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 Inequalities/317339: 8y-6<-541 solutions Answer 227209 by jim_thompson5910(28550)   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(28550)   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(28550)   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(28550)   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(28550)   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(28550)   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(28550)   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(28550)   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(28550)   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(28550)   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,

------------------------------------------------------------------------
# 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).

------------------------------------------------------------------------
# 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(28550)   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(28550)   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(28550)   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(28550)   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

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

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).

expressions/317057: Factor the following trinomial, if possible. If the coefficient of the first term is negative, factor out -1 to make the first term positive.
8b^2 + 10b - 25
1 solutions

Answer 226993 by jim_thompson5910(28550)   on 2010-06-23 21:56:09 (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 :
1,2,4,5,8,10,20,25,40,50,100,200
-1,-2,-4,-5,-8,-10,-20,-25,-40,-50,-100,-200

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

These factors pair up and multiply to .
1*(-200) = -200
2*(-100) = -200
4*(-50) = -200
5*(-40) = -200
8*(-25) = -200
10*(-20) = -200
(-1)*(200) = -200
(-2)*(100) = -200
(-4)*(50) = -200
(-5)*(40) = -200
(-8)*(25) = -200
(-10)*(20) = -200

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

First NumberSecond NumberSum
1-2001+(-200)=-199
2-1002+(-100)=-98
4-504+(-50)=-46
5-405+(-40)=-35
8-258+(-25)=-17
10-2010+(-20)=-10
-1200-1+200=199
-2100-2+100=98
-450-4+50=46
-540-5+40=35
-825-8+25=17
-1020-10+20=10

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).

 expressions/317056: Factor the following expression. Factor out any common factors first. 4m+n + 16m^2- n^21 solutions Answer 226992 by jim_thompson5910(28550)   on 2010-06-23 21:55:02 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor to get Factor out the GCF So factors to In other words,
 Radicals/317005: simplify the following radical expression: 4 sqrt (625) a) 5 b) sqrt (25) c) 25 d no solution exists1 solutions Answer 226938 by jim_thompson5910(28550)   on 2010-06-23 18:44:10 (Show Source): You can put this solution on YOUR website! which means that
 Human-and-algebraic-language/316999: an airport has a sloping ramp from the terminal down to the door of the airplane. the door of the airplane is 43 ft away from terminal( where the ramp starts) and is 4 ft below the terminal side of the ramp. how long is the ramp?1 solutions Answer 226937 by jim_thompson5910(28550)   on 2010-06-23 18:40:55 (Show Source): You can put this solution on YOUR website!We basically have this triangle set up: To find the unknown length, we need to use the Pythagorean Theorem. Remember, the Pythagorean Theorem is where "a" and "b" are the legs of a triangle and "c" is the hypotenuse. Since the legs are and this means that and Also, since the hypotenuse is , this means that . Start with the Pythagorean theorem. Plug in , , Square to get . Square to get . Combine like terms. Rearrange the equation. Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense). ================================================================ Answer: So the solution is which approximates to . So the ramp is about 43.186 ft long.
 Linear-equations/317008: I am in need of a simplified way of doing equation of a line. The question being find an equation of the line containing the given pair of paints (-5, -2) and (-3, -1). The equation of the line in slope interecept form is y= ___ Then simplify the naswer. Use integer or fractions for nay numbers in the expression. I know that the formula is y = mx + b but just cannot make it work in my head. Can you help?1 solutions Answer 226927 by jim_thompson5910(28550)   on 2010-06-23 18:10:03 (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 2 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
 Linear-equations/317007: The graph of y = -4 + 5 is shown on the next page. Use it to find the answers to Exercises 6–8. Check your work The value of y when x = 1 I am not sure what to do or what the question is asking?? Thanks1 solutions Answer 226926 by jim_thompson5910(28550)   on 2010-06-23 18:08:56 (Show Source): You can put this solution on YOUR website!I'm assuming that the equation is really Start with the given equation. Plug in Multiply -4 and 1 to get -4 Add -4 to 5 to get 1. So when , the value of y is
 Equations/317002: Find the following. Assume that variables can represent any real number. sqrt(a+7)^21 solutions Answer 226925 by jim_thompson5910(28550)   on 2010-06-23 18:06:45 (Show Source): You can put this solution on YOUR website!Using the identity , where 'x' is a real number, this means that
 Radicals/317006: simplify the following radical expression: 4 sqrt (81/16) a) 3/2 b) 2 c)3 d) 2/31 solutions Answer 226924 by jim_thompson5910(28550)   on 2010-06-23 18:05:01 (Show Source): You can put this solution on YOUR website!Hint: and
 Polynomials-and-rational-expressions/316995: Factor -uz+2t+tu-2z1 solutions Answer 226921 by jim_thompson5910(28550)   on 2010-06-23 17:46:31 (Show Source): You can put this solution on YOUR website! Start with the given expression Rearrange the terms. Group the 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 Rearrange the terms. So factors to In other words,
 Radicals/316994: find the distance between (-2,9) and (-5,15) a)45.02 b) 6.17 c)24.18 d) 18.671 solutions Answer 226920 by jim_thompson5910(28550)   on 2010-06-23 17:43:44 (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 . Simplify the square root. So our answer is Which approximates to So the distance between the two points is approximately 6.708 units.
Polynomials-and-rational-expressions/316992: Factor:
3x^2+2xy-16y^2
1 solutions

Answer 226918 by jim_thompson5910(28550)   on 2010-06-23 17:38:24 (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 3 and -16 respectively.

Now multiply the first coefficient 3 and the last coefficient -16 to get -48. Now what two numbers multiply to -48 and add to the middle coefficient 2? Let's list all of the factors of -48:

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

-1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...List the negative factors as well. This will allow us to find all possible combinations

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

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2

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 this list we can see that -6 and 8 add up to 2 and multiply to -48

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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So factors to

In other words,

 Polynomials-and-rational-expressions/316990: factor: 9z^2+zu+27z+3u1 solutions Answer 226917 by jim_thompson5910(28550)   on 2010-06-23 17:37:15 (Show Source): You can put this solution on YOUR website! Start with the given expression Group the 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,
 Polynomials-and-rational-expressions/316987: Factor: 6y+zu+6u+yz1 solutions Answer 226916 by jim_thompson5910(28550)   on 2010-06-23 17:36:14 (Show Source): You can put this solution on YOUR website! Start with the given expression Rearrange the terms. Group the 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,
 Polynomials-and-rational-expressions/316985: Factor completely: 8z^3+1251 solutions Answer 226913 by jim_thompson5910(28550)   on 2010-06-23 17:26:34 (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,
Polynomials-and-rational-expressions/316984: Factor:
3x^2-10xy+8y^2
1 solutions

Answer 226912 by jim_thompson5910(28550)   on 2010-06-23 17:25:56 (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 3 and 8 respectively.

Now multiply the first coefficient 3 and the last coefficient 8 to get 24. Now what two numbers multiply to 24 and add to the middle coefficient -10? Let's list all of the factors of 24:

Factors of 24:
1,2,3,4,6,8,12,24

-1,-2,-3,-4,-6,-8,-12,-24 ...List the negative factors as well. This will allow us to find all possible combinations

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

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -10? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -10

First NumberSecond NumberSum
1241+24=25
2122+12=14
383+8=11
464+6=10
-1-24-1+(-24)=-25
-2-12-2+(-12)=-14
-3-8-3+(-8)=-11
-4-6-4+(-6)=-10

From this list we can see that -4 and -6 add up to -10 and multiply to 24

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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