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 Triangles/422949: in a right triangle there a two acute angles what is there measure1 solutions Answer 295114 by jim_thompson5910(28715)   on 2011-03-16 15:26:14 (Show Source): You can put this solution on YOUR website!If one of the angles is x degrees, then the other acute angle is degrees.
 Functions/422923: Find any value (s) for which the rational expression is undefined. X2-4/5x-101 solutions Answer 295113 by jim_thompson5910(28715)   on 2011-03-16 15:23:06 (Show Source): You can put this solution on YOUR website!The expression is undefined when the denominator . Solve for x to get ----> So if , then is true. So if , the expression is undefined. If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 test/422926: Find the numerial value of each expression when the variable =-3 3k/(3k-2)^21 solutions Answer 295112 by jim_thompson5910(28715)   on 2011-03-16 15:21:09 (Show Source): You can put this solution on YOUR website! So when If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Linear-equations/422929: Write y = x + 7 in standard form using integers.1 solutions Answer 295109 by jim_thompson5910(28715)   on 2011-03-16 15:18:44 (Show Source): You can put this solution on YOUR website! So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Equations/422931: Hi, how can I simplify even more than this? I already have: I know that is right, but the solver on this website does not come up with that, and and my teacher says it can be simplified even more..1 solutions Answer 295108 by jim_thompson5910(28715)   on 2011-03-16 15:16:58 (Show Source): You can put this solution on YOUR website!Well, you can multiply every term by the LCD to get and then you can isolate z by dividing both sides by to get If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 expressions/422749: 1) 4h-4(3h-1)=0 2) 1-(4r-1)=2(t-3) 3) -12=3(2n-3)1 solutions Answer 295020 by jim_thompson5910(28715)   on 2011-03-16 00:59:57 (Show Source): You can put this solution on YOUR website!I'll do the first one to get you started. # 1 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 If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
Polynomials-and-rational-expressions/422731: What is 2y squared + 20y + 18
1 solutions

Answer 295012 by jim_thompson5910(28715)   on 2011-03-15 23:32:24 (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor this.

Factor out the GCF .

Now let's try to factor the inner expression

---------------------------------------------------------------

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 :
1,3,9
-1,-3,-9

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

These factors pair up and multiply to .
1*9 = 9
3*3 = 9
(-1)*(-9) = 9
(-3)*(-3) = 9

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

First NumberSecond NumberSum
191+9=10
333+3=6
-1-9-1+(-9)=-10
-3-3-3+(-3)=-6

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 then factors further to

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

So completely 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, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

Polynomials-and-rational-expressions/422701: This is on factoring completely. Most of them I have been able to do, but this one I am stuck on. I can't find a GCF for all the terms. According to the back of the book it is factorable. How would I completely factor this:
a^2-8ab-33b^2
Thanks
1 solutions

Answer 294994 by jim_thompson5910(28715)   on 2011-03-15 22:13:43 (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 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 :
1,3,11,33
-1,-3,-11,-33

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

These factors pair up and multiply to .
1*(-33) = -33
3*(-11) = -33
(-1)*(33) = -33
(-3)*(11) = -33

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

First NumberSecond NumberSum
1-331+(-33)=-32
3-113+(-11)=-8
-133-1+33=32
-311-3+11=8

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 the GCF from the second group.

Factor out from the entire expression.

So completely factors to

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

Distributive-associative-commutative-properties/422690: 72x^3-11x^2-380x

1 solutions

Answer 294986 by jim_thompson5910(28715)   on 2011-03-15 21:51:53 (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor this.

Factor out the GCF .

Now let's try to factor the inner expression

---------------------------------------------------------------

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 :
1,2,3,4,5,6,8,9,10,12,15,16,18,19,20,24,30,32,36,38,40,45,48,57,60,72,76,80,90,95,96,114,120,144,152,160,171,180,190,228,240,285,288,304,342,360,380,456,480,570,608,684,720,760,855,912,1140,1368,1440,1520,1710,1824,2280,2736,3040,3420,4560,5472,6840,9120,13680,27360
-1,-2,-3,-4,-5,-6,-8,-9,-10,-12,-15,-16,-18,-19,-20,-24,-30,-32,-36,-38,-40,-45,-48,-57,-60,-72,-76,-80,-90,-95,-96,-114,-120,-144,-152,-160,-171,-180,-190,-228,-240,-285,-288,-304,-342,-360,-380,-456,-480,-570,-608,-684,-720,-760,-855,-912,-1140,-1368,-1440,-1520,-1710,-1824,-2280,-2736,-3040,-3420,-4560,-5472,-6840,-9120,-13680,-27360

