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 Equations/401882: 3x+1=101 solutions Answer 284363 by jim_thompson5910(28715)   on 2011-01-30 16:38:43 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Miscellaneous_Word_Problems/401605: 32 basketball teams went to a single elimination tournament. How many games were played at the tournament? I don't really know how to figure this one out. If you do decide to help me, can you please show me how you did it? Many tutors just tell me the answer. I would like to know the steps for future reference. Thank you! :)1 solutions Answer 284237 by jim_thompson5910(28715)   on 2011-01-30 01:34:25 (Show Source): You can put this solution on YOUR website!The first answer is correct if there's only one actual game and you're trying to figure out how many ways to pair up two teams out of 32 (to play this only game). However, in this case, it's much simpler. Since there are 32 teams, and each team is playing someone else, there are such pairings. Out of each pair, only one team will move on. So after the first round, there are 16 teams left. Those 16 teams pair up to have pairings. So after the 2nd round, 8 teams remain. See the pattern? So we go from 32, to 16, then to 8. Now divide 8 in 2 to get 4 and divide 4 in half to get 2. Finally, we have 2 teams that compete for the finals. If you cut 2 in half, you'll get 1, which will be the tournament champion. So we have 16 (first round), 8 (second round), 4 (third round), 2 (fourth round) games and then 1 final game Note: Count the pairings (NOT the actual teams). Draw a chart or a picture if you need to. Note: the "fourth" round is probably more commonly known as the "semifinals". Also, the "third" round may be referred to as the "conference semifinals" or "quarterfinals" So add up all of these games to get: 16 + 8 + 4 + 2 + 1 = 31 So this means that there are 31 games played total.
 Numbers_Word_Problems/398716: how can i writte and simplify this: six times the sum of a number and 9, added to 4 times the number1 solutions Answer 282436 by jim_thompson5910(28715)   on 2011-01-23 21:40:46 (Show Source): You can put this solution on YOUR website!"the sum of a number and 9" translates to where 'x' is some number Now multiply that whole thing by 6 to get and then add 4x (4 times the number to get So "six times the sum of a number and 9, added to 4 times the number" translates to Now distribute to get and combine like terms to get So the simplified expression is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Probability-and-statistics/398695: you have 7 rotten apples in a batch of 2 apples. what percent of the apple are good ? round to the nearest tenth if needed1 solutions Answer 282419 by jim_thompson5910(28715)   on 2011-01-23 20:19:13 (Show Source): You can put this solution on YOUR website!If you only have 2 apples total in your batch, how can you possible have 7 bad apples? I'm missing something here. There has to be a typo.
 Word_Problems_With_Coins/398683: what does three quarters,three nickels,six dimes,and four pennies egual??1 solutions Answer 282418 by jim_thompson5910(28715)   on 2011-01-23 20:17:01 (Show Source): You can put this solution on YOUR website!1 penny = 0.01 dollars 1 nickel = 0.05 dollars 1 dime = 0.10 dollars 1 quarter = 0.25 dollars So 3 quarters = 3*0.25 = 0.75 dollars, 3 nickels = 3*0.05 = 0.15 dollars, 6 dimes = 6*0.10 = 0.60 dollars, and 4 pennies = 4*0.01 = 0.04 dollars Add these figures up to get 0.75+0.15+0.60+0.04 = 1.54 dollars So the answer is \$1.54 If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Graphs/398678: how do you solve this problem y^3=8-x1 solutions Answer 282417 by jim_thompson5910(28715)   on 2011-01-23 20:12:45 (Show Source): You can put this solution on YOUR website!If you're solving for y, simply take the cube root of both sides to get If on the other hand you're solving for 'x', simply subtract 8 from both sides and multiply every term by -1 to get or If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Linear-equations/398680: Write an equation that has no solution.1 solutions Answer 282416 by jim_thompson5910(28715)   on 2011-01-23 20:11:12 (Show Source): You can put this solution on YOUR website!Take any number x. Surely is true for ALL x. Now simply add any number you want to the left or right side. I'm going to add the number 1 to the right side to get . This equation has no solution. Here's why: Start with the given equation. Subtract from both sides. Combine like terms on the left side. Simplify. Since this equation is NEVER true for any x value, this means that there are no solutions. So this confirms our original claim. If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Linear-equations/398681: Solve the system by the substitution method. -2x + y = -2 x - 4y = 9 1 solutions Answer 282415 by jim_thompson5910(28715)   on 2011-01-23 20:08:54 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y. So let's isolate y in the first equation Start with the first equation Add to both sides Rearrange the equation --------------------- Since , we can now replace each in the second equation with to solve for Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute to Multiply Combine like terms on the left side Subtract 8 from both sides Combine like terms on the right side Divide both sides by -7 to isolate x Reduce -----------------First Answer------------------------------ So the first part of our answer is: Since we know that we can plug it into the equation (remember we previously solved for in the first equation). Start with the equation where was previously isolated. Plug in Multiply Combine like terms (note: if you need help with fractions, check out this solver) -----------------Second Answer------------------------------ So the second part of our answer is: -----------------Summary------------------------------ So our answers are: and which form the point If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Proportions/398687: if -2x+-8x=-48 find the value of 1/2x why whould they need 1/2x? and how do i solve? i tried to multiply 2x8 which is -16 then -48--16 which got -32 divided and that confused me very much please help! 1 solutions Answer 282413 by jim_thompson5910(28715)   on 2011-01-23 20:07:17 (Show Source): You can put this solution on YOUR website!Note: is the same as Start with the given equation. Combine like terms on the left side. Divide both sides by to isolate . Reduce. Now that we know the value of x, plug it into to get So if (ie ) If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Equations/398685: Could you please explain to me how I could solve this equation. 2(x+3)=5(x-1). Thank you in advance.1 solutions Answer 282411 by jim_thompson5910(28715)   on 2011-01-23 20:04:53 (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. 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, feel free to check out my tutoring website Jim
 Quadratic_Equations/398591: How do you solve (x-1/2)^2=3/2 ?1 solutions Answer 282382 by jim_thompson5910(28715)   on 2011-01-23 17:27:27 (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 Simplify the square root. or Add to both sides. or Combine the fractions. -------------------------------------- Answer: So the solutions are or . If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Probability-and-statistics/398554: What determines whether a hypothesis test will be one-tailed or two-tailed? 1 solutions Answer 282377 by jim_thompson5910(28715)   on 2011-01-23 17:11:53 (Show Source): You can put this solution on YOUR website!If you have key words like "less than" or "at most", then that will signify that you're dealing with inequality signs. This consequently means that the alternative hypothesis will have an inequality sign. So all this means that you have a one-tailed test. Or... If on the other hand you have key words like "not equal to" or "is different than", then you'll have a two-tailed test. Post the actual problem so we can see whether the test is one-tailed or two-tailed. If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Quadratic_Equations/398558: How do you solve 3(x+7/3)^2=1 i've tried to do it but i just cant figure it out my teacher did not teach me how do to a question like his. Please help, Thank you!1 solutions Answer 282368 by jim_thompson5910(28715)   on 2011-01-23 16:56:19 (Show Source): You can put this solution on YOUR website! Start with the given equation. Divide both sides by . Take the square root of both sides. or Break up the "plus/minus" to form two equations. or Simplify the square root. or Subtract from both sides. or Combine the fractions. -------------------------------------- Answer: So the solutions are or . If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Probability-and-statistics/398500: A single six person jury must be selected from a pool of 15 jurors how many ways can a group of 6 be selected ? 1 solutions Answer 282350 by jim_thompson5910(28715)   on 2011-01-23 15:32:36 (Show Source): You can put this solution on YOUR website!There are 15 P 6 = different ways to make up a 6 person jury. If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Linear-equations/398483: -4(2-3x)=7-2(x-3)1 solutions Answer 282348 by jim_thompson5910(28715)   on 2011-01-23 14:50:21 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the right side. Add to 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, feel free to check out my tutoring website Jim
 Equations/398463: what is the value of x inthe equation 2(x-3)+1=191 solutions Answer 282347 by jim_thompson5910(28715)   on 2011-01-23 14:49:31 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Add to 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, feel free to check out my tutoring website Jim
 Equations/398478: How do I do.......1.1-1t+2.2t=5.9 I don't just want the answer but how you did it1 solutions Answer 282344 by jim_thompson5910(28715)   on 2011-01-23 14:35:37 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by 10 to clear out the decimals. Distribute and multiply. 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, feel free to check out my tutoring website Jim
Polynomials-and-rational-expressions/398464: factor each completely:
n^2-11n+10
1 solutions

