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 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(28598)   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(28598)   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(28598)   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(28598)   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(28598)   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(28598)   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(28598)   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(28598)   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(28598)   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(28598)   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(28598)   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(28598)   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(28598)   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(28598)   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.
 Radicals/481044: Please evaluate expression Give the exact value, if possible, otherwise, approximate to two decimal places. THANKS! :) -- -√ ̅ 81/121 1 solutions Answer 329396 by jim_thompson5910(28598)   on 2011-08-12 18:47:53 (Show Source): You can put this solution on YOUR website! So
 Miscellaneous_Word_Problems/481030: Could you please help me with this problem, showing steps? Thank you, mch appreciated!-- Your parents ask you to fertilize the lawn. It is a square plot that is 13 feet on each side and it has a sqare cement fountain in the center that is 6 feet on each side. What is the area of the lawn that you will fertilize?1 solutions Answer 329388 by jim_thompson5910(28598)   on 2011-08-12 18:28:47 (Show Source): You can put this solution on YOUR website!Lawn Area = Area of Big Square - Area of Small Square (drawing a picture will help you see this) Lawn Area = 13^2 - 6^2 Lawn Area = 169 - 36 Lawn Area = 133 So the area of the lawn to be fertilized is 133 square feet.
 test/481032: How do you find the area of a rectangle?1 solutions Answer 329385 by jim_thompson5910(28598)   on 2011-08-12 18:24:32 (Show Source): You can put this solution on YOUR website!Area of a rectangle = Length * Width
 real-numbers/481019: solve (10x^2+5x)/5x1 solutions Answer 329374 by jim_thompson5910(28598)   on 2011-08-12 17:38:33 (Show Source): You can put this solution on YOUR website! So
 Polynomials-and-rational-expressions/478688: please help me solve this problem. I have to factor it. 8x^3+1251 solutions Answer 327980 by jim_thompson5910(28598)   on 2011-08-06 22:42:11 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as . Now factor by using the sum of cubes formula. Remember the sum of cubes formula is Multiply ----------------------------------- Answer: So factors to . In other words,
 Expressions-with-variables/477330: simplify 3/151 solutions Answer 327198 by jim_thompson5910(28598)   on 2011-08-03 00:28:50 (Show Source):
 Polynomials-and-rational-expressions/477247: 3x squared=39....solve by using square root property1 solutions Answer 327154 by jim_thompson5910(28598)   on 2011-08-02 19:14:01 (Show Source): You can put this solution on YOUR website! Start with the given equation. Divide both sides by . Reduce. Take the square root of both sides. or Break up the "plus/minus" to form two equations. -------------------------------------- Answer: So the solutions are or .
 absolute-value/477244: Find the following. Assume that x can represent any real number. Use absolute value notation when necessary. SQRT(16X^2)=______ Any help would be much appreciated thx.1 solutions Answer 327153 by jim_thompson5910(28598)   on 2011-08-02 19:07:35 (Show Source):
 Probability-and-statistics/477232: Find the range, standard deviation, and variance for the following sample data: 33, 55, 29, 40, 43, 8, 90, 61, 41, 17, 80, 56, 17, 59, 21, 78 Thank you 1 solutions Answer 327145 by jim_thompson5910(28598)   on 2011-08-02 18:38:51 (Show Source): You can put this solution on YOUR website!Range = Largest Value - Smallest Value Range = 90 - 8 Range = 82 ========================================================================= Finding the sample variance and sample standard deviation: First, we need to find the sample mean xbar xbar = (33+55+29+40+43+8+90+61+41+17+80+56+17+59+21+78)/16 = 728/16 = 45.5 So the sample mean is xbar = 45.5 -------------------------- Now subtract the sample mean from EVERY data value: 33-45.5 = -12.5 55-45.5 = 9.5 29-45.5 = -16.5 40-45.5 = -5.5 43-45.5 = -2.5 8-45.5 = -37.5 90-45.5 = 44.5 61-45.5 = 15.5 41-45.5 = -4.5 17-45.5 = -28.5 80-45.5 = 34.5 56-45.5 = 10.5 17-45.5 = -28.5 59-45.5 = 13.5 21-45.5 = -24.5 78-45.5 = 32.5 So the differences are: -12.5, 9.5, -16.5, -5.5, -2.5, -37.5, 44.5, 15.5, -4.5, -28.5, 34.5, 10.5, -28.5, 13.5, -24.5, 32.5 Now square each difference: (-12.5)^2 = 156.25 (9.5)^2 = 90.25 (-16.5)^2 = 272.25 (-5.5)^2 = 30.25 (-2.5)^2 = 6.25 (-37.5)^2 = 1406.25 (44.5)^2 = 1980.25 (15.5)^2 = 240.25 (-4.5)^2 = 20.25 (-28.5)^2 = 812.25 (34.5)^2 = 1190.25 (10.5)^2 = 110.25 (-28.5)^2 = 812.25 (13.5)^2 = 182.25 (-24.5)^2 = 600.25 (32.5)^2 = 1056.25 Now add up each square: 156.25+90.25+272.25+30.25+6.25+1406.25+1980.25+240.25+20.25+812.25+1190.25+110.25+812.25+182.25+600.25+1056.25 = 8966 Now divide that sum by n-1 = 16-1 = 15 to get 8966/15 = 597.733333333333 So the sample variance is 597.733333333333 Finally, take the square root of 597.733333333333 to get 24.448585507823 So the sample standard deviation is 24.448585507823
 absolute-value/477227: how do i wrte |-203| with out the value bars?1 solutions Answer 327140 by jim_thompson5910(28598)   on 2011-08-02 18:33:20 (Show Source):
 Percentage-and-ratio-word-problems/477230: another question...2 percent of 50 students scored a 96% on an exam. What was the exact number of students that scored the 2%? i multiplied 0.02 y 50 and got the answer 1... is that correct? thanks so much! 1 solutions Answer 327138 by jim_thompson5910(28598)   on 2011-08-02 18:32:26 (Show Source): You can put this solution on YOUR website!You are correct. Good job.
 absolute-value/477229: also i would like to know how to write|7-pi| with out the valuue bars as well.1 solutions Answer 327137 by jim_thompson5910(28598)   on 2011-08-02 18:31:15 (Show Source): You can put this solution on YOUR website!Since is positive, this means that
 Rectangles/477221: please help me solve this question... a pool has two pumps. Pump A empties the pool in 4 hours. Pump B empties the pool in 12 hours. How long will it take to empty the pool if both pumps are working together? thanks so much i think the answer is 3?...i divided 3 into 12..not sure if thats correct1 solutions Answer 327125 by jim_thompson5910(28598)   on 2011-08-02 17:52:22 (Show Source): You can put this solution on YOUR website!Rate of pump A: 1/4 of a pool per hour Rate of pump B: 1/12 of a pool per hour Combined rate: 1/4+1/12 = 3/12+1/12 = 4/12 = 1/3 So if they work together, the two pumps have a combined rate of 1/3 of a pool per hour (ie in one hour, the two pumps will empty 1/3 of the pool) But we want to empty ONE pool (not 1/3 of one). So we need to multiply 1/3 by some number x to get 1. So Now solve for x So it will take the two pumps 3 hours to empty the pool.
 test/477223: What is 3X + 1 over 8 + 4X + 8 over 7 = 61 solutions Answer 327124 by jim_thompson5910(28598)   on 2011-08-02 17:48:58 (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. 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
 Rectangles/477211: please help me solve this question... a rectangle has a width of 8cm and length of 14cm what would be the perimeter if it increases by 50 percent?.. i tried to add all sides and got 44...do i multiply by 0.50? I'm confused...thanks so much1 solutions Answer 327122 by jim_thompson5910(28598)   on 2011-08-02 17:46:57 (Show Source): You can put this solution on YOUR website!"increases by 50 percent" means you add half of it to the original value. Or put another way, you multiply it by 1.5 (since 100%+50% = 150% = 1.5) So in your case, increasing 44 by 50% is increasing it to 44+22 = 66 (note: 22 is half or 50% of 44) Or... Multiply 44 by 1.5 to get 44*1.5 = 66, which is the same answer.
 Polynomials-and-rational-expressions/477218: evaluate the polynomial for x=1 2x^2-4x+11 solutions Answer 327121 by jim_thompson5910(28598)   on 2011-08-02 17:43:52 (Show Source): You can put this solution on YOUR website! Start with the given expression. Plug in . Square to get . Multiply and to get . Multiply and to get . Combine like terms.
 Equations/477217: What is 35X + 12= 40X + 421 solutions Answer 327120 by jim_thompson5910(28598)   on 2011-08-02 17:42:19 (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