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 Permutations/508054: if six numbers are picked from 1 to 45 and if a number is not repeated.How many sets of six numbers could be picked1 solutions Answer 340848 by jim_thompson5910(28595)   on 2011-10-02 17:18:33 (Show Source): You can put this solution on YOUR website!I'm assuming order does not matter. C(n, r) = (n!)/(r!(n-r)!) C(45, 6) = (45!)/(6!*(45-6)!) C(45, 6) = (45!)/(6!*39!) C(45, 6) = (45*44*43*42*41*40*39!)/(6!*39!) C(45, 6) = (45*44*43*42*41*40)/(6!) C(45, 6) = (45*44*43*42*41*40)/(6*5*4*3*2*1) C(45, 6) = (5864443200)/(720) C(45, 6) = 8145060 So there are 8145060 different ways.
 Polynomials-and-rational-expressions/508051: In 1930s, the Indian physicist Chandrasekhar and others predicted the existence of neutron stars. These stars can have a density of 10 billion tons per teaspoonful. Express this density in scientific Notation1 solutions Answer 340847 by jim_thompson5910(28595)   on 2011-10-02 17:15:54 (Show Source): You can put this solution on YOUR website!10 billion = 10,000,000,000 10 billion =
 Geometry_proofs/508029: The given is :m<1 =m<2, and the conclusion is <1 is congruent to <2. What is the reason for that?1 solutions Answer 340838 by jim_thompson5910(28595)   on 2011-10-02 16:34:40 (Show Source): You can put this solution on YOUR website!This is the definition of congruent angles. Definition: Two angles are congruent if and only if the two angles are equal.
 Expressions-with-variables/507980: -3+x=-2x+61 solutions Answer 340824 by jim_thompson5910(28595)   on 2011-10-02 15:18:03 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim
 test/507941: I have a problem that I don't know how to solve. The problem is 4/x=12 four divided by X is equal to twelve1 solutions Answer 340817 by jim_thompson5910(28595)   on 2011-10-02 14:18:07 (Show Source): You can put this solution on YOUR website!4/x=12 4=12x 4/12=x 1/3=x x=1/3 Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim
 Linear-systems/507933: how do i put 5-y = -3x into standard form (ax+ by= c)1 solutions Answer 340816 by jim_thompson5910(28595)   on 2011-10-02 14:08:18 (Show Source): You can put this solution on YOUR website!5-y = -3x 5-y + 3x = 0 -y + 3x = -5 3x-y = -5
 Inequalities/507923: Solve -6(x+5)<-x+11. write solution using set builder notation.1 solutions Answer 340815 by jim_thompson5910(28595)   on 2011-10-02 14:07:24 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. 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 . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is Answer in set-builder notation is
 test/507930: 20 is 50% of what1 solutions Answer 340814 by jim_thompson5910(28595)   on 2011-10-02 14:04:28 (Show Source): You can put this solution on YOUR website!Hint: "20 is 50% of what" translates to 20 = 0.5x
 Numeric_Fractions/507927: Convert the decimal to a fraction .251 solutions Answer 340813 by jim_thompson5910(28595)   on 2011-10-02 14:03:31 (Show Source): You can put this solution on YOUR website!0.25 = 25/100 = 1/4
 percentage/507929: What is 30% of 651 solutions Answer 340812 by jim_thompson5910(28595)   on 2011-10-02 14:02:46 (Show Source): You can put this solution on YOUR website!30% = 0.3 So 30% of 65 = 0.3*65 = 19.5
 Inequalities/505853: solve using multiplication principle -2x<-81 solutions Answer 340811 by jim_thompson5910(28595)   on 2011-10-02 14:00:41 (Show Source): You can put this solution on YOUR website!-2x < -8 x > -8/(-2) x > 4
 Equations/506422: solve each equation justify each step p-7/-2=51 solutions Answer 340810 by jim_thompson5910(28595)   on 2011-10-02 13:58:48 (Show Source): You can put this solution on YOUR website!(p-7)/(-2)=5 p-7=5*(-2) p-7=-10 p=-10+7 p=-3
 Equations/505495: 5.4t+14.6-10.0t=12.8-3.5t-0.61 solutions Answer 340809 by jim_thompson5910(28595)   on 2011-10-02 13:57:33 (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. Combine like terms on the right side. 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
 Equations/503786: how do you solve 3x+8=501 solutions Answer 340808 by jim_thompson5910(28595)   on 2011-10-02 13:56:17 (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 solution is
 Equations/505384: 3X+6-10=2X-21 solutions Answer 340807 by jim_thompson5910(28595)   on 2011-10-02 13:55:45 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/505597: what is the equation 5y+6=-12+3y1 solutions Answer 340806 by jim_thompson5910(28595)   on 2011-10-02 13:55:10 (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
 Equations/506514: 8-3(4x-2)=35-5x1 solutions Answer 340805 by jim_thompson5910(28595)   on 2011-10-02 13:54:31 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. 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 Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim
 Equations/507396: Solve: -2x-8(x-2)=41 solutions Answer 340804 by jim_thompson5910(28595)   on 2011-10-02 13:53:59 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim
 Inequalities/507879: x-9>=-7(x+2) write solutions using set builder notation. show work1 solutions Answer 340802 by jim_thompson5910(28595)   on 2011-10-02 13:53:04 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. 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 . ---------------------------------------------------------------------- Answer: So the solution is Answer in set-builder notation is Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim
 expressions/497754: formula,solve for the variables indicated. p=s + t + u for u1 solutions Answer 340800 by jim_thompson5910(28595)   on 2011-10-02 13:49:25 (Show Source): You can put this solution on YOUR website!p=s + t + u p-s = t + u p-s - t = u u = p-s - t
 Equations/505572: 8x-10=6x1 solutions Answer 340799 by jim_thompson5910(28595)   on 2011-10-02 13:47:42 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/507791: Make x the subject of 3x - 5y = y - mx1 solutions Answer 340798 by jim_thompson5910(28595)   on 2011-10-02 13:46:45 (Show Source): You can put this solution on YOUR website!3x - 5y = y - mx 3x = y - mx+ 5y 3x+mx = y + 5y 3x+mx =6y x(3+m) = 6y x = 6y/(3+m) Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim
 Complex_Numbers/507903: what is 8 plus(+)71 solutions Answer 340794 by jim_thompson5910(28595)   on 2011-10-02 13:38:50 (Show Source): You can put this solution on YOUR website!8 + 7 = 15
 Miscellaneous_Word_Problems/507732: The expression for figuring a student’s average test score is p/t, where p is the total points earned on all the tests, and t is the number of tests. Find a student’s average when 483 points are earned on 7 tests. What is the average?1 solutions Answer 340697 by jim_thompson5910(28595)   on 2011-10-02 00:06:55 (Show Source): You can put this solution on YOUR website!Average = p/t Average = 483/7 Average = 69
 Polynomials-and-rational-expressions/507707: 9. A 150-ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 30 ft longer than the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace. Calling all math genius please help me!1 solutions Answer 340696 by jim_thompson5910(28595)   on 2011-10-02 00:05:27 (Show Source): You can put this solution on YOUR website!Let x = height, so x+30 is the horizontal distance So use the pythagorean theorem to find the height a^2 + b^2 = c^2 x^2 + (x+30)^2 = 150^2 x^2 + x^2+60x+900 = 22500 x^2 + x^2+60x+900 - 22500 = 0 2x^2+60x-21600 = 0 2(x^2+30x-10800) = 0 x^2+30x-10800 = 0 Now use the quadratic formula to solve for x x = (-B +- sqrt( B^2-4AC ))/(2A) x = (-(30) +- sqrt( (30)^2-4(1)(-10800) ))/(2(1)) x = (-30 +- sqrt( 900+43200 ))/(2(1)) x = (-30 +- sqrt( 44100 ))/(2(1)) x = (-30 +- 210)/(2) x = (-30 + 210)/(2) or x = (-30 - 210)/(2) x = (180)/(2) or x = (-240)/(2) x = 90 or x = -120 Now throw out the negative solution to get the only solution of x = 90 So the height is 90 ft and the horizontal distance is 120 ft (since 90+30 = 120) Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim
 Permutations/507701: how many ways are there to choose 3 separate officeholder positions (pres,vp etc) from a group of 12 people? at first i tried 12*11*10=1320 i tried this formula 12!/3!(12-3)!= 220 But then i was told it was just 12! just want a conformation, thank you ahead of time1 solutions Answer 340695 by jim_thompson5910(28595)   on 2011-10-01 23:56:34 (Show Source): You can put this solution on YOUR website!Since order matters, you'll use the permutation formula P(n,r) = n!/(n-r)! In this case, n = 12 and r = 3 P(n,r) = n!/(n-r)! P(12,3) = (12!)/((12-3)!) P(12,3) = (12!)/(9!) P(12,3) = (12*11*10*9!)/(9!) P(12,3) = 12*11*10 P(12,3) = 1320 So there are 1320 different ways to choose 3 separate officeholder positions. Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim
 Polynomials-and-rational-expressions/507700: 4. Use the “difference of squares” rule to factor the following expression: 25b^6-36c^4 someone please rescue me!!1 solutions Answer 340694 by jim_thompson5910(28595)   on 2011-10-01 23:53:45 (Show Source): You can put this solution on YOUR website! So factors to In other words, Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim
Polynomials-and-rational-expressions/507702: 6. Completely factor the following expression:
36a^2 – 84ab + 49b^2

7. Completely factor the following expression:
9y^2 – 16z^2

1 solutions

Answer 340693 by jim_thompson5910(28595)   on 2011-10-01 23:50:51 (Show Source):
You can put this solution on YOUR website!
# 6

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 :
1,2,3,4,6,7,9,12,14,18,21,28,36,42,49,63,84,98,126,147,196,252,294,441,588,882,1764
-1,-2,-3,-4,-6,-7,-9,-12,-14,-18,-21,-28,-36,-42,-49,-63,-84,-98,-126,-147,-196,-252,-294,-441,-588,-882,-1764

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

These factors pair up and multiply to .
1*1764 = 1764
2*882 = 1764
3*588 = 1764
4*441 = 1764
6*294 = 1764
7*252 = 1764
9*196 = 1764
12*147 = 1764
14*126 = 1764
18*98 = 1764
21*84 = 1764
28*63 = 1764
36*49 = 1764
42*42 = 1764
(-1)*(-1764) = 1764
(-2)*(-882) = 1764
(-3)*(-588) = 1764
(-4)*(-441) = 1764
(-6)*(-294) = 1764
(-7)*(-252) = 1764
(-9)*(-196) = 1764
(-12)*(-147) = 1764
(-14)*(-126) = 1764
(-18)*(-98) = 1764
(-21)*(-84) = 1764
(-28)*(-63) = 1764
(-36)*(-49) = 1764
(-42)*(-42) = 1764

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

First NumberSecond NumberSum
117641+1764=1765
28822+882=884
35883+588=591
44414+441=445
62946+294=300
72527+252=259
91969+196=205
1214712+147=159
1412614+126=140
189818+98=116
218421+84=105
286328+63=91
364936+49=85
424242+42=84
-1-1764-1+(-1764)=-1765
-2-882-2+(-882)=-884
-3-588-3+(-588)=-591
-4-441-4+(-441)=-445
-6-294-6+(-294)=-300
-7-252-7+(-252)=-259
-9-196-9+(-196)=-205
-12-147-12+(-147)=-159
-14-126-14+(-126)=-140
-18-98-18+(-98)=-116
-21-84-21+(-84)=-105
-28-63-28+(-63)=-91
-36-49-36+(-49)=-85
-42-42-42+(-42)=-84

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.

Factor out the GCF

Condense the terms.

So completely factors to

In other words,
=======================================================
# 7

Rewrite as .

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:

Plug in and .

So this shows us that factors to .

In other words .

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim

 test/507675: x^2+6x-6=6, then x=?1 solutions Answer 340692 by jim_thompson5910(28595)   on 2011-10-01 23:46:49 (Show Source): You can put this solution on YOUR website! Start with the given equation. Get every term to the left side. Combine like terms. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) Break up the fraction. Reduce. or Break up the expression. So the solutions are or Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim
 Polynomials-and-rational-expressions/507705: 8. The length of a rectangle is 3 meters more than its width. If the area is 108 square meters, what are the length and width? OK I definetly need some help with these, please! 1 solutions Answer 340691 by jim_thompson5910(28595)   on 2011-10-01 23:45:05 (Show Source): You can put this solution on YOUR website!Let x = width, so length is then x+3 Area = Length*Width A = LW 108 = (x+3)*x 108 = x(x+3) 108 = x^2+3x 0 = x^2+3x-108 0 = (x-9)(x+12) (x-9)(x+12)=0 x-9 = 0 or x+12 = 0 x=9 or x=-12 Throw out the negative width to get x = 9 So the width is 9 meters and the length is 12 meters (since 9+3=12) Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim
 Miscellaneous_Word_Problems/507723: Use multiplying by 1 to find an expression equivalent to 3/13 with a denominator of 117a 1 solutions Answer 340690 by jim_thompson5910(28595)   on 2011-10-01 23:41:05 (Show Source): You can put this solution on YOUR website!Since 117/13 = 9, this means that 13*9a = 117a. So multiply top and bottom of the fraction by 9a to get So Let me know if you need more help or if you need me to explain a step in more detail. Feel free to email me at jim_thompson5910@hotmail.com or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html Thanks, Jim