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# Recent problems solved by 'jim_thompson5910'

 Equations/640719: 6.02x10^23/3.00 = 1 solutions Answer 403381 by jim_thompson5910(33401)   on 2012-08-24 00:55:06 (Show Source): You can put this solution on YOUR website! (6.02x10^23)/3.00 = 2.006667 x 10^23
 Geometry_Word_Problems/640717: how do you solve a rectangle that has length=20 W=10? 1 solutions Answer 403376 by jim_thompson5910(33401)   on 2012-08-24 00:24:48 (Show Source): You can put this solution on YOUR website! If you want the perimeter, then P = 2L + 2W P = 2*20 + 2*10 P = 60 units ------------------------------------------------------- If you want the area, then A = LW A = 20*10 A = 200 square units
 Money_Word_Problems/640714: How do i find the purchase price of a product if the sales tax is \$76 and the rate is 9.5%? 1 solutions Answer 403375 by jim_thompson5910(33401)   on 2012-08-24 00:19:10 (Show Source): You can put this solution on YOUR website! 0.095x = 76 x = 76/0.095 x = 800
 Equations/640702: How do you do 5x-2x+x=15 1 solutions Answer 403373 by jim_thompson5910(33401)   on 2012-08-23 23:50:11 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is
Polynomials-and-rational-expressions/640704: 35x^2+3xy-54y^2
1 solutions

Answer 403372 by jim_thompson5910(33401)   on 2012-08-23 23:40:56 (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor this.

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 :
1,2,3,5,6,7,9,10,14,15,18,21,27,30,35,42,45,54,63,70,90,105,126,135,189,210,270,315,378,630,945,1890
-1,-2,-3,-5,-6,-7,-9,-10,-14,-15,-18,-21,-27,-30,-35,-42,-45,-54,-63,-70,-90,-105,-126,-135,-189,-210,-270,-315,-378,-630,-945,-1890

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

These factors pair up and multiply to .
1*(-1890) = -1890
2*(-945) = -1890
3*(-630) = -1890
5*(-378) = -1890
6*(-315) = -1890
7*(-270) = -1890
9*(-210) = -1890
10*(-189) = -1890
14*(-135) = -1890
15*(-126) = -1890
18*(-105) = -1890
21*(-90) = -1890
27*(-70) = -1890
30*(-63) = -1890
35*(-54) = -1890
42*(-45) = -1890
(-1)*(1890) = -1890
(-2)*(945) = -1890
(-3)*(630) = -1890
(-5)*(378) = -1890
(-6)*(315) = -1890
(-7)*(270) = -1890
(-9)*(210) = -1890
(-10)*(189) = -1890
(-14)*(135) = -1890
(-15)*(126) = -1890
(-18)*(105) = -1890
(-21)*(90) = -1890
(-27)*(70) = -1890
(-30)*(63) = -1890
(-35)*(54) = -1890
(-42)*(45) = -1890

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

First NumberSecond NumberSum
1-18901+(-1890)=-1889
2-9452+(-945)=-943
3-6303+(-630)=-627
5-3785+(-378)=-373
6-3156+(-315)=-309
7-2707+(-270)=-263
9-2109+(-210)=-201
10-18910+(-189)=-179
14-13514+(-135)=-121
15-12615+(-126)=-111
18-10518+(-105)=-87
21-9021+(-90)=-69
27-7027+(-70)=-43
30-6330+(-63)=-33
35-5435+(-54)=-19
42-4542+(-45)=-3
-11890-1+1890=1889
-2945-2+945=943
-3630-3+630=627
-5378-5+378=373
-6315-6+315=309
-7270-7+270=263
-9210-9+210=201
-10189-10+189=179
-14135-14+135=121
-15126-15+126=111
-18105-18+105=87
-2190-21+90=69
-2770-27+70=43
-3063-30+63=33
-3554-35+54=19
-4245-42+45=3

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).

 Exponents/640710: 80r^2-125 1 solutions Answer 403371 by jim_thompson5910(33401)   on 2012-08-23 23:39:57 (Show Source): You can put this solution on YOUR website! So the expression factors to
 Expressions-with-variables/640692: Please help me solve this equation for y. 3y - yz = 2z 1 solutions Answer 403369 by jim_thompson5910(33401)   on 2012-08-23 23:24:23 (Show Source): You can put this solution on YOUR website! <<--- Answer
 Polynomials-and-rational-expressions/640699: [9-2(5-4)] 1 solutions Answer 403368 by jim_thompson5910(33401)   on 2012-08-23 23:23:10 (Show Source): You can put this solution on YOUR website! [9-2(5-4)] [9-2(1)] [9-2] [7] 7 So [9-2(5-4)] = 7
 Quadratic_Equations/640695: Solve using the quadratic formula: 20 = 2(2a - 5)squared + 8 Quadratic formula: -b +- radical b squared - 4ac over 2a 1 solutions Answer 403367 by jim_thompson5910(33401)   on 2012-08-23 23:10:46 (Show Source): You can put this solution on YOUR website! ... Temporarily replace 'a' with 'x' (you'll see why below) Now use the quadratic formula to solve for x is in the form . So... a = 8 b = -40 c = 38 Plug this into the quadratic formula or or or or Note: The last solutions above are approximate ------------------------------------------------------------------------------------ So the exact solutions are or and the approximate solutions are or Note: remember to replace 'x' with 'a'
 expressions/640684: 11+4(x-2)-17x 1 solutions Answer 403365 by jim_thompson5910(33401)   on 2012-08-23 22:43:06 (Show Source): You can put this solution on YOUR website! So simplifies to
 Equations/640686: Which ordered pair has an x-coordinate value of 3 and y coordinate value of -2 (-2,3) (3,-2) (-3,2) (2,-3) 1 solutions Answer 403364 by jim_thompson5910(33401)   on 2012-08-23 22:40:57 (Show Source): You can put this solution on YOUR website! The point (3,-2) has an x-coordinate value of 3 and y coordinate value of -2
Matrices-and-determiminant/640638: 3/x-4/y+6/z=1
9/x+8/y-12/z=3
9/x-4/y+12/=4
solve for D, Dx, Dy, Dz and x, y, z
tnx..xD

1 solutions

Answer 403362 by jim_thompson5910(33401)   on 2012-08-23 22:32:39 (Show Source):
You can put this solution on YOUR website!
I'm assuming the system is really

3x-4y+6z=1
9x+8y-12z=3
9x-4y+12z=4

Note: I'm going to be using |A| in place of D, |Ax| in place of Dx, |Ay| in place of Dy and |Az| in place of Dz.

 Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 3 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 and they 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 . To save space, I'm not showing the calculations for the determinant. However, if you need help with calculating the determinant of the matrix A, 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 . Again, as a space saver, I didn't include the calculations of the determinant. Check out this solver to see how to find this determinant. 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 two solutions. 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 --------------------------------------------------------- Let's reset again by letting which is the coefficient matrix. Replace the third column of A (that corresponds to the variable 'z') with the values that form the right hand side of the system of equations. We will denote this new matrix Now compute the determinant of to get . To find the third solution, divide the determinant of by the determinant of to get: So the third solution is ==================================================================================== Final Answer: So the three solutions are , , and giving the ordered triple (1/3, 1/4, 1/6) Note: there is a lot of work that is hidden in finding the determinants. Take a look at this 3x3 Determinant Solver to see how to get each determinant.

 Numeric_Fractions/640608: 2/3+3m/5=31/15 1 solutions Answer 403361 by jim_thompson5910(33401)   on 2012-08-23 22:31:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Trigonometry-basics/640630: So I am in AP calc this year, and I have to do a review test, and can't find any of my old trig stuff.. So I was wondering if I could get a refresher on how to: Find all solutions of the equation in the interval [0,2pi] A) 4cos(theta)=1+2cos(theta) 1 solutions Answer 403360 by jim_thompson5910(33401)   on 2012-08-23 22:29:19 (Show Source): You can put this solution on YOUR website! I'm going to use x in place of theta (it's easier to type) 4cos(x)=1+2cos(x) 4cos(x)-2cos(x) = 1 2cos(x) = 1 cos(x) = 1/2 x = arccos(1/2) x = pi/3 or x = -pi/3 x = pi/3 or x = -pi/3+2pi x = pi/3 or x = -pi/3+6pi/3 x = pi/3 or x = 5pi/3
 Exponents/640606: N to the 2nd power + n over 4n 1 solutions Answer 403359 by jim_thompson5910(33401)   on 2012-08-23 22:23:09 (Show Source): You can put this solution on YOUR website! So the original expression simplifies to
 Trigonometry-basics/640629: evaluate sin 10deg cos 50deg+cos 10deg sin 50deg exact answer 1 solutions Answer 403358 by jim_thompson5910(33401)   on 2012-08-23 22:22:08 (Show Source): You can put this solution on YOUR website! sin(10)*cos(50) + cos(10)*sin(50) sin(10+50) sin(60) sqrt(3)/2 So the answer is
 test/640613: 1 solutions Answer 403356 by jim_thompson5910(33401)   on 2012-08-23 22:20:54 (Show Source): You can put this solution on YOUR website! Problem missing.
 Inequalities/640654: How to solve the inequality 3-4x<5+6x with the intermediate steps shown 1 solutions Answer 403355 by jim_thompson5910(33401)   on 2012-08-23 22:20:24 (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 . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/640632: Find an equation of the line containing the given pair of points. (-5,-9) and (-2,-8) 1 solutions Answer 403347 by jim_thompson5910(33401)   on 2012-08-23 20:40:08 (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 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 Rewrite as Rewrite as Distribute Multiply Subtract 9 from both sides. Combine like terms. note: If you need help with fractions, check out this solver. So the equation that goes through the points and is
 Complex_Numbers/640633: Find each sum or difference. WErite answer in standard form. (-2+4i)-(-4+4i) 1 solutions Answer 403346 by jim_thompson5910(33401)   on 2012-08-23 20:38:57 (Show Source): You can put this solution on YOUR website! (-2+4i)-(-4+4i) -2+4i+4-4i (-2+4)+(4i-4i) 2+0i 2 So the answer is 2
 Equations/640635: Heather and Matthew take 45s to walk eastward along a straight road to a store 72m away. what is their average velocity 1 solutions Answer 403345 by jim_thompson5910(33401)   on 2012-08-23 20:37:50 (Show Source): You can put this solution on YOUR website! Their average velocity is 72/45 = 1.6 meters per second
 Rational-functions/640636: What is the solution of 3(x-2)-2(x+7)=2x+17? 1 solutions Answer 403344 by jim_thompson5910(33401)   on 2012-08-23 20:37:06 (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. 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
 Angles/640621: < A is the complement of < C and < C is the complement of < E < A= (x+30) < E= (9-6x) 1 solutions Answer 403342 by jim_thompson5910(33401)   on 2012-08-23 20:25:50 (Show Source): You can put this solution on YOUR website!
 Probability-and-statistics/640611: If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours? 1 solutions Answer 403335 by jim_thompson5910(33401)   on 2012-08-23 19:50:47 (Show Source): You can put this solution on YOUR website! Half of the distribution lies below the mean. So 50% of the bulbs have a life less than 2500 hours.
 Equations/640610: My book says: write an equation in standard form Ax + By=C of the line that satisfies the given conditions. Use integer values for A,b,c. Then the problem is: m=4/5, passes through(2,3) Here's what i did but i didn't and can't solve it to find the right answer. y-3=4/5(x-2) y-3=4/5x-8/5 that's all i really got 1 solutions Answer 403332 by jim_thompson5910(33401)   on 2012-08-23 19:48:47 (Show Source): You can put this solution on YOUR website! y-3 = 4/5x-8/5 5y-15 = 4x-8 ... Multiply EVERY term by LCD by 5. 5y = 4x-8+15 5y = 4x+7 5y-4x = 7 -4x+5y = 7 -1(-4x+5y) = -1*7 4x - 5y = -7 So the answer is 4x - 5y = -7
 test/640598: Can 1 be an additive identity? and why? pleaaaaase!!!:) 1 solutions Answer 403325 by jim_thompson5910(33401)   on 2012-08-23 19:25:03 (Show Source): You can put this solution on YOUR website! No, 0 is the only additive identity since 0+x = x and x+0 = x for all x Basically, adding 0 to any number will NOT change that number.
 Functions/640597: Please help me find the domain of this function f(x)=5x^3-5x 1 solutions Answer 403324 by jim_thompson5910(33401)   on 2012-08-23 19:24:44 (Show Source): You can put this solution on YOUR website! The domain is the set of all real numbers since you can plug in any real number and get some real number as an output.
 Distributive-associative-commutative-properties/640592: Use distributive property to simplify. 2c(9+5a) 1 solutions Answer 403317 by jim_thompson5910(33401)   on 2012-08-23 18:58:54 (Show Source): You can put this solution on YOUR website! So the answer is
 test/640584: Find the next three terms in sequence : 1, - 1/3, 1/9, - 1/27 1 solutions Answer 403314 by jim_thompson5910(33401)   on 2012-08-23 18:54:24 (Show Source): You can put this solution on YOUR website! Hint: you're dividing each term by -3 to get the next term. Equivalently, you're multiplying each term by to get the next term.
 Numeric_Fractions/640588: 8-x=12 help im 11. 1 solutions Answer 403313 by jim_thompson5910(33401)   on 2012-08-23 18:53:03 (Show Source): You can put this solution on YOUR website! 8-x=12 8-x+x=12+x 8=12+x 8-12=12+x-12 -4 = x x = -4 So the answer is x = -4
 Finance/640573: What is the answer to 7-9r+2r-3 ? 1 solutions Answer 403311 by jim_thompson5910(33401)   on 2012-08-23 18:50:26 (Show Source): You can put this solution on YOUR website! 7-9r+2r-3 (-9r+2r)+(7-3) -7r+4