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 Proofs/617771: 1. R v ~T 2. ~T>O 3. ~O :. R1 solutions Answer 388571 by jim_thompson5910(28510)   on 2012-06-04 19:27:54 (Show Source): You can put this solution on YOUR website!```1. R v ~T 2. ~T>O 3. ~O :. R ----------------------------------------- 4. ~~T 2,3 Modus Tollens 5. ~T v R 1 Commutation 6. R 5,4 Disjunctive Syllogism ```
 Rational-functions/617731: 1 over x= 2 over x^21 solutions Answer 388570 by jim_thompson5910(28510)   on 2012-06-04 19:24:27 (Show Source): You can put this solution on YOUR website!1/x = 2/x^2 1*x^2 = 2x x^2 = 2x x^2 - 2x = 0 x(x-2) = 0 x = 0 or x-2 = 0 x = 0 or x = 2 Keep in mind that you cannot divide by zero. So the only solution is x = 2
 Geometry_Word_Problems/617810: two flower beds are shaped like right triangles. what measurement can you show that two triangular flowers are beds congruent ?1 solutions Answer 388569 by jim_thompson5910(28510)   on 2012-06-04 19:18:09 (Show Source): You can put this solution on YOUR website!If you know the hypotenuse of one triangle is equal to the other and if you know that one leg is equal to it's corresponding counterpart, then you will have shown that the two triangles are congruent.
 Functions/617809: Solve using the multiplication principle. 9x=-721 solutions Answer 388568 by jim_thompson5910(28510)   on 2012-06-04 19:14:16 (Show Source): You can put this solution on YOUR website!Multiply both sides by 1/9 to completely isolate x. Remember to reduce/simplify as much as possible.
 Rational-functions/617729: 3 over x= 4 over x-11 solutions Answer 388567 by jim_thompson5910(28510)   on 2012-06-04 19:13:26 (Show Source): You can put this solution on YOUR website!3/x=4/(x-1) 3(x-1)=4x 3x-3=4x -3=4x-3x -3=x x = -3
 Functions/617808: Simplify. -5[-10-(-4-9)]1 solutions Answer 388565 by jim_thompson5910(28510)   on 2012-06-04 19:10:33 (Show Source): You can put this solution on YOUR website!-5[-10-(-4-9)] -5[-10-(-13)] -5[-10+13] -5[13] -65 So -5[-10-(-4-9)] = -65
 Rational-functions/617728: x+2 over x-8= 4 over x-81 solutions Answer 388564 by jim_thompson5910(28510)   on 2012-06-04 19:09:35 (Show Source): You can put this solution on YOUR website!(x+2)/(x-8)=4/(x-8) x+2 = 4 x = 4-2 x = 2
 Radicals/617727: 3/x=4/x-11 solutions Answer 388563 by jim_thompson5910(28510)   on 2012-06-04 19:08:29 (Show Source): You can put this solution on YOUR website!3/x=4/(x-1) 3(x-1)=4x 3x-3=4x -3=4x-3x -3=x x = -3
 Functions/617794: Find the domain of thr function. p(x)=x^2-2x+10. What is the domain of p?1 solutions Answer 388562 by jim_thompson5910(28510)   on 2012-06-04 19:07:25 (Show Source): You can put this solution on YOUR website!Since you can plug in any number you want for x and get some number out for p(x), the domain is the set of all real numbers.
 t e s t/617798: please help me use long division to solve this: (x^2+5x+6)/(x+2)1 solutions Answer 388561 by jim_thompson5910(28510)   on 2012-06-04 19:06:54 (Show Source): You can put this solution on YOUR website!Hint: x^2+5x+6 factors to (x+3)(x+2)
 Square-cubic-other-roots/617783: I cant figure this out any help on this problem would be great the square root of open parenthesis a plus 3 close parenthesis super 2 Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this. 1 solutions Answer 388558 by jim_thompson5910(28510)   on 2012-06-04 18:39:28 (Show Source): You can put this solution on YOUR website! and So in either case, the answer is
 Exponents/617699: Express using a positive exponent: 1/x^-n1 solutions Answer 388489 by jim_thompson5910(28510)   on 2012-06-04 14:52:39 (Show Source): You can put this solution on YOUR website! So
 Travel_Word_Problems/617691: Please help me solve: The american dietetic association states that 11 out of every 25 people do not eat breakfast. If there are 175 students in a large lecture class, about how many did not eat breakfast? Thanks1 solutions Answer 388485 by jim_thompson5910(28510)   on 2012-06-04 14:20:08 (Show Source): You can put this solution on YOUR website!There are roughly (11/25)*(175) = (11*175)/25 = 1925/25 = 77 people who did not eat breakfast.
 Rectangles/617684: Suppose two sides of a square are given as x + 3 and 12 - x. What is its area? 1 solutions Answer 388483 by jim_thompson5910(28510)   on 2012-06-04 14:11:30 (Show Source): You can put this solution on YOUR website!If this is a square, then it has equal sides. So x+3 = 12-x Solve for x x+3 = 12-x x+x = 12-3 2x = 9 x = 9/2 x = 4.5 So each side is 4.5 + 3 = 7.5 units. So the area is 7.5^2 = 56.25 square units. ------------------------------------------------------------------ If this is really a rectangle, then the area is simply A = (x+3)(12-x) A = 12x - x^2 + 36 - 3x A = -x^2 + 9x + 36
 Quadratic_Equations/617682: (x + 2)^2 = 1211 solutions Answer 388481 by jim_thompson5910(28510)   on 2012-06-04 14:07:18 (Show Source): You can put this solution on YOUR website! Start with the given equation. Take the square root of both sides. or Break up the "plus/minus" to form two equations. or Take the square root of to get . or Subtract from both sides. or Combine like terms. -------------------------------------- Answer: So the solutions are or .
 Linear-systems/617580: 5x3+5y+3x-3y+2y 1 solutions Answer 388469 by jim_thompson5910(28510)   on 2012-06-04 13:22:13 (Show Source): You can put this solution on YOUR website!5x^3+5y+3x-3y+2y 5x^3+3x+(5y-3y+2y) 5x^3+3x+4y So 5x^3+5y+3x-3y+2y simplifies to 5x^3+3x+4y
 test/617588: 1 solutions Answer 388468 by jim_thompson5910(28510)   on 2012-06-04 13:21:12 (Show Source): You can put this solution on YOUR website!Problem is missing.
 Miscellaneous_Word_Problems/617586: A carpenter was in a terrible hurry. He had to work as quickly as possible to cut a very heavy 10 foot plank into 10 equal sections. If it takes 1 minute per cut, how long will it take him to get the 10 equal pieces?1 solutions Answer 388467 by jim_thompson5910(28510)   on 2012-06-04 13:20:37 (Show Source): You can put this solution on YOUR website!He needs 10-1 = 9 cuts, so it will take him 1*9 = 9 minutes.
 Polygons/617638: The measure of an interior angle of a regular polygon is 160. How many sides does the polygon have? 1 solutions Answer 388466 by jim_thompson5910(28510)   on 2012-06-04 13:19:17 (Show Source): You can put this solution on YOUR website!I = (180(n-2))/n 160 = (180(n-2))/n 160n = 180(n-2) 160n = 180n-360 160n - 180n = -360 -20n = -360 n = -360/(-20) n = 18 So the solution is n = 18, which means that there are 18 sides.
 Rational-functions/617587: What does "Q" represent in rational numbers?1 solutions Answer 388465 by jim_thompson5910(28510)   on 2012-06-04 13:17:38 (Show Source): You can put this solution on YOUR website!Q represents Quotient.
Expressions-with-variables/614551: factor by grouping
9a^(2)-40a-25=
1 solutions

