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 Expressions-with-variables/598406: I need help immediately :( I don't understand these equations , I was absent. I'm crying :(( I can't do all of these. [ Substitution ] y=3x-4 y= -5x + 4 y=2x+13 y=-4x-23 y=3x+20 y=x+4 y=-4x-8 y=3x+13 ------ -x+y=6 y=-7+14 y=-5x+12 x+y=-3 x+y=-6 y=-3x-10 -4x+5y=-15 4x+y=211 solutions Answer 378569 by jim_thompson5910(28708)   on 2012-04-12 23:01:41 (Show Source): You can put this solution on YOUR website!The basic idea is to replace one variable with another expression (of that other variable) so you can eliminate one variable. This way, you'll have a single equation with one variable. You then solve that equation to find the value of that variable. Then you use the solution to find the value of the previously eliminated variable. ======================================================= # 1 y=3x-4 y= -5x + 4 y=3x-4 -5x+4=3x-4 ... Note: I'm replacing the 'y' with -5x+4 (since y = -5x+4) -5x-3x=-4-4 -8x=-8 x=-8/(-8) x = 1 ------------- y = 3x-4 y = 3(1)-4 ... Here I'm replacing 'x' with 1 (since x = 1) y = 3-4 y = -1 So x = 1 and y = -1 ======================================================= # 2 y=2x+13 y=-4x-23 y=2x+13 -4x-23=2x+13 -4x-2x=13+23 -6x=36 x=36/(-6) x = -6 -------------- y = 2x+13 y = 2(-6)+13 y = -12+13 y = 1 So x = -6 and y = 1 ======================================================= # 3 y=3x+20 y=x+4 y=3x+20 x+4=3x+20 x-3x=20-4 -2x=16 x=16/(-2) x = -8 ---------------- y = 3x+20 y = 3(-8)+20 y = -24+20 y = -4 So x = -8 and y = -4 ======================================================= # 4 y=-4x-8 y=3x+13 y=-4x-8 3x+13=-4x-8 3x+4x=-8-13 7x=-21 x=-21/7 x=-3 ----------------- y = -4x-8 y = -4(-3)-8 y = 12-8 y = 4 So x = -3 and y = 4 ======================================================= # 5 -x+y=6 y=-7+14 There's a typo in the second equation. Please repost this one. Thanks ======================================================= # 6 y=-5x+12 x+y=-3 x+y=-3 x+(-5x+12)=-3 x-5x+12=-3 x-5x=-3-12 -4x=-15 x=-15/(-4) x=15/4 ---------------- y = -5x+12 y = -5(15/4)+12 y = -75/4+12 y = -75/4+48/4 y = -27/4 So x = 15/4 and y = -27/4 ======================================================= # 7 x+y=-6 y=-3x-10 x+y=-6 x+(-3x-10)=-6 x-3x-10=-6 x-3x=-6+10 -2x=4 x=4/(-2) x = -2 ------------------ y = -3x-10 y = -3(-2)-10 y = 6-10 y = -4 So x = -2 and y = -4 ======================================================= # 8 -4x+5y=-15 4x+y=21 First we need to solve one equation for one variable. I'm going to solve the second equation for y. 4x+y=21 y=21-4x y = -4x+21 ----------- Now use substitution to solve -4x+5y=-15 -4x+5(-4x+21)=-15 -4x-20x+105=-15 -4x-20x=-15-105 -24x=-120 x=-120/(-24) x = 5 ----------- y = -4x+21 y = -4(5)+21 y = -20+21 y = 1 So x = 5 and y = 1
 Equations/598236: How do you simplify 4x+x-2x+3=54? 1 solutions Answer 378559 by jim_thompson5910(28708)   on 2012-04-12 22:22:12 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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
 Equations/598352: x^2 - x - 6/x^2 - 4=1 solutions Answer 378558 by jim_thompson5910(28708)   on 2012-04-12 22:10:14 (Show Source): You can put this solution on YOUR website! So fully simplifies to In other words, for all values of x where or
 Polynomials-and-rational-expressions/598315: I need help factoring out this problem I did it in two group (20x^3+16x^2) (25x+20)=0 4x^2(5x+4) 5(5x+4)=0 (5x+4) (4x^2+5)=0 5x+4=0 5x+4-4=0-4 5x=-4 divide x= -4/5 I could not factor out (4x^2+5)=0 1 solutions Answer 378549 by jim_thompson5910(28708)   on 2012-04-12 21:19:23 (Show Source): You can put this solution on YOUR website!You are correct. You cannot factor . So you simply solve for x. Now if you haven't learned about complex/imaginary numbers yet, then you would ignore this (and the rest of the solution) and simply say that the only solution is However, if you have learned about complex/imaginary numbers, then... or So if you have learned about complex/imaginary numbers, then there are three solutions and they are , or
 Numeric_Fractions/598338: 14 / N=___ when N=2 What is the work and conclusion (answer)? Thank You, Bax1 solutions Answer 378545 by jim_thompson5910(28708)   on 2012-04-12 21:09:43 (Show Source): You can put this solution on YOUR website!14/N = 14/2 = 7 So 14/N = 7 when N = 2
 Linear-systems/598345: Find the product of the equation below ( 6 x - 5) ( 6 x + 5)1 solutions Answer 378544 by jim_thompson5910(28708)   on 2012-04-12 21:08:43 (Show Source): You can put this solution on YOUR website! Start with the given expression. Now let's FOIL the expression. Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms:. Multiply the Outer terms:. Multiply the Inner terms:. Multiply the Last terms:. --------------------------------------------------- So we have the terms: , , , Now add every term listed above to make a single expression. Now combine like terms. So FOILs to . In other words, . -------------------------------------------------------------------------------------------------------------- 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/597944: If a sample size of 121 is chosen then what would be the actual degrees of freedom?1 solutions Answer 378406 by jim_thompson5910(28708)   on 2012-04-11 21:36:58 (Show Source): You can put this solution on YOUR website!If you're working with a student T distribution, then the degrees of freedom is 121-1 = 120
 Probability-and-statistics/597928: A laboratory tested 71 chicken eggs and found that the mean amount of cholesterol was 230 milligrams with σ = 10.4 milligrams. construct a 95% confidence interval for the true mean cholesterol content, u, of all such eggs1 solutions Answer 378405 by jim_thompson5910(28708)   on 2012-04-11 21:36:01 (Show Source): You can put this solution on YOUR website!( xbar - z*sigma/sqrt(n), xbar + z*sigma/sqrt(n) ) ( 230 - 1.95996*10.4/sqrt(71), 230 + 1.95996*10.4/sqrt(71) ) ... Note: use a table or a calculator to find the value of z (227.58091, 232.419086) So the 95% confidence interval is (227.58091, 232.419086)
test/597922: 3x^2-36x+60. Can you help me solve this as a grouping polynomial.

1 solutions

Answer 378399 by jim_thompson5910(28708)   on 2012-04-11 21:28:00 (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 :
1,2,4,5,10,20
-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
1201+20=21
2102+10=12
454+5=9
-1-20-1+(-20)=-21
-2-10-2+(-10)=-12
-4-5-4+(-5)=-9

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).

 Money_Word_Problems/597924: In order ti start a small business, a student takes out a simple interest loan for \$4000 for 9 months at a rate of 8.25%. a-) How much interest must the student pay? b-) Find the future value of the loan.1 solutions Answer 378398 by jim_thompson5910(28708)   on 2012-04-11 21:27:00 (Show Source): You can put this solution on YOUR website!FV = PV*(1+rt) FV = 4000*(1+0.0825*(9/12)) FV = 4247.5 a) The student must pay 4247.5 - 4000 = 247.50 dollars in interest b) The future value of the loan is 4247.50 dollars.
 Polynomials-and-rational-expressions/597877: I am trying to finish a problem where I am multiplying rational expressions. This is what I have simplified it down to: (c-1)*(2c+1)/(c^(2)-1). I know I must factor out (c-1) and (c^(2)-1) and the greatest common factor is (c-1). I have used algebra.com's solver and I know the answer is (2c+1)/(c+1). But how do I get (c+1) from factoring (c^(2)-1) by (c-1)? Thank you!1 solutions Answer 378375 by jim_thompson5910(28708)   on 2012-04-11 20:10:42 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Notice how we have a difference of squares where in this case and . So let's use the difference of squares formula to factor the expression: Start with the difference of squares formula. Plug in and . So this shows us that factors to . In other words . Hopefully this helps. If not, let me know.
 sets-and-operations/597828: Let A = {5, 10, 15, 20} and B = {10, 20, 30}. What is the intersection of A and B? 1 solutions Answer 378357 by jim_thompson5910(28708)   on 2012-04-11 19:03:43 (Show Source): You can put this solution on YOUR website!A intersect B = set of all things found in both sets A and B A intersect B = {10, 20}
 Volume/597829: If you have a dimensional box and it is 8 inches tall, 12 inches wide and 4 inches long. What would the volume be? 1 solutions Answer 378356 by jim_thompson5910(28708)   on 2012-04-11 19:02:55 (Show Source): You can put this solution on YOUR website!The volume would be 8*12*4 = 384 cubic inches.
 Trigonometry-basics/597824: Suppose that a 16-foot ladder is leaning against a wall, making a 75 angle with the ground (as measured from a perpendicular line from the base of the ladder to the wall). How high up the wall is the end of the ladder?1 solutions Answer 378355 by jim_thompson5910(28708)   on 2012-04-11 18:59:55 (Show Source): You can put this solution on YOUR website!sin(theta) = opposite/hypotenuse sin(75) = x/16 16*sin(75) = x x = 16*sin(75) x = 16*0.965925826289068 x = 15.4548132206251 So the ladder reaches approximately 15.4548 feet up the wall.
 Polynomials-and-rational-expressions/597823: Completely factor the following expression:y^2-121z^2 show all work please 1 solutions Answer 378353 by jim_thompson5910(28708)   on 2012-04-11 18:56:58 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Notice how we have a difference of squares where in this case and . So let's use the difference of squares formula to factor the expression: Start with the difference of squares formula. Plug in and . So this shows us that factors to . In other words .
 Volume/597820: If the radius is 6 and the volume is 8595.4 cubic centimeters, how do you find the length of a cylinder? e-mail: ky_taylor2002@yahoo.com1 solutions Answer 378352 by jim_thompson5910(28708)   on 2012-04-11 18:56:20 (Show Source): You can put this solution on YOUR website!V = pi*r^2*h 8595.4 = (3.14159)*(6)^2*h 8595.4 = (3.14159)*(36)*h 8595.4 = 113.09724*h 8595.4/113.09724 = h 76.0000862974198 = h h = 76.0000862974198 So the height (or length) of the cylinder is approximately 76.0000862974198 cm