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Polynomials-and-rational-expressions/168158: 18a^4b^2-24a^3b^3+8a^2b^4
1 solutions

Answer 123951 by jim_thompson5910(28595)   on 2008-11-17 19:45:07 (Show Source):
You can put this solution on YOUR website!

Factor out the GCF

Now let's focus on the inner expression

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

Looking at we can see that the first term is and the last term is where the coefficients are 9 and 4 respectively.

Now multiply the first coefficient 9 and the last coefficient 4 to get 36. Now what two numbers multiply to 36 and add to the middle coefficient -12? Let's list all of the factors of 36:

Factors of 36:
1,2,3,4,6,9,12,18

-1,-2,-3,-4,-6,-9,-12,-18 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 36
1*36
2*18
3*12
4*9
6*6
(-1)*(-36)
(-2)*(-18)
(-3)*(-12)
(-4)*(-9)
(-6)*(-6)

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

Now which of these pairs add to -12? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -12

First NumberSecond NumberSum
1361+36=37
2182+18=20
3123+12=15
494+9=13
666+6=12
-1-36-1+(-36)=-37
-2-18-2+(-18)=-20
-3-12-3+(-12)=-15
-4-9-4+(-9)=-13
-6-6-6+(-6)=-12

From this list we can see that -6 and -6 add up to -12 and multiply to 36

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 )

note: is equivalent to since the term occurs twice. So also factors to

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

So our expression goes from and factors further to

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

So factors to

 Linear-equations/168179: 7x+4y=21 solutions Answer 123949 by jim_thompson5910(28595)   on 2008-11-17 19:44:05 (Show Source): You can put this solution on YOUR website!Do you want to solve for y? Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce.
 Equations/168180: This question is from textbook Please help me with this equation. The title of the page is Solving two-step eqautions. 37-4v=57.41 solutions Answer 123948 by jim_thompson5910(28595)   on 2008-11-17 19:42:54 (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. Divide both sides by to isolate . Divide. ---------------------------------------------------------------------- Answer: So the answer is
 Proportions/168181: im having a really hard time on this one it is due tomorrow 7/5=10.5/b solve the proportion ? really confussed from bad at math need help1 solutions Answer 123943 by jim_thompson5910(28595)   on 2008-11-17 19:24:23 (Show Source): You can put this solution on YOUR website! Start with the given ratio Multiply both sides by b Multiply both sides by 5 Multiply 10.5 and 5 to get 52.5 Divide both sides by 7 to isolate "b" Divide So our answer is
 Points-lines-and-rays/168152: This question is from textbook Skills Practice Workbook Algebra 1 What is the slope intercept form of (3,2), y= 3x + 4 and is it parallel to what would be the graph of the given equation?1 solutions Answer 123941 by jim_thompson5910(28595)   on 2008-11-17 19:20:39 (Show Source): You can put this solution on YOUR website! Since the equation is in slope intercept form , this means that the equation has the slope and the y-intercept . Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is . Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point . Start with the point slope formula Plug in , , and Distribute Multiply Add 2 to both sides. Combine like terms. So the equation of the line parallel to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the parallel line (green) through the point .
 Polynomials-and-rational-expressions/168155: 9x^2-4y^81 solutions Answer 123940 by jim_thompson5910(28595)   on 2008-11-17 19:17:07 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as . Notice how we have a difference of squares. So let's use the difference of squares formula to factor the expression: Factor the expression using the difference of squares. So factors to . In other words .
 Polynomials-and-rational-expressions/168156: 49a^7-9a^51 solutions Answer 123939 by jim_thompson5910(28595)   on 2008-11-17 19:16:00 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out the GCF Now let's focus on the inner expression ------------------------------------------------------------ Start with the given expression. Rewrite as . Rewrite as . Notice how we have a difference of squares. So let's use the difference of squares formula to factor the expression: Factor the expression using the difference of squares. So factors to . So this means that factors to . ------------------------------------------------------------ Answer: So completely factors to
Polynomials-and-rational-expressions/168159: 3x^2+37xy-86y^2
1 solutions

Answer 123936 by jim_thompson5910(28595)   on 2008-11-17 19:11:59 (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 -86 respectively.

Now multiply the first coefficient 3 and the last coefficient -86 to get -258. Now what two numbers multiply to -258 and add to the middle coefficient 37? Let's list all of the factors of -258:

Factors of -258:
1,2,3,6,43,86,129,258

-1,-2,-3,-6,-43,-86,-129,-258 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -258
(1)*(-258)
(2)*(-129)
(3)*(-86)
(6)*(-43)
(-1)*(258)
(-2)*(129)
(-3)*(86)
(-6)*(43)

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

Now which of these pairs add to 37? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 37

First NumberSecond NumberSum
1-2581+(-258)=-257
2-1292+(-129)=-127
3-863+(-86)=-83
6-436+(-43)=-37
-1258-1+258=257
-2129-2+129=127
-386-3+86=83
-643-6+43=37

From this list we can see that -6 and 43 add up to 37 and multiply to -258

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 )

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

So factors to

 Polynomials-and-rational-expressions/168161: 2x^2+2ax+5x+5a1 solutions Answer 123934 by jim_thompson5910(28595)   on 2008-11-17 19:10:00 (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
 real-numbers/168178: my teacher doesn't know whay his doing in our class we all have f's even the people that does his work. so can you help me get my grades up1 solutions Answer 123933 by jim_thompson5910(28595)   on 2008-11-17 19:07:16 (Show Source): You can put this solution on YOUR website!Please post the problem (the entire problem). Remember, we don't have access to your book.
 Equations/168165: This question is from textbook Algerbra 1 55x-3(9x+12)= -641 solutions Answer 123921 by jim_thompson5910(28595)   on 2008-11-17 18:46:35 (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 answer is
 Polynomials-and-rational-expressions/168055: For the polynomial, -9x^4+6x^3-4x^2+2x-9 Complete the following table. Term____Coefficient___Degree of term ???________???__________??? 6x^3________6___________??? ???________???__________2 2x_________???__________1 -9_________???__________??? What is the Degree of the Polynomial? ??? I have no clue on this, Please Help! Thank you 1 solutions Answer 123863 by jim_thompson5910(28595)   on 2008-11-17 11:52:37 (Show Source): You can put this solution on YOUR website!For any polynomial, the terms are simply separated by either a '+' or a '-' Remember, the coefficient is the number that is right in front of the variable. Also, the degree of each term is simply equal to the exponent of the term. For example, the term -9x^4 has the number -9 out front of the variable, so the coefficient is -9. The exponent is 4, which means that the degree is 4. So here's the completed table:  Term Coefficient Degree of term -9x^4 -9 4 6x^3 6 3 -4x^2 -4 2 2x 2 1 -9 -9 0  Note: the degrees of each term is decreasing by 1
 Exponential-and-logarithmic-functions/167970: How do I solve for x? Log x 1/64= -3 1 solutions Answer 123798 by jim_thompson5910(28595)   on 2008-11-16 19:33:23 (Show Source): You can put this solution on YOUR website! Start with the given equation Rewrite as Rewrite as Rewrite the equation using the property: ====> Since the exponents are equal, this means that the bases are equal. So this means that So the solution is
Polynomials-and-rational-expressions/167956: The factoring Strategy
Factor each polynomial completely. If a polynomial is prime, say so.
66. 8b2 + 24b + 18

1 solutions

Answer 123797 by jim_thompson5910(28595)   on 2008-11-16 19:29:15 (Show Source):
You can put this solution on YOUR website!

Factor out the GCF

Now let's focus on 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 :
1,2,3,4,6,9,12,18,36
-1,-2,-3,-4,-6,-9,-12,-18,-36

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

These factors pair up and multiply to .
1*36
2*18
3*12
4*9
6*6
(-1)*(-36)
(-2)*(-18)
(-3)*(-12)
(-4)*(-9)
(-6)*(-6)

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

First NumberSecond NumberSum
1361+36=37
2182+18=20
3123+12=15
494+9=13
666+6=12
-1-36-1+(-36)=-37
-2-18-2+(-18)=-20
-3-12-3+(-12)=-15
-4-9-4+(-9)=-13
-6-6-6+(-6)=-12

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

Simplify

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

So our expression goes from and factors further to

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

So completely factors to

 Linear-equations/167967: put this equation in standard form: y=2x+91 solutions Answer 123796 by jim_thompson5910(28595)   on 2008-11-16 19:26:17 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Multiply EVERY term by -1 to make the "x" coefficient positive So the answer in standard form is .
 Linear-equations/167968: put this equation in standard form: y=2x+91 solutions Answer 123795 by jim_thompson5910(28595)   on 2008-11-16 19:25:56 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Multiply EVERY term by -1 to make the "x" coefficient positive So the answer in standard form is .
 Equations/167962: I have four more problems that I am struggling with, help me. Solve for x. - 14 + x - 6 = 12 - 6 + 181 solutions Answer 123794 by jim_thompson5910(28595)   on 2008-11-16 19:23:19 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Combine like terms on the right side. Add to both sides. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the answer is
 Equations/167964: Solve for x. - 2(x + 4) + 5 = 2(x + 3) + 61 solutions Answer 123793 by jim_thompson5910(28595)   on 2008-11-16 19:22:19 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. Add to 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 answer is which in decimal form is .
 Linear-equations/167965: So if you have coordinates of: 1620,3 4860,9 that would be 9-4860/3-1620 which=-4851/-1617 slope=3 Am I right?1 solutions Answer 123792 by jim_thompson5910(28595)   on 2008-11-16 19:21:25 (Show Source): You can put this solution on YOUR website!I'm assuming that you're looking for the slope (and just the slope) right? Since we're dealing with the points (1620,3) and (4860,9), this means that , , , and Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is
 Inequalities/167887: 1.Is this ordered pair(-8,3) a solution of this inequality? 6x+y<-3 2.-18is less than or equal to3x-7less than or equal to-2 what is the solutuion? 1 solutions Answer 123774 by jim_thompson5910(28595)   on 2008-11-16 17:53:40 (Show Source): You can put this solution on YOUR website!# 1 Start with the given inequality. Plug in and . Multiply Add Since the inequality is true, this means that (-8,3) is a solution to the inequality. # 2 Start with the given compound inequality. Add 7 to ALL sides Add Divide all sides by 3. This is where the problem occurs: There is NO such number that is greater than AND less than So either there are no solutions, or you might have entered the problem incorrectly. So double check your book/worksheet.
 Distributive-associative-commutative-properties/167893: Use FOIL to multiply: (3x – 8)(x – 7) Help!!!1 solutions Answer 123770 by jim_thompson5910(28595)   on 2008-11-16 17:37:22 (Show Source): You can put this solution on YOUR website! 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. So FOILs to . In other words, .
 Problems-with-consecutive-odd-even-integers/167923: the sum of three consecutive odd numbers is 39.1 solutions Answer 123768 by jim_thompson5910(28595)   on 2008-11-16 17:34:14 (Show Source): You can put this solution on YOUR website!consecutive odd numbers follow the pattern 2x+1, 2x+3, 2x+5, etc So the equation is Start with the given equation. 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. Go back to the first number Plug in Multiply Add. So the first number is 11 ------------------- Go back to the second number Plug in Multiply Add. So the second number is 13 ------------------- Go back to the third number Plug in Multiply Add. So the third number is 15 ---------------------------------------------------------------------- Answer: So the consecutive odd integers are 11, 13 and 15 Check 11+13+15 = 39 39 = 39
 Exponential-and-logarithmic-functions/167904: Please help with this question "Express as a single logarithm and, if possible, simplity." 1. 2/5 log(a)x - 1/3 log(a) y 2. ln 2x + 3(1n x - ln y) Thank you.1 solutions Answer 123766 by jim_thompson5910(28595)   on 2008-11-16 17:29:57 (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 expression Rewrite the expression using the identity . In other words, take the coefficient that is in front of the logs and place them as exponents Combine the logs using the identity This next step is optional: Convert from exponent notation to radical notation. So the answer is (which is in exponent notation) or (which is in radical notation)
 Equations/167915: can you show me how to do this problem 2/3 x +1/6x=21 solutions Answer 123765 by jim_thompson5910(28595)   on 2008-11-16 17:23:35 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply EVERY term by the LCD to clear any fractions. Multiply and simplify. Combine like terms on the left side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the answer is which in decimal form is .
 Inequalities/167918: -2x-4<101 solutions Answer 123757 by jim_thompson5910(28595)   on 2008-11-16 16:52:29 (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 . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Equations/167919: solve 3x +4y = 8 for y1 solutions Answer 123756 by jim_thompson5910(28595)   on 2008-11-16 16:51:27 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce.
 Trigonometry-basics/167797: This question is from textbook Trigonometry: A Graphing Approach Find the solutions of the equation in the interval [0,2∏) cos(X/2)-sin(X)= 01 solutions Answer 123700 by jim_thompson5910(28595)   on 2008-11-15 23:25:22 (Show Source): You can put this solution on YOUR website!Let u=x/2. So this means that 2u=2(x/2)=x (ie 2u=x) cos(x/2)-sin(x)= 0 ... Start with the given equation cos(u)-= 0 ... Replace x/2 with u and x with 2u cos(u)-2sin(u)cos(u)= 0 ... Use the identity sin(2A) = 2sin(A)cos(A) cos(u)(1-2sin(u))= 0 ... Factor out the GCF cos(u) cos(u)=0 ... or ... 1-2sin(u)=0 ... Set each factor equal to zero Let's solve the first equation cos(u)=0 By taking the arccosine of both sides, we get u=pi/2 or u=3pi/2 But remember, we let u=x/2. So this means that x/2=pi/2 or x/2=3pi/2 Solving for x, we get x=pi or x=3pi (we must discard this solution as it is NOT in the given interval) So the first solution is x=pi ----------------- Now let's solve the second equation 1-2sin(u)=0 -2sin(u)=-1 ... Subtract 1 from both sides sin(u)=1/2 ... Divide both sides by -2 Taking the arcsine of both sides gives us u = pi/6 or u = 5pi/6 Once again, recall that we said that u = x/2. So x/2=pi/6 or x/2=5pi/6 So this means that the values of x are x=pi/3 or x=5pi/3 (both of which are within the given interval) ================================================== Answer: So the three solutions in the interval [0,2∏) are x=pi, x=pi/3 or x=5pi/3
 Miscellaneous_Word_Problems/167793: we use these formulas...S=CrC and S=R-R Bedroom set with a regular price of $1395.00 is on sale for$995.00. Find the discount rate .Round answer to the nearest tenth of a %.1 solutions Answer 123691 by jim_thompson5910(28595)   on 2008-11-15 22:32:16 (Show Source): You can put this solution on YOUR website!In this case, we'll use the discount formula . Also, take note that the regular price is and the selling price is . The goal is to find "r" Start with the given formula Plug in and Add to both sides. Subtract from both sides. Subtract. Divide both sides by 1395.00 to isolate "r" Divide. So the answer in decimal form is . Now multiply this number by 100 to get =28.67% So the discount rate (rounded to the nearest tenth) is 28.7%
 Miscellaneous_