Answer 282343 by jim_thompson5910(28715)   on 2011-01-23 14:34:33 (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 :
1,2,5,10
-1,-2,-5,-10

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

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

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

First NumberSecond NumberSum
1101+10=11
252+5=7
-1-10-1+(-10)=-11
-2-5-2+(-5)=-7

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

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

Answer:

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, feel free to check out my tutoring website

Jim

 expressions/397838: Evaluate the expression. 7d – 5c if d = 7 and c = 31 solutions Answer 281852 by jim_thompson5910(28715)   on 2011-01-21 10:34:33 (Show Source): You can put this solution on YOUR website! So when d = 7 and c = 3
 Quadratic_Equations/397839: Demonstrate how your quadratic equation expression is solved by the Square Root Property. Explain your steps. $\bg_white (x-1)^2=6$1 solutions Answer 281851 by jim_thompson5910(28715)   on 2011-01-21 10:31:41 (Show Source): You can put this solution on YOUR website! Start with the given equation. Take the square root of both sides (don't forget about the plus/minus). or Break up the "plus/minus" to form two equations. or Add to both sides. -------------------------------------- Answer: So the solutions are or .
Polynomials-and-rational-expressions/397336: I need to factor this trinomial completely, I thinks it is "not factorable" using integers but I want to be sure.
8t^2 - 3t - 4
Thanks in advance!
1 solutions

Answer 281660 by jim_thompson5910(28715)   on 2011-01-20 14:20:11 (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 8 and -4 respectively.

