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 Rational-functions/317794: What is the value of the expression 2x^2y / 4xy when x = 2 and y = 1? a) 1 b) 2 c) 4 d) 31 solutions Answer 227562 by jim_thompson5910(28717)   on 2010-06-26 19:16:19 (Show Source): You can put this solution on YOUR website! Start with the given expression. Plug in and Square 2 to get 4. Multiply Reduce. So when and
 Polynomials-and-rational-expressions/317789: calculate and write in standard form: (1-2i)^2, I have worked it down to 4i^2-4i+1 but can't figure out how to work it down even more.1 solutions Answer 227554 by jim_thompson5910(28717)   on 2010-06-26 18:44:09 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand FOIL. Multiply. Replace with . Note: . Multiply. Combine like terms. So .
 Equations/317788: 5x-9=361 solutions Answer 227550 by jim_thompson5910(28717)   on 2010-06-26 17:47:24 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Proportions/317783: If 5 tractors can plow a field in 4 hours,how many hours will it take 3 tractors to plow a field?1 solutions Answer 227549 by jim_thompson5910(28717)   on 2010-06-26 17:35:05 (Show Source): You can put this solution on YOUR website!Hint: Solve the proportion .
Polynomials-and-rational-expressions/317784: factorize 6x^2+17x+5 by splitting middle term snd by using the factor theorm
1 solutions

Answer 227548 by jim_thompson5910(28717)   on 2010-06-26 17:34:18 (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 :
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30

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

These factors pair up and multiply to .
1*30 = 30
2*15 = 30
3*10 = 30
5*6 = 30
(-1)*(-30) = 30
(-2)*(-15) = 30
(-3)*(-10) = 30
(-5)*(-6) = 30

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

First NumberSecond NumberSum
1301+30=31
2152+15=17
3103+10=13
565+6=11
-1-30-1+(-30)=-31
-2-15-2+(-15)=-17
-3-10-3+(-10)=-13
-5-6-5+(-6)=-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 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).

 Matrices-and-determiminant/317782: A movie theater charges $7 for adults,$4.50 for children, and $1 for senior citizens. On one day, the theater sold 635 tickets and collected$2910.00 in receipts. there were 2 times as many children's tickets sold as adult tickets. How many adults, children, and senior citizens went to the movies that day? (solve using matrices. find the reduced row echelon form). x = adults y = children and z = senior citizens equation 1: x + y + z = 635 equation 2: $7x +$4.5y + $1z =$2910.00 equation 3: x = 2y (IS THIS RIGHT????) equation 4: x greater than or equal to 0 equation 5: y is greater than or equal to 0 How do I figure out the third equation and solve using a matrix and putting it into reduced row echelon form? I need to know how to figure that part out, I can get it into reduced row echelon form. Your help is appreciated. Thank you!1 solutions Answer 227545 by jim_thompson5910(28717)   on 2010-06-26 16:49:32 (Show Source): You can put this solution on YOUR website!Since "there were 2 times as many children's tickets sold as adult tickets", this means that . Let's say that there were x=10 adult tickets. This then means that there are y=2(10)=20 children's tickets since "there were 2 times as many children's tickets sold as adult tickets". So the third equation is . If you get everything to one side, you get So the three equations are Note: I multiplied ALL of the terms of the second equation by 10 to make every number a whole number. which translates into the matrix equation Now append the right side to the 3x3 matrix on the left side to get the augmented matrix Now let's row reduce. Note: Solution provided by the Linear Algebra Toolkit Now look at the last column of the last matrix (ie the last step shown). This column has the values 175, 350, and 110. This means that , and So 175 adults, 350 children, and 110 seniors went to the movies that day.
 Parallelograms/317780: Given points A(3, 3), B(3, -2), C(-1, -1), D(-1, 4). Determine whether quadrilateral ABCD with the given vertices is a parallelogram or not.1 solutions Answer 227540 by jim_thompson5910(28717)   on 2010-06-26 16:01:09 (Show Source): You can put this solution on YOUR website!Hint: Find the slope of the line segments AB, BC, CD, and AD. If you can show that the slope of AB is equal to the slope of CD and show that the slope of BC is equal to the slope of AD, then you will have shown that ABCD is a parallelogram.
 logarithm/317778: find log 4 64 1 solutions Answer 227535 by jim_thompson5910(28717)   on 2010-06-26 15:39:37 (Show Source): You can put this solution on YOUR website!Let . Now convert to exponential form to get . We can rewrite 64 as and 4 as which means that and . Since the bases are equal, the exponents must be equal. So . Solve for 'y' to get . This then means that
 logarithm/317772: Write as a single logarithm. ln5x+4(lnx-lny)1 solutions Answer 227534 by jim_thompson5910(28717)   on 2010-06-26 15:31:58 (Show Source): You can put this solution on YOUR website! So
 Inequalities/317771: problem:-2/3z+9 > and = 2/3z+1 I subtracted 2/3z from right side ande added it to the left side. I subtracted 9 from left and added to right. I ended up with -4/3z >and = -8. I dont think that is right. 1 solutions Answer 227533 by jim_thompson5910(28717)   on 2010-06-26 15:29:38 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. 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
 Average/317669: find a number between 9/8 and 10/8. write your answer as improper fraction and as mixed number.1 solutions Answer 227500 by jim_thompson5910(28717)   on 2010-06-26 04:44:19 (Show Source): You can put this solution on YOUR website!One easy way to find a number between two numbers is to simply average the two given numbers. Ie add them up and divide by 2: So the number , which is the mixed number , is in between the numbers and Other ways would involve you picking a number between 9 and 10, say 9.7, and writing that as a fraction over 8 like this: So , which is the mixed number , is another number in between the numbers and
 Numeric_Fractions/317676: Please help me to solve these problems: Write them as an integer or a fraction (-8)^2= (1/5)^2=1 solutions Answer 227499 by jim_thompson5910(28717)   on 2010-06-26 04:36:45 (Show Source): You can put this solution on YOUR website!1. which means that 2. which means that
 Equations/317395: Solve for the variable. Noninteger answers may be left in fractional or decimal form. 5/6y + 4/9 = 1/6y - 2/5 I can not solve it! can you should me how to work it out?1 solutions Answer 227258 by jim_thompson5910(28717)   on 2010-06-25 00:53:00 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply EVERY term by the LCD to clear the fractions. Multiply and simplify. Multiply. 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
 Inequalities/317381: use the properties of inequalities to solve the following inequality. write the solution set using set-builder notation. 9(x-8)>or=to -9x-7. thank you 1 solutions Answer 227257 by jim_thompson5910(28717)   on 2010-06-25 00:50:04 (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 The answer in set-builder notation is
 Radicals/317346: Rarional Exponents and Radicals 1.√90-√10 2.√75a+√12a 3.(-7√3)(-4√10) 4. √16/36 5.y/√7+√3 1 solutions Answer 227213 by jim_thompson5910(28717)   on 2010-06-24 20:51:33 (Show Source): You can put this solution on YOUR website!Only post one problem at a time please. # 1 which means that
 Equations/317341: x+6=-31 solutions Answer 227210 by jim_thompson5910(28717)   on 2010-06-24 20:36:02 (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. ---------------------------------------------------------------------- Answer: So the solution is
 Inequalities/317339: 8y-6<-541 solutions Answer 227209 by jim_thompson5910(28717)   on 2010-06-24 20:32:41 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/317310: find the value of a in this proportion (a+1)/4=2/31 solutions Answer 227172 by jim_thompson5910(28717)   on 2010-06-24 18:09:45 (Show Source): You can put this solution on YOUR website! Start with the given equation. Cross multiply. Multiply 2 and 4 to get 8. Distribute. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is
 Exponents/317312: Rewrite the following without an exponent. (-3)-11 solutions Answer 227170 by jim_thompson5910(28717)   on 2010-06-24 18:07:03 (Show Source): You can put this solution on YOUR website!. So
Equations/317306: (x-2)(x-3)
THANK YOU.
1 solutions

Answer 227164 by jim_thompson5910(28717)   on 2010-06-24 17:57:18 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: FOIL (ie Expand) Two Binomials Start with the given expression Now let's FOIL the expression Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms: Multiply the Outer terms: Multiply the Inner terms: Multiply the Last terms: Now collect every term to make a single expression Now combine like terms --------------------- Answer: So FOILs and simplifies to In other words,

 Systems-of-equations/317308: Simplify z4.z.z4 1 solutions Answer 227163 by jim_thompson5910(28717)   on 2010-06-24 17:56:26 (Show Source): You can put this solution on YOUR website! which means that
 Quadratic_Equations/317304: Using the FOIL method create an quadratic equation using solutions of 4,-81 solutions Answer 227161 by jim_thompson5910(28717)   on 2010-06-24 17:51:13 (Show Source): You can put this solution on YOUR website!Hint: If 'a' and 'b' are solutions of a quadratic equation, then
 Polygons/317301: fint the value of a in this proportions a/4=9/a1 solutions Answer 227158 by jim_thompson5910(28717)   on 2010-06-24 17:45:10 (Show Source): You can put this solution on YOUR website! Start with the given equation. Cross multiply. Multiply. Take the square root of both sides. or Break up the plus/minus. or Take the square root of 36 to get 6. So the solutions are or
 Equations/317100: The product of page numbers on two facing pages of a book is 182. How would you find the page numbers? I have tried and cannot figure out how to do this.Can you show me how?1 solutions Answer 227022 by jim_thompson5910(28717)   on 2010-06-24 04:42:25 (Show Source): You can put this solution on YOUR website!Hint: Since "The product of page numbers on two facing pages of a book is 182", this means that where 'x' is the first of the two pages and 'x+1' is the next page.
 test/317096: evaluate f(-1)=-2x+20 when x=-11 solutions Answer 227021 by jim_thompson5910(28717)   on 2010-06-24 04:41:22 (Show Source): You can put this solution on YOUR website!Hint: Simply replace 'x' with -1 and compute the right side.
Equations/317097: I am having trouble figuring out how to factor the three problems listed below:1. x^2+2x-2x-4;2.v^2+9v+14;3. r^2-2r-48. I have been working on them for about 1 1/2 hours at this time and just can not seem to get any where can you help?
1 solutions

Answer 227020 by jim_thompson5910(28717)   on 2010-06-24 04:40:48 (Show Source):
You can put this solution on YOUR website!
# 1

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,

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# 2

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 :
1,2,7,14
-1,-2,-7,-14

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

These factors pair up and multiply to .
1*14 = 14
2*7 = 14
(-1)*(-14) = 14
(-2)*(-7) = 14

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

First NumberSecond NumberSum
1141+14=15
272+7=9
-1-14-1+(-14)=-15
-2-7-2+(-7)=-9

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).

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# 3

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 :
1,2,3,4,6,8,12,16,24,48
-1,-2,-3,-4,-6,-8,-12,-16,-24,-48

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

These factors pair up and multiply to .
1*(-48) = -48
2*(-24) = -48
3*(-16) = -48
4*(-12) = -48
6*(-8) = -48
(-1)*(48) = -48
(-2)*(24) = -48
(-3)*(16) = -48
(-4)*(12) = -48
(-6)*(8) = -48

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

First NumberSecond NumberSum
1-481+(-48)=-47
2-242+(-24)=-22
3-163+(-16)=-13
4-124+(-12)=-8
6-86+(-8)=-2
-148-1+48=47
-224-2+24=22
-316-3+16=13
-412-4+12=8
-68-6+8=2

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).

 Equations/317098: Using the principle of zero products how would you solve the following problems:1. (9b+5)(4b-12)=0; 2.b^2+8b+12=0. I have been trying and can not seem to get the correct answer. Can you help?1 solutions Answer 227019 by jim_thompson5910(28717)   on 2010-06-24 04:38:07 (Show Source): You can put this solution on YOUR website!# 1 Start with the given equation Now set each factor equal to zero: or Now solve for b for each factor: or So the solutions are or ---------------------------------------------------------------- # 2 Start with the given equation Factor the left side Now set each factor equal to zero: or or Now solve for b in each case So the solutions are or
 Square-cubic-other-roots/317101: from special relativity, I can get most of the way apart from the very last step how do you simplify , the answer should be but I don't see how it's done thanks John 1 solutions Answer 227018 by jim_thompson5910(28717)   on 2010-06-24 04:34:18 (Show Source): You can put this solution on YOUR website!It's not much of a simplification (in my opinion) as the expression doesn't get any simpler, but here it goes... Start with the given expression. Divide both the numerator and the denominator by 'c' Reduce to get 1. Rewrite as . Note: this implies that 'c' is a non-negative number, which it is. Combine the lower square roots using the identity Break up the lower inner fraction. Reduce to get 1. So
 Square-cubic-other-roots/317086: Square root 10x multiplied by square root 8x1 solutions Answer 227013 by jim_thompson5910(28717)   on 2010-06-24 00:38:31 (Show Source): You can put this solution on YOUR website! So where
expressions/317059: Factor the following trinomial, if possible. If the coefficient of the first term is negative, factor out -1 to make the first term positive.
10a^2 - 9a + 2
1 solutions

Answer 226994 by jim_thompson5910(28717)   on 2010-06-23 21:56:58 (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 :
1,2,4,5,10,20
-1,-2,-4,-5,-10,-20

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

These factors pair up and multiply to .
1*20 = 20
2*10 = 20
4*5 = 20
(-1)*(-20) = 20
(-2)*(-10) = 20
(-4)*(-5) = 20

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

First NumberSecond NumberSum
1201+20=21
2102+10=12
454+5=9
-1-20-1+(-20)=-21
-2-10-2+(-10)=-12
-4-5-4+(-5)=-9

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

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