50 numbers on the lottery ticket to choose from. In order to win you must pick the correct six numbers. Find the probability of selecting exactly one of the 6 correct winning numbers, where the order in which these numbers are selected does not matter from the set of positive numbers not exceeding 50 (that is the positive integers from 1,2,3,4,5,6...50) So far I know that the denominator is 50C6 but I cannot figure out the numerator. Any help would be appreciated, thank you.1 solutions Answer 354153 by jim_thompson5910(28598)   on 2011-12-04 13:41:11 (Show Source): You can put this solution on YOUR website!The answer to your question can be found buried in the sentence "Find the probability of selecting exactly ONE of the 6 correct winning numbers..." So the numerator is simply 1.
 Quadratic_Equations/541323: compute the discriminant of the quadratic equation 3x^2+x+2=0 then write a brief sentence describing the number and type of solution for this equation1 solutions Answer 354152 by jim_thompson5910(28598)   on 2011-12-04 13:37:50 (Show Source): You can put this solution on YOUR website!From we can see that , , and Start with the discriminant formula. Plug in , , and Square to get Multiply to get Subtract from to get So the discriminant is Since the discriminant is less than zero, this means that there are two complex solutions. In other words, there are no real solutions. 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/541319: how do I solve this problem solve using the multiplication principle 2/3x=101 solutions Answer 354149 by jim_thompson5910(28598)   on 2011-12-04 13:24:05 (Show Source): You can put this solution on YOUR website!2/3x=10 2x=10*3 2x = 30 x = 30/2 x = 15 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/541312: find the domain if the function: x+6/x^2-3241 solutions Answer 354148 by jim_thompson5910(28598)   on 2011-12-04 13:22:46 (Show Source): You can put this solution on YOUR website!Hint: You CANNOT divide by zero. So the denominator x^2-324 CANNOT be zero. If it were, then x^2-324 = 0. Solve this equation for x. Any solutions you get will be the values you exclude from the domain (to avoid division 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
 test/541315: Find the inverse of (4-x)/31 solutions Answer 354147 by jim_thompson5910(28598)   on 2011-12-04 13:21:00 (Show Source): You can put this solution on YOUR website!y = (4-x)/3 x = (4-y)/3 3x = 4-y 3x - 4 = -y -3x + 4 = y y = -3x + 4 So the inverse is -3x + 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
 Probability-and-statistics/541308: if a recipe for cake calls 2 1/2 cups of flour and Mary wishes to make three such cakes the number of cups of flour she use is 1 solutions Answer 354145 by jim_thompson5910(28598)   on 2011-12-04 13:09:19 (Show Source): You can put this solution on YOUR website!Multiply 3 by 2 1/2 to get 3*(2 1/2) = 3*(2+1/2) = 3*2 + 3*(1/2) = 6 + 3/2 = 6 + 1 1/2 = 7 1/2 So she needs 7 1/2 cups of flour (seven and a half cups of flour) 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/541305: what does x equal if 2x^2=5121 solutions Answer 354142 by jim_thompson5910(28598)   on 2011-12-04 12:54:56 (Show Source): You can put this solution on YOUR website! or 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
 Polynomials-and-rational-expressions/541303: (a^3 * 2a^3b^2)^21 solutions Answer 354141 by jim_thompson5910(28598)   on 2011-12-04 12:53:21 (Show Source): You can put this solution on YOUR website!(a^3 * 2a^3b^2)^2 (a^3)^2*(2)^2*(a^3)^2*(b^2)^2 a^(3*2)*(2)^2*(a^(3*2))*(b^(2*2)) a^6*4*a^6*b^4 4a^(6+6)b^4 4a^12b^4 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
180w^2+300wf+125f^2
1 solutions

Answer 354140 by jim_thompson5910(28598)   on 2011-12-04 12:46:26 (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 coefficient is .

Now multiply the first coefficient by the last coefficient 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 :
1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900
-1,-2,-3,-4,-5,-6,-9,-10,-12,-15,-18,-20,-25,-30,-36,-45,-50,-60,-75,-90,-100,-150,-180,-225,-300,-450,-900

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

These factors pair up and multiply to .
1*900 = 900
2*450 = 900
3*300 = 900
4*225 = 900
5*180 = 900
6*150 = 900
9*100 = 900
10*90 = 900
12*75 = 900
15*60 = 900
18*50 = 900
20*45 = 900
25*36 = 900
30*30 = 900
(-1)*(-900) = 900
(-2)*(-450) = 900
(-3)*(-300) = 900
(-4)*(-225) = 900
(-5)*(-180) = 900
(-6)*(-150) = 900
(-9)*(-100) = 900
(-10)*(-90) = 900
(-12)*(-75) = 900
(-15)*(-60) = 900
(-18)*(-50) = 900
(-20)*(-45) = 900
(-25)*(-36) = 900
(-30)*(-30) = 900

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

First NumberSecond NumberSum
19001+900=901
24502+450=452
33003+300=303
42254+225=229
51805+180=185
61506+150=156
91009+100=109
109010+90=100
127512+75=87
156015+60=75
185018+50=68
204520+45=65
253625+36=61
303030+30=60
-1-900-1+(-900)=-901
-2-450-2+(-450)=-452
-3-300-3+(-300)=-303
-4-225-4+(-225)=-229
-5-180-5+(-180)=-185
-6-150-6+(-150)=-156
-9-100-9+(-100)=-109
-10-90-10+(-90)=-100
-12-75-12+(-75)=-87
-15-60-15+(-60)=-75
-18-50-18+(-50)=-68
-20-45-20+(-45)=-65
-25-36-25+(-36)=-61
-30-30-30+(-30)=-60

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

Condense the terms.

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

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

 Triangles/541301: a triangle has sides 6 and 15. What is the range of values for the third side?1 solutions Answer 354139 by jim_thompson5910(28598)   on 2011-12-04 12:45:04 (Show Source): You can put this solution on YOUR website!The smallest side must be greater than 15 - 6 = 9 And the largest side must be smaller than 15 + 6 = 21 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/541280: Please help me solve and find the solution set x-1 = radical 6x + 101 solutions Answer 354138 by jim_thompson5910(28598)   on 2011-12-04 12:42:54 (Show Source): You can put this solution on YOUR website!x-1 = sqrt(6x + 10) (x-1)^2 = (sqrt(6x + 10))^2 x^2-2x+1 = 6x+10 x^2-2x+1 - 6x-10 = 0 x^2-8x-9 = 0 (x-9)(x+1) = 0 x-9=0 or x+1=0 x=9 or x=-1 So the possible solutions are x=9 or x=-1 However, checking the possible solutions only gives us the true solution to be x = 9 (I'll let you do the check) So the only solution is x = 9 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/541034: 1-(a+b)^3 Factor the polynomial completely, write prime if the polynomial cannot be factored.1 solutions Answer 354000 by jim_thompson5910(28598)   on 2011-12-03 17:56:30 (Show Source): You can put this solution on YOUR website! Note: use the difference of cubes factoring formula here 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
 Graphs/541035: Determine the domain and range: y=5x squared +5.1 solutions Answer 353997 by jim_thompson5910(28598)   on 2011-12-03 17:46:42 (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 of is the set of all real numbers. ------------------------------------------------------- The range of is when We can rewrite into and we can see that , and Since (which is greater than zero), and , this means that the range 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/541032: x^3+7x^2-4x-28=0 Solve.1 solutions Answer 353994 by jim_thompson5910(28598)   on 2011-12-03 17:35:36 (Show Source): You can put this solution on YOUR website!x^3+7x^2-4x-28=0 (x^3+7x^2)+(-4x-28)=0 x^2(x+7)+(-4x-28)=0 x^2(x+7)-4(x+7)=0 (x^2-4)(x+7)=0 (x-2)(x+2)(x+7)=0 x-2=0, x+2=0, x+7=0 x=2, x=-2, x=-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