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

These factors pair up and multiply to .
1*(-27360) = -27360
2*(-13680) = -27360
3*(-9120) = -27360
4*(-6840) = -27360
5*(-5472) = -27360
6*(-4560) = -27360
8*(-3420) = -27360
9*(-3040) = -27360
10*(-2736) = -27360
12*(-2280) = -27360
15*(-1824) = -27360
16*(-1710) = -27360
18*(-1520) = -27360
19*(-1440) = -27360
20*(-1368) = -27360
24*(-1140) = -27360
30*(-912) = -27360
32*(-855) = -27360
36*(-760) = -27360
38*(-720) = -27360
40*(-684) = -27360
45*(-608) = -27360
48*(-570) = -27360
57*(-480) = -27360
60*(-456) = -27360
72*(-380) = -27360
76*(-360) = -27360
80*(-342) = -27360
90*(-304) = -27360
95*(-288) = -27360
96*(-285) = -27360
114*(-240) = -27360
120*(-228) = -27360
144*(-190) = -27360
152*(-180) = -27360
160*(-171) = -27360
(-1)*(27360) = -27360
(-2)*(13680) = -27360
(-3)*(9120) = -27360
(-4)*(6840) = -27360
(-5)*(5472) = -27360
(-6)*(4560) = -27360
(-8)*(3420) = -27360
(-9)*(3040) = -27360
(-10)*(2736) = -27360
(-12)*(2280) = -27360
(-15)*(1824) = -27360
(-16)*(1710) = -27360
(-18)*(1520) = -27360
(-19)*(1440) = -27360
(-20)*(1368) = -27360
(-24)*(1140) = -27360
(-30)*(912) = -27360
(-32)*(855) = -27360
(-36)*(760) = -27360
(-38)*(720) = -27360
(-40)*(684) = -27360
(-45)*(608) = -27360
(-48)*(570) = -27360
(-57)*(480) = -27360
(-60)*(456) = -27360
(-72)*(380) = -27360
(-76)*(360) = -27360
(-80)*(342) = -27360
(-90)*(304) = -27360
(-95)*(288) = -27360
(-96)*(285) = -27360
(-114)*(240) = -27360
(-120)*(228) = -27360
(-144)*(190) = -27360
(-152)*(180) = -27360
(-160)*(171) = -27360

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

First NumberSecond NumberSum
1-273601+(-27360)=-27359
2-136802+(-13680)=-13678
3-91203+(-9120)=-9117
4-68404+(-6840)=-6836
5-54725+(-5472)=-5467
6-45606+(-4560)=-4554
8-34208+(-3420)=-3412
9-30409+(-3040)=-3031
10-273610+(-2736)=-2726
12-228012+(-2280)=-2268
15-182415+(-1824)=-1809
16-171016+(-1710)=-1694
18-152018+(-1520)=-1502
19-144019+(-1440)=-1421
20-136820+(-1368)=-1348
24-114024+(-1140)=-1116
30-91230+(-912)=-882
32-85532+(-855)=-823
36-76036+(-760)=-724
38-72038+(-720)=-682
40-68440+(-684)=-644
45-60845+(-608)=-563
48-57048+(-570)=-522
57-48057+(-480)=-423
60-45660+(-456)=-396
72-38072+(-380)=-308
76-36076+(-360)=-284
80-34280+(-342)=-262
90-30490+(-304)=-214
95-28895+(-288)=-193
96-28596+(-285)=-189
114-240114+(-240)=-126
120-228120+(-228)=-108
144-190144+(-190)=-46
152-180152+(-180)=-28
160-171160+(-171)=-11
-127360-1+27360=27359
-213680-2+13680=13678
-39120-3+9120=9117
-46840-4+6840=6836
-55472-5+5472=5467
-64560-6+4560=4554
-83420-8+3420=3412
-93040-9+3040=3031
-102736-10+2736=2726
-122280-12+2280=2268
-151824-15+1824=1809
-161710-16+1710=1694
-181520-18+1520=1502
-191440-19+1440=1421
-201368-20+1368=1348
-241140-24+1140=1116
-30912-30+912=882
-32855-32+855=823
-36760-36+760=724
-38720-38+720=682
-40684-40+684=644
-45608-45+608=563
-48570-48+570=522
-57480-57+480=423
-60456-60+456=396
-72380-72+380=308
-76360-76+360=284
-80342-80+342=262
-90304-90+304=214
-95288-95+288=193
-96285-96+285=189
-114240-114+240=126
-120228-120+228=108
-144190-144+190=46
-152180-152+180=28
-160171-160+171=11

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 then factors further to

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

So completely 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, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