Answer 388464 by jim_thompson5910(28510)   on 2012-06-04 13:16:45 (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 :
1,3,5,9,15,25,45,75,225
-1,-3,-5,-9,-15,-25,-45,-75,-225

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

These factors pair up and multiply to .
1*(-225) = -225
3*(-75) = -225
5*(-45) = -225
9*(-25) = -225
15*(-15) = -225
(-1)*(225) = -225
(-3)*(75) = -225
(-5)*(45) = -225
(-9)*(25) = -225
(-15)*(15) = -225

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

First NumberSecond NumberSum
1-2251+(-225)=-224
3-753+(-75)=-72
5-455+(-45)=-40
9-259+(-25)=-16
15-1515+(-15)=0
-1225-1+225=224
-375-3+75=72
-545-5+45=40
-925-9+25=16
-1515-15+15=0

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).

 Expressions-with-variables/617639: Simplify the expression -(12b-10) + 5(3b - 2) 1 solutions Answer 388463 by jim_thompson5910(28510)   on 2012-06-04 13:15:42 (Show Source): You can put this solution on YOUR website!-(12b-10) + 5(3b - 2) -12b + 10 + 15b - 10 3b + 0 3b So -(12b-10) + 5(3b - 2) simplifies to 3b
 test/617670: Write an expression for the perimeter. Here are the letter/numbers on my shape. X,9,4,5 please help if you can1 solutions Answer 388461 by jim_thompson5910(28510)   on 2012-06-04 13:13:49 (Show Source): You can put this solution on YOUR website!It looks like these values are the lengths of the side of this quadrilateral. If so, then the perimeter is x+9+4+5 or x+18
 Age_Word_Problems/617540: if my sister is turning 18 this year. what year was she born in ?1 solutions Answer 388394 by jim_thompson5910(28510)   on 2012-06-04 04:06:44 (Show Source): You can put this solution on YOUR website!She was born in 2012 - 18 = 1994
 Quadratic_Equations/617512: (5y+3)^2+144=01 solutions Answer 388364 by jim_thompson5910(28510)   on 2012-06-03 21:52:39 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms. Take the square root of both sides. or Break up the "plus/minus" to form two equations. or Simplify to get . or Subtract from both sides. or Divide both sides by 5
 Probability-and-statistics/617465: Its a True or False question. The test statistics for a problem involving a small sample of under 30 and the population standard deviation is unknown is the t distribution. 1 solutions Answer 388342 by jim_thompson5910(28510)   on 2012-06-03 19:25:55 (Show Source): You can put this solution on YOUR website!This is true since you should use a t distribution to do hypothesis testing for samples less than 30 and you don't know the population standard deviation.
 Inequalities/617461: how do you do this problem? 4c+6<(3+2c)1 solutions Answer 388338 by jim_thompson5910(28510)   on 2012-06-03 19:06:30 (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. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is
 Permutations/617424: in how many ways can 5 different kittens be lined up for a calendat Photograph?1 solutions Answer 388324 by jim_thompson5910(28510)   on 2012-06-03 17:56:57 (Show Source): You can put this solution on YOUR website!There are 5! = 5*4*3*2*1 = 120 different ways.
 Linear-equations/617433: how do this problem? 4h+6=2h-81 solutions Answer 388322 by jim_thompson5910(28510)   on 2012-06-03 17:56:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Probability-and-statistics/617401: In a bag are 4 yellow and 8 blue marbles. 3 are selected at random without replacement. What is the probability that all 3 are yellow or all 3 are blue?1 solutions Answer 388308 by jim_thompson5910(28510)   on 2012-06-03 16:57:11 (Show Source): You can put this solution on YOUR website!P(3 yellow) = (4/12)*(3/11)*(2/10) = 24/1320 = 1/55 P(3 blue) = (8/12)*(7/11)*(6/10) = 336/1320 = 14/55 ------------------------------------ P(3 Yellow OR 3 Blue) = P(3 yellow) + P(3 blue) P(3 Yellow OR 3 Blue) = 1/55 + 14/55 P(3 Yellow OR 3 Blue) = 15/55 P(3 Yellow OR 3 Blue) = 3/11 Note: we can simply add the probabilities because the two events are mutually exclusive.