Now multiply the first coefficient 8 and the last coefficient -4 to get -32. Now what two numbers multiply to -32 and add to the middle coefficient -3? Let's list all of the factors of -32:

Factors of -32:
1,2,4,8,16,32

-1,-2,-4,-8,-16,-32 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -32
(1)*(-32)
(2)*(-16)
(4)*(-8)
(-1)*(32)
(-2)*(16)
(-4)*(8)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -3

First NumberSecond NumberSum
1-321+(-32)=-31
2-162+(-16)=-14
4-84+(-8)=-4
-132-1+32=31
-216-2+16=14
-48-4+8=4

None of these pairs of factors add to -3. So the expression cannot be factored

So you are correct. Good job.

 Equations/397375: solve the equation for k. -8(k+7)-(8+7k)=-16k1 solutions Answer 281659 by jim_thompson5910(28715)   on 2011-01-20 14:18:01 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Add to both sides. Add to both sides. Combine like terms on the left side. ---------------------------------------------------------------------- Answer: So the answer is
 real-numbers/397397: Can someone help me with this problem? Find the following Assume that variables can represent real numbers? √(a+3)^21 solutions Answer 281657 by jim_thompson5910(28715)   on 2011-01-20 14:16:12 (Show Source): You can put this solution on YOUR website!Recall that where 'x' is a real number. So this means that
 Polynomials-and-rational-expressions/397156: if you subtract a number from four times its square, the result is three1 solutions Answer 281537 by jim_thompson5910(28715)   on 2011-01-19 23:05:37 (Show Source): You can put this solution on YOUR website!Hint: "if you subtract a number from four times its square, the result is three" translates to . Let me know if you still need more help.
 Coordinate-system/397155: Find the x-intercept of the straight line passing through P = (2, 3) and perpendicular to y + 3x = 8 .1 solutions Answer 281536 by jim_thompson5910(28715)   on 2011-01-19 23:04:48 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. We can see that the equation has a slope and a y-intercept . Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is . Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point . Start with the point slope formula Plug in , , and Distribute Multiply Add 3 to both sides. Combine like terms. note: If you need help with fractions, check out this solver. So the equation of the line perpendicular to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the perpendicular line (green) through the point . If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Equations/397153: What is the value of [(3x+8Y)/(x-2Y)]; if x/2y=2?1 solutions Answer 281534 by jim_thompson5910(28715)   on 2011-01-19 23:00:25 (Show Source): You can put this solution on YOUR website!If , then (multiply both sides by 2y) So plug this into to get , multiply to get , combine like terms to get and reduce to get So if If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Linear-equations/397150: i am working on linear equations for my test tomorrow, but I am stumped on one problem right now with these points M (3,6) and N (-3,-4)...what is the answer to y=mx+b for this1 solutions Answer 281532 by jim_thompson5910(28715)   on 2011-01-19 22:51:29 (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 Distribute Multiply Add 6 to both sides. Combine like terms. 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, feel free to check out my tutoring website Jim
 expressions/397147: I need to know if i am evaluating this expression right? 9xy-4xz+3yz, x=7, y=3, and z=2 I got 151 as the answer. What I did: 9(7)(3)-4(7)(2)+3(3)(2), 9(21)-4(14)+3(6), 189-56+18=151, 1 solutions Answer 281531 by jim_thompson5910(28715)   on 2011-01-19 22:50:33 (Show Source): You can put this solution on YOUR website!You are correct. when x=7, y=3, and z=2. Good job.
 Equations/397098: Find the slope, if it exists, of the line containing the pair of points. (2,5) and (3,-1).1 solutions Answer 281495 by jim_thompson5910(28715)   on 2011-01-19 21:46:20 (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, feel free to check out my tutoring website Jim
 Evaluation_Word_Problems/397095: how do i write an algebraic expession for nine times m then incresed by six??1 solutions Answer 281494 by jim_thompson5910(28715)   on 2011-01-19 21:44:12 (Show Source): You can put this solution on YOUR website!"nine times m" means and " incresed by six" means we're adding 6 to the previous result to get So the answer is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Exponents-negative-and-fractional/397079: Rewrite the following expression with positive exponents. In case you can't see it, that exponent is a 1 solutions Answer 281486 by jim_thompson5910(28715)   on 2011-01-19 21:38:19 (Show Source): You can put this solution on YOUR website!Recall that where k is some positive number So in our case, this means that If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim