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 Linear-equations/481683: What is the equation of the line containg the given pair of points (-7,0) and )0,5)1 solutions Answer 329808 by jim_thompson5910(28705)   on 2011-08-14 21:22:12 (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 Distribute Multiply Simplify 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
 Polynomials-and-rational-expressions/481679: factoring a monomial from a polynomial : find the greatest common factor of a5b3,a3b8 My answer was : GCF = a3,b3 is this correct1 solutions Answer 329805 by jim_thompson5910(28705)   on 2011-08-14 21:18:40 (Show Source): You can put this solution on YOUR website!You are correct. The GCF is
 Subset/481642: what are the possible subsets of numbers 1,2and3?1 solutions Answer 329771 by jim_thompson5910(28705)   on 2011-08-14 20:01:37 (Show Source): You can put this solution on YOUR website!Possible subsets of {1,2,3} are {1,2,3} {1,2},{1,3},{2,3} {1},{2},{3} { } Note: { } is the empty set.
 Square-cubic-other-roots/481631: the square root of 8 divided by 3 :)1 solutions Answer 329766 by jim_thompson5910(28705)   on 2011-08-14 19:41:19 (Show Source): You can put this solution on YOUR website! So
 Equations/481619: -8x+9x+(-3x)1 solutions Answer 329762 by jim_thompson5910(28705)   on 2011-08-14 19:08:27 (Show Source): You can put this solution on YOUR website!-8x+9x+(-3x) -8x+9x-3x -2x So -8x+9x+(-3x) = -2x
 Equations/481618: Garrett purchases 3 1/4 lbs of lean angus ground chunk for \$8.16. Explain his purchase as a unit price1 solutions Answer 329760 by jim_thompson5910(28705)   on 2011-08-14 19:07:12 (Show Source): You can put this solution on YOUR website!Hint: The unit price is the price per 1 unit of the item. In other words, the unit price is the cost to buy 1 unit of that item. So in your case, the unit price refers to the price to buy one pound of lean angus ground chunk.
Quadratic_Equations/481616: write a quadric equation having the given numbers as solutions -6 and -1
1 solutions

Answer 329758 by jim_thompson5910(28705)   on 2011-08-14 18:58:13 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Find A Quadratic Equation Given The Solutions or Start with the given solutions. or Get everything to one side so that only 0 remains on the right side (for both equations). Use the zero product property to combine the equations. FOIL out the left side.So the answer is To check your work, simply solve for x. Doing so will show you that the solutions are or , which confirm the answer.

 Travel_Word_Problems/481613: Traveling at 70 miles/hour, how many minutes will it take to drive 175 miles to San Antonio?1 solutions Answer 329754 by jim_thompson5910(28705)   on 2011-08-14 18:44:18 (Show Source): You can put this solution on YOUR website!Hint: Use the formula where in this case and . Plug those values in and solve for 't'. Don't forget to convert from hours to minutes.
 Functions/481611: solve the problem. (f-g)(-3) when f(x)=5x^2-5 and g(x)=x-71 solutions Answer 329752 by jim_thompson5910(28705)   on 2011-08-14 18:38:24 (Show Source): You can put this solution on YOUR website!Hint: (f-g)(x) means f(x)-g(x). So first find f(x)-g(x) and simplify. Afterward, plug in x=3 to get f(3)-g(3).
 Subset/481610: List all subsets of the set given in the problem. {1,4,7} 1 solutions Answer 329751 by jim_thompson5910(28705)   on 2011-08-14 18:37:22 (Show Source): You can put this solution on YOUR website!Subsets of {1,4,7} {1,4,7} {1,4},{1,7},{4,7} {1},{4},{7} { } Note: { } is the empty set. Also, notice how the set {1,4,7} is a subset of {1,4,7} (ie the set itself is a subset)
 Equations/481524: What is the GCF of 48y,16?1 solutions Answer 329750 by jim_thompson5910(28705)   on 2011-08-14 18:35:47 (Show Source): You can put this solution on YOUR website!The GCF of 48 and 16 is 16 (since 48=16*3, which shows that this is the largest factor they share). Since the term 16 has no 'y' variable in it, this means we ignore the variable. So the GCF of 48y and 16 is 16.
 Coordinate-system/481604: whitch of the following statements is false bout slope A the slope of any horizontal line is 0 B the slope of any vertical line is 1 C the paralle; lines have the same slope D the slope can be found using any two points on a straight line 1 solutions Answer 329748 by jim_thompson5910(28705)   on 2011-08-14 18:34:29 (Show Source): You can put this solution on YOUR website!A the slope of any horizontal line is 0 ... True B the slope of any vertical line is 1 ... False. Slope is undefined. C the parallel lines have the same slope ... True D the slope can be found using any two points on a straight line ... True So the answer is choice B.
 Systems-of-equations/481572: what is x if : logx^(16)=-21 solutions Answer 329747 by jim_thompson5910(28705)   on 2011-08-14 18:32:58 (Show Source): You can put this solution on YOUR website!Hint: Convert to exponential form to get . From there, rewrite the left side to get
 Quadratic_Equations/481569: Solve for X by factoring. (x-6)^2 = 491 solutions Answer 329746 by jim_thompson5910(28705)   on 2011-08-14 18:31:33 (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 Add to both sides. or Combine like terms. -------------------------------------- Answer: So the solutions are or .
 Functions/481609: Please help me solve for the intercepts in this equation: f(x)=(2x-4)(x+2)1 solutions Answer 329745 by jim_thompson5910(28705)   on 2011-08-14 18:29:59 (Show Source): You can put this solution on YOUR website!Hint: First replace f(x) with 0. Now use the fact that if then or
 Equations/481543: Please solve 8x-(6x+5) =91 solutions Answer 329744 by jim_thompson5910(28705)   on 2011-08-14 18:29:00 (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
 Graphs/481542: Footbal team gains 7 yards, loses 27 yards, gains 13 yards. What is total net yardage?1 solutions Answer 329743 by jim_thompson5910(28705)   on 2011-08-14 18:27:46 (Show Source): You can put this solution on YOUR website!Total Net Yardage = +7 - 27 + 13 = -7 Total Net Yardage = -7 yards. So the team lost 7 yards overall.
 Problems-with-consecutive-odd-even-integers/481537: using correct mathematical notation and symbols, express the following in set builder notaion: z={2,3,4,5,6,7,8,9,10,11,12}1 solutions Answer 329741 by jim_thompson5910(28705)   on 2011-08-14 18:26:27 (Show Source):
 Linear-equations/481605: Parallel to y=3x+5 and passes through (10,4) needs to be in y=mx+b form Thank you!1 solutions Answer 329739 by jim_thompson5910(28705)   on 2011-08-14 18:24:26 (Show Source): You can put this solution on YOUR website!Hint: Parallel lines have equal slopes. So because slope of given line is 3, this means that m=3 for the unknown parallel line. Also, the line needs to pass through (10,4). So when x=10, then y=4. We have 3 pieces of info: m=3, x=10, and y=4. Plug all this into y=mx+b to get 4 = 3(10)+b and now solve for b. The answer will be y = 3x+b where 'b' is the answer you got above.
 Triangles/481531: have a triangle with 30-60-90 degree angles shorter leg 8.5ft need to find perimeter1 solutions Answer 329738 by jim_thompson5910(28705)   on 2011-08-14 18:22:10 (Show Source): You can put this solution on YOUR website!Hint: For a 30-60-90 triangle, if the shorter leg is , then the longer leg is and the hypotenuse is
 Graphs/481535: Please solve and graph for me 4x is greater or equal to 161 solutions Answer 329737 by jim_thompson5910(28705)   on 2011-08-14 18:20:55 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is So the answer in interval notation is [) Also, the answer in set-builder notation is Here's the graph of the solution set on the number line Note: there is a closed circle at the endpoint.
 Radicals/481591: how to simplify by taking roots of numerator and denominator of 4/811 solutions Answer 329736 by jim_thompson5910(28705)   on 2011-08-14 18:18:44 (Show Source):
 Polynomials-and-rational-expressions/481600: I am having a hard time finding the GCF of 8x^2, -4x, and -20. I understand that the GCF of 8, 4 and 20 is 4 but I am not sure what to do with the letter x or the exponent of 2. Any help would be greatly appreciated.1 solutions Answer 329735 by jim_thompson5910(28705)   on 2011-08-14 18:17:54 (Show Source): You can put this solution on YOUR website!You can factor into x*x You can't factor 'x' any further (in the term -4x). So the GCF between and is because they both have an 'x' in common. However, there are no 'x' terms in -20. So this means that the GCF of the variable terms is not 'x'. This then means that the GCF of , and -20 is 1 (since and ), but this is a trivial factor. So we can ignore it. Therefore, the GCF of 8x^2, -4x, and -20 is 4
 Linear-systems/481597: How you derived the following? x+x/3+2x/3+x+x/3=150 (10x)/3 = 150 My exact question here is how do you get the 10x? thanks 1 solutions Answer 329733 by jim_thompson5910(28705)   on 2011-08-14 18:15:06 (Show Source):
 Polynomials-and-rational-expressions/481196: Rewrite with rational exponent 3cube sqrt 231 solutions Answer 329603 by jim_thompson5910(28705)   on 2011-08-13 21:31:40 (Show Source):
 Polynomials-and-rational-expressions/481197: State the value of the discriminant and then describe the nature of the solutions 3x^2+4x-11=01 solutions Answer 329602 by jim_thompson5910(28705)   on 2011-08-13 21:31:05 (Show Source): You can put this solution on YOUR website!From we can see that , , and Start with the discriminant formula. Plug in , , and Square to get Multiply to get Rewrite as Add to to get So the discriminant is Since the discriminant is greater than zero, this means that there are two real solutions.
Linear-systems/481201: 135x^2-222x+91

I have to factor this problem.
1 solutions

Answer 329600 by jim_thompson5910(28705)   on 2011-08-13 21:30:24 (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 :
1,3,5,7,9,13,15,21,27,35,39,45,63,65,91,105,117,135,189,195,273,315,351,455,585,819,945,1365,1755,2457,4095,12285
-1,-3,-5,-7,-9,-13,-15,-21,-27,-35,-39,-45,-63,-65,-91,-105,-117,-135,-189,-195,-273,-315,-351,-455,-585,-819,-945,-1365,-1755,-2457,-4095,-12285

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

These factors pair up and multiply to .
1*12285 = 12285
3*4095 = 12285
5*2457 = 12285
7*1755 = 12285
9*1365 = 12285
13*945 = 12285
15*819 = 12285
21*585 = 12285
27*455 = 12285
35*351 = 12285
39*315 = 12285
45*273 = 12285
63*195 = 12285
65*189 = 12285
91*135 = 12285
105*117 = 12285
(-1)*(-12285) = 12285
(-3)*(-4095) = 12285
(-5)*(-2457) = 12285
(-7)*(-1755) = 12285
(-9)*(-1365) = 12285
(-13)*(-945) = 12285
(-15)*(-819) = 12285
(-21)*(-585) = 12285
(-27)*(-455) = 12285
(-35)*(-351) = 12285
(-39)*(-315) = 12285
(-45)*(-273) = 12285
(-63)*(-195) = 12285
(-65)*(-189) = 12285
(-91)*(-135) = 12285
(-105)*(-117) = 12285

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

First NumberSecond NumberSum
1122851+12285=12286
340953+4095=4098
524575+2457=2462
717557+1755=1762
913659+1365=1374
1394513+945=958
1581915+819=834
2158521+585=606
2745527+455=482
3535135+351=386
3931539+315=354
4527345+273=318
6319563+195=258
6518965+189=254
9113591+135=226
105117105+117=222
-1-12285-1+(-12285)=-12286
-3-4095-3+(-4095)=-4098
-5-2457-5+(-2457)=-2462
-7-1755-7+(-1755)=-1762
-9-1365-9+(-1365)=-1374
-13-945-13+(-945)=-958
-15-819-15+(-819)=-834
-21-585-21+(-585)=-606
-27-455-27+(-455)=-482
-35-351-35+(-351)=-386
-39-315-39+(-315)=-354
-45-273-45+(-273)=-318
-63-195-63+(-195)=-258
-65-189-65+(-189)=-254
-91-135-91+(-135)=-226
-105-117-105+(-117)=-222

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).

 Complex_Numbers/481210: Multiply. (c+g)(c^2 - cg+g^2)1 solutions Answer 329599 by jim_thompson5910(28705)   on 2011-08-13 21:29:43 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Distribute. Multiply. Now combine like terms. So expands to . In other words, .
 expressions/481217: 2x^2 + 3x -1 = 01 solutions Answer 329596 by jim_thompson5910(28705)   on 2011-08-13 21:19:50 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 . or Break up the expression. So the solutions are or
 Equations/481049: Please simplify- 4√3+5√3-3√3 i understand it should come to 6√3, do i need to simplify it further?1 solutions Answer 329399 by jim_thompson5910(28705)   on 2011-08-12 19:00:22 (Show Source): You can put this solution on YOUR website!You have the correct answer and you cannot simplify that any further.