 Permutations/422683: In how many ways can 3 red, 4 blue, and 2 green pens be distributed to 9 students seated in a row if each student receives one pen? What I've tried so far: I added the given numbers of pens to get the total amount of pens which equals 9. I then mulitiplied that by the number of students in each row, which is also nine. So I finished with 81...1 solutions Answer 294983 by jim_thompson5910(28715)   on 2011-03-15 21:45:07 (Show Source): You can put this solution on YOUR website!There are 9! = 9*8*7*6*5*4*3*2*1 = 362880 different ways to distribute the 9 pens to the 9 students. If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Expressions-with-variables/422685: n+3=2n-11 solutions Answer 294981 by jim_thompson5910(28715)   on 2011-03-15 21:40:52 (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 If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Radicals/422666: the cubed root of 6 multiply by the cubed root of 16?1 solutions Answer 294971 by jim_thompson5910(28715)   on 2011-03-15 21:10:31 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Average/422534: how do u factor x^3+8x^2+2x+16?1 solutions Answer 294918 by jim_thompson5910(28715)   on 2011-03-15 16:53:47 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms So factors to In other words, If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Length-and-distance/422495: What is the distance of the line segment connecting A(-2,4) and B (6,10) thank you1 solutions Answer 294904 by jim_thompson5910(28715)   on 2011-03-15 15:54:38 (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 distance formula. Plug in , , , and . Subtract from to get . Subtract from to get . Square to get . Square to get . Add to to get . Take the square root of to get . So our answer is So the distance between the two points is 10 units. If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Probability-and-statistics/422488: One letter is randomly selected from the word PRIME and one letter is randomly slected from the word MATH. What is the proability that both letters slected are vowels?1 solutions Answer 294903 by jim_thompson5910(28715)   on 2011-03-15 15:45:13 (Show Source): You can put this solution on YOUR website!P(Both Vowels) = P(Vowel from PRIME) * P(Vowel from MATH) P(Both Vowels) = (2/5)*(1/4) P(Both Vowels) = 2/20 P(Both Vowels) = 1/10 So the probability is
 Equations/422473: Solve the equation: x/13 = -181 solutions Answer 294901 by jim_thompson5910(28715)   on 2011-03-15 15:43:26 (Show Source): You can put this solution on YOUR website!Multiply both sides by 13 to get which becomes So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Probability-and-statistics/422481: Four coins are tossed. What is the probaility of tossing all heads? 1 solutions Answer 294899 by jim_thompson5910(28715)   on 2011-03-15 15:41:13 (Show Source): You can put this solution on YOUR website!There are ways to toss 4 coins, but only 1 way to toss all 4 heads. So the probability is
 Linear-equations/422464: What is the slope and y-intercept of y=3x-41 solutions Answer 294890 by jim_thompson5910(28715)   on 2011-03-15 15:16:08 (Show Source): You can put this solution on YOUR website!In general, the slope of is m and the y-intercept is (0,b). Since m=3, the slope is 3. Because b=-4, the y-intercept is (0,-4) If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Expressions-with-variables/422148: I'd really appreciate some help with this problem, I've been stuck on it and I need help really soon. y-3=x+2 Thanks!!!!! :)1 solutions Answer 294676 by jim_thompson5910(28715)   on 2011-03-14 19:55:10 (Show Source): You can put this solution on YOUR website!Simply add 3 to both sides to get which simplifies to If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Problems-with-consecutive-odd-even-integers/422121: Please translate this into a number form. the product of five more than a number and six is thirty1 solutions Answer 294663 by jim_thompson5910(28715)   on 2011-03-14 18:34:14 (Show Source): You can put this solution on YOUR website!"the product of five more than a number and six is thirty" translates to If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Human-and-algebraic-language/422114: 6. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue? I tried to solve it on my own by dividing all 3 into 41 and then subtracted 6 hrs from sue and the subtracted 5 yrs from Leah and I am not coming up anywhere close to any of the answers provided. I don't know how to figure out what method to use when solving word problems. Can you please help? Sorry I just sent this ? In but I added a y in my e mail name but this one is correct. Sorry for the confusion. 1 solutions Answer 294662 by jim_thompson5910(28715)   on 2011-03-14 18:32:35 (Show Source): You can put this solution on YOUR website!Let L = Leah's age, S = Sue's age, and J = John's age So because "Leah is 6 years older than Sue", we know that L = S+6 (ie add 6 years to Sue's age to get Leah's age) Since "John is 5 years older than Leah", we also know that J = L+5 Finally, we know that "the total of their ages is 41", which tells us that L + S + J = 41 So simply plug in J = L+5 to get L + S + (L+5) = 41 L + S + L + 5 = 41 Now plug in L = S + 6 to get (S+6) + S + (S+6) + 5 = 41 S + 6 + S + S + 6 + 5 = 41 Now let's solve for S S + 6 + S + S + 6 + 5 = 41 3S + 17 = 41 3S = 41 - 17 3S = 24 S = 24/3 S = 8 So Sue is 8 years old (since S = 8 ) So Leah is L = S+6 = 8+6 = 14 years old (since L = 14) And John is J = L + 5 = 14 + 5 = 19 years old. Notice that the sum of their ages is 8+14+19 = 22+19 = 41 If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Human-and-algebraic-language/422111: 6. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue? I tried to solve it on my own by dividing all 3 into 41 and then subtracted 6 hrs from sue and the subtracted 5 yrs from Leah and I am not coming up anywhere close to any of the answers provided. I don't know how to figure out what method to use when solving word problems. Can you please help?1 solutions Answer 294661 by jim_thompson5910(28715)   on 2011-03-14 18:30:18 (Show Source): You can put this solution on YOUR website!Let L = Leah's age, S = Sue's age, and J = John's age So because "Leah is 6 years older than Sue", we know that L = S+6 (ie add 6 years to Sue's age to get Leah's age) Since "John is 5 years older than Leah", we also know that J = L+5 Finally, we know that "the total of their ages is 41", which tells us that L + S + J = 41 So simply plug in J = L+5 to get L + S + (L+5) = 41 L + S + L + 5 = 41 Now plug in L = S + 6 to get (S+6) + S + (S+6) + 5 = 41 S + 6 + S + S + 6 + 5 = 41 Now let's solve for S S + 6 + S + S + 6 + 5 = 41 3S + 17 = 41 3S = 41 - 17 3S = 24 S = 24/3 S = 8 So Sue is 8 years old (since S = 8 ) So Leah is L = S+6 = 8+6 = 14 years old (since L = 14) And John is J = L + 5 = 14 + 5 = 19 years old. Notice that the sum of their ages is 8+14+19 = 22+19 = 41 If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Probability-and-statistics/422103: The question is, What is the probability that a randomly selected student is either a male student or an international student. See chart below for numbers Female Male US Resident 435 395 International 57 63 I can solve these when there is only one choice (i.e either male or international) but I'm having a hard time understanding when I have to find two things. 1 solutions Answer 294650 by jim_thompson5910(28715)   on 2011-03-14 17:56:31 (Show Source): You can put this solution on YOUR website!Hint: Given events A and B, P(A or B) = P(A) + P(B) - P(A and B)
 Triangles/422101: I need your help please. I dont understand how to find the perimeter of an isosceles triangle with one side that measures 5ft. and two sides that measure 11ft. each?1 solutions Answer 294649 by jim_thompson5910(28715)   on 2011-03-14 17:55:09 (Show Source): You can put this solution on YOUR website!Perimeter = sum of 3 sides = 5 + 11 + 11 = 16 + 11 = 27 So the perimeter is 27 ft. If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
Polynomials-and-rational-expressions/422089: What is the completely factored form of 12d^2+14d-6
1 solutions

Answer 294645 by jim_thompson5910(28715)   on 2011-03-14 17:34:18 (Show Source):
You can put this solution on YOUR website!

Factor out the GCF .

Now let's try to factor the inner expression

---------------------------------------------------------------

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 :
1,2,3,6,9,18
-1,-2,-3,-6,-9,-18

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

These factors pair up and multiply to .
1*(-18) = -18
2*(-9) = -18
3*(-6) = -18
(-1)*(18) = -18
(-2)*(9) = -18
(-3)*(6) = -18

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

First NumberSecond NumberSum
1-181+(-18)=-17
2-92+(-9)=-7
3-63+(-6)=-3
-118-1+18=17
-29-2+9=7
-36-3+6=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 then factors further to

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

So completely 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, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

 Volume/422080: A cylindrical oil tank had a diameter of 4th and a length of 40ft. Find the volume of the tank, round to the nearest hundredth.1 solutions Answer 294635 by jim_thompson5910(28715)   on 2011-03-14 17:11:07 (Show Source): You can put this solution on YOUR website!Since the diameter is 4 ft, the radius is 4/2=2 ft. So r=2 Start with the volume of a cylinder formula. Plug in and . Replace with (note: Use more digits of to get better accuracy). Square to get . Multiply , and to get (this value is approximate). So the volume is approximately 502.654824 cubic ft. If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim
 Polynomials-and-rational-expressions/422079: I am currently working on the Question "Consider the following equation of a line, rewrite this equation in slope intercept form. Reduce all factors to lowest terms." I can work the whole problem all the way to the end and then I can't figure out where one number is coming from. This is a two part problem. I will only list the one I can't figure out. The numbers are (3,13) seek 3/7. Steps are y-(-13)=3/7(x-(3)) second step y+13=3/7x-9/7 third step y=3/7x-9/7-13 fourth and last step y=3/7x-100/7. I can not figure out how they get 100 for the answer. Hope you can help. Amy1 solutions Answer 294631 by jim_thompson5910(28715)   on 2011-03-14 17:07:38 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim