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 Equations/660080: 2(4-2r)=-2(r+5)1 solutions Answer 411028 by jim_thompson5910(28595)   on 2012-10-01 17:59:50 (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 --------------------------------------------------------------------------------------------------------------
 Triangles/659916: an obtuse angle measures 3x-12 find the values of x 1 solutions Answer 410983 by jim_thompson5910(28595)   on 2012-10-01 14:48:06 (Show Source): You can put this solution on YOUR website!90 < 3x-12 < 180 90+12 < 3x < 180+12 102 < 3x < 192 102/3 < x < 192/3 34 < x < 64 So x is between 34 and 64 (not including 34 or 64) -------------------------------------------------------------------------------------------------------------- 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/659630: What does x equal in 3x-1=11+2x? 1 solutions Answer 410837 by jim_thompson5910(28595)   on 2012-09-30 21:14:10 (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 --------------------------------------------------------------------------------------------------------------
 Graphs/659456: what is the answer to -5[4-(-3)(2)]1 solutions Answer 410794 by jim_thompson5910(28595)   on 2012-09-30 17:59:32 (Show Source): You can put this solution on YOUR website!-5[4-(-3)(2)] -5[4-(-6)] -5[4+6] -5[10] -50 -------------------------------------------------------------------------------------------------------------- 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/659434: (-3p)^21 solutions Answer 410780 by jim_thompson5910(28595)   on 2012-09-30 17:14:12 (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 --------------------------------------------------------------------------------------------------------------
 Exponents/659418: (6x)^-21 solutions Answer 410778 by jim_thompson5910(28595)   on 2012-09-30 17:07:45 (Show Source): You can put this solution on YOUR website! where -------------------------------------------------------------------------------------------------------------- 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/659398: I know how to factorise equations and solve such as x^2+4x-21=0 already, but Im not sure how to do it when there is a number in front of x^2. For example:
3b^2+5b+2=0
How could I factorize and then solve this equation?
1 solutions

Answer 410772 by jim_thompson5910(28595)   on 2012-09-30 16:38:38 (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 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 :
1,2,3,6
-1,-2,-3,-6

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

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

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

First NumberSecond NumberSum
161+6=7
232+3=5
-1-6-1+(-6)=-7
-2-3-2+(-3)=-5

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, .

I'll leave the rest to you.

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

 Rectangles/659392: Five times the sum of a number and seven is twenty. Find the number1 solutions Answer 410770 by jim_thompson5910(28595)   on 2012-09-30 16:33:38 (Show Source): You can put this solution on YOUR website!Hint: Five times the sum of a number and seven is twenty. translates to 5(x+7) = 20 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Angles/659381: 5x+107=8x-11 find the measures ? 1 solutions Answer 410764 by jim_thompson5910(28595)   on 2012-09-30 16:07:38 (Show Source): You can put this solution on YOUR website! From here, use this solution of x to find the angle measures. -------------------------------------------------------------------------------------------------------------- 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/659379: Write the equation of the line given by the following graph in standard form. 2x-y=-11 solutions Answer 410763 by jim_thompson5910(28595)   on 2012-09-30 16:05:07 (Show Source): You can put this solution on YOUR website!The equation is already in standard form. If you want to convert to slope-intercept form, then... 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 --------------------------------------------------------------------------------------------------------------
 Graphs/659369: If y=4 how do I graph this and find what my slope is?1 solutions Answer 410760 by jim_thompson5910(28595)   on 2012-09-30 15:49:34 (Show Source): You can put this solution on YOUR website!The slope is 0 since this is a horizontal line (shown in green below) -------------------------------------------------------------------------------------------------------------- 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/659370: I need help solving a system of equations for x and y using Cramer's rule. I'm completely lost. The answers I came up with are x=1/2 and y=28/23. Is this correct? Thank you.
2x-5y=16
3x-4y=10
1 solutions

Answer 410759 by jim_thompson5910(28595)   on 2012-09-30 15:48:45 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 2 variables First let . This is the matrix formed by the coefficients of the given system of equations. Take note that the right hand values of the system are and which are highlighted here: These values are important as they will be used to replace the columns of the matrix A. Now let's calculate the the determinant of the matrix A to get . Remember that the determinant of the 2x2 matrix is . If you need help with calculating the determinant of any two by two matrices, then check out this solver. Notation note: denotes the determinant of the matrix A. --------------------------------------------------------- Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'x' column so to speak). Now compute the determinant of to get . Once again, remember that the determinant of the 2x2 matrix is To find the first solution, simply divide the determinant of by the determinant of to get: So the first solution is --------------------------------------------------------- We'll follow the same basic idea to find the other solution. Let's reset by letting again (this is the coefficient matrix). Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'y' column in a way). Now compute the determinant of to get . To find the second solution, divide the determinant of by the determinant of to get: So the second solution is ==================================================================================== Final Answer: So the solutions are and giving the ordered pair (-2, -4) Once again, Cramer's Rule is dependent on determinants. Take a look at this 2x2 Determinant Solver if you need more practice with determinants.

 Rational-functions/659359: Graph the equation. Label any intercepts. y=1.5 I don't know how to solve it without an x variable in there. If there was an x variable you would just put zero in for x to find y and zero in for y to find x, right? SO CONFUSING. 1 solutions Answer 410757 by jim_thompson5910(28595)   on 2012-09-30 15:40:05 (Show Source): You can put this solution on YOUR website!This is the horizontal line that passes through 1.5 on the y-axis (shown in green below) -------------------------------------------------------------------------------------------------------------- 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_And_Systems_Word_Problems/659365: I need find an equation of the line in standard form passing through the two points. (10 , 9) and (10, 1) Thanks1 solutions Answer 410756 by jim_thompson5910(28595)   on 2012-09-30 15:38:03 (Show Source): You can put this solution on YOUR website!The x coordinates are the same, so this is a vertical line that passes through 10 on the x-axis. So the equation of the line is x = 10 -------------------------------------------------------------------------------------------------------------- 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/659348: I need help solving a system of equations for x and y using Cramer's rule.
2x-5y=16
3x-4y=10

1 solutions

Answer 410754 by jim_thompson5910(28595)   on 2012-09-30 15:23:20 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 2 variables First let . This is the matrix formed by the coefficients of the given system of equations. Take note that the right hand values of the system are and which are highlighted here: These values are important as they will be used to replace the columns of the matrix A. Now let's calculate the the determinant of the matrix A to get . Remember that the determinant of the 2x2 matrix is . If you need help with calculating the determinant of any two by two matrices, then check out this solver. Notation note: denotes the determinant of the matrix A. --------------------------------------------------------- Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'x' column so to speak). Now compute the determinant of to get . Once again, remember that the determinant of the 2x2 matrix is To find the first solution, simply divide the determinant of by the determinant of to get: So the first solution is --------------------------------------------------------- We'll follow the same basic idea to find the other solution. Let's reset by letting again (this is the coefficient matrix). Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'y' column in a way). Now compute the determinant of to get . To find the second solution, divide the determinant of by the determinant of to get: So the second solution is ==================================================================================== Final Answer: So the solutions are and giving the ordered pair (-2, -4) Once again, Cramer's Rule is dependent on determinants. Take a look at this 2x2 Determinant Solver if you need more practice with determinants.

 Sequences-and-series/659345: 3a=2-b 3a=4-b use the substitution method to solve the linear equations1 solutions Answer 410751 by jim_thompson5910(28595)   on 2012-09-30 15:13:16 (Show Source): You can put this solution on YOUR website!Since 3a is both 2-b and 4-b, we can say 2-b = 4-b Solve for b and tell me what you get. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com --------------------------------------------------------------------------------------------------------------
 Inequalities/659342: Solve the inequality x^2>64. type the answer in interval notation.1 solutions Answer 410750 by jim_thompson5910(28595)   on 2012-09-30 15:12:00 (Show Source): You can put this solution on YOUR website!x^2 > 64 sqrt(x^2) > sqrt(64) |x| > 8 x < -8 or x > 8 So the answer in interval notation is $\Large \left(-\infty,-8\right)\cup\left(8,\infty\right)$ -------------------------------------------------------------------------------------------------------------- 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/658899: 3x + 8 = 2(x + 6) x =1 solutions Answer 410747 by jim_thompson5910(28595)   on 2012-09-30 15:04:55 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right 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 --------------------------------------------------------------------------------------------------------------
 Equations/658068: Find all real solutions of equation 2x^2+5x-6=01 solutions Answer 410746 by jim_thompson5910(28595)   on 2012-09-30 15:03:41 (Show Source): You can put this solution on YOUR website!Use the quadratic formula to solve for x or or So the exact solutions are or and the approximate solutions are or (rounded to 3 decimal places) -------------------------------------------------------------------------------------------------------------- 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/657686: Solve -5x + 15 > 45 1 solutions Answer 410744 by jim_thompson5910(28595)   on 2012-09-30 15:01:12 (Show Source): You can put this solution on YOUR website! Note: the sign flips here. -------------------------------------------------------------------------------------------------------------- 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/657683: Solve 18 (y - 3) - 13 (2 y + 5) > 7 y + 8 1 solutions Answer 410743 by jim_thompson5910(28595)   on 2012-09-30 15:00:22 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Combine like terms on the left side. 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 Which in decimal form 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/657638: Solve for x: 2p+3q-3x=13-4p1 solutions Answer 410742 by jim_thompson5910(28595)   on 2012-09-30 14:59:29 (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/657681: 2(3b-5)=4-(2b+3) If you can show me the steps of the solution that would be extremely helpfull :) thank you1 solutions Answer 410740 by jim_thompson5910(28595)   on 2012-09-30 14:58:17 (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/657676: Solve 3 x < -7 1 solutions Answer 410738 by jim_thompson5910(28595)   on 2012-09-30 14:57:53 (Show Source): You can put this solution on YOUR website!3x < -7 3x/3 < -7/3 x < -7/3 -------------------------------------------------------------------------------------------------------------- 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/659143: 2/3x= -81 solutions Answer 410737 by jim_thompson5910(28595)   on 2012-09-30 14:57:20 (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 --------------------------------------------------------------------------------------------------------------
 Equations/659303: -8(x+3)=-8-5(x+1)1 solutions Answer 410736 by jim_thompson5910(28595)   on 2012-09-30 14:56:35 (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 --------------------------------------------------------------------------------------------------------------
 Systems-of-equations/659286: Tell whether the relationship between x and y is an inverse variation, If it is, Write an equation for it: x 1 2 3 4 5 6 7 8 9 10 y 48 24 16 12 9.6 8 6.8 6 5.3 4.8 I think it's an inverse variation but I dont know how to write an equation for it. 1 solutions Answer 410735 by jim_thompson5910(28595)   on 2012-09-30 14:55:28 (Show Source): You can put this solution on YOUR website!Since 1*48 = 48, 2*24 = 48, 3*16 = 48, etc etc This means x*y = 48, which tells us that this is an inverse variation. Solve for y to get which is your 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 --------------------------------------------------------------------------------------------------------------
 Equations/659338: What are the values for x that satisfy the equation (x+a) (x+b) =0? F. -a and -b G. -a and b H. -ab J. a and -b K. a and b1 solutions Answer 410734 by jim_thompson5910(28595)   on 2012-09-30 14:53:37 (Show Source): You can put this solution on YOUR website!(x+a)(x+b) =0 x+a=0 or x+b=0 x+a-a=0-a or x+b-b=0-b x = -a or x = -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 --------------------------------------------------------------------------------------------------------------
 Graphs/659319: Use the elimination method to solve the system of equations. a+7b=15 a+4b=6 These are the chooses of answers. A. There is one solution, it is____. B. There are infinitely many solutions. C. There is no solutions.1 solutions Answer 410733 by jim_thompson5910(28595)   on 2012-09-30 14:52:16 (Show Source): You can put this solution on YOUR website!Hint: a+7b=15 a+4b=6 a+7b=15 -1(a+4b)=-1*6 a+7b=15 -a-4b=-6 --------- 0a+3b=9 So 3b = 9 Solve that for b. Then use this solution for b to find the solution for 'a'. -------------------------------------------------------------------------------------------------------------- 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/659326: 3. Select a counterexample to show that the statement is false. When an odd number is added to the product of two even numbers, the result will be even. 1 solutions Answer 410732 by jim_thompson5910(28595)   on 2012-09-30 14:50:41 (Show Source): You can put this solution on YOUR website!When an odd number is added to the product of two even numbers Example: 3 + 2 * 4 = 3+8 = 11 which is NOT even. So the statement is false. -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Systems-of-equations/659284: Tell whether the relationship between x and y is an inverse variation, If it is, Write an equation for it: x 1 2 3 4 5 6 7 8 9 10 y 10 9 8 7 6 5 4 3 2 1 I think it is an inverse variation but I dont know how to write an equation for it. 1 solutions Answer 410731 by jim_thompson5910(28595)   on 2012-09-30 14:47:03 (Show Source): You can put this solution on YOUR website!If it was an inverse variation, then x*y = k for some fixed number k. But 1*10 = 10 and 2*9 = 18 so the two pairs do NOT multiply to the same constant, which means that this relationship is NOT an inverse variation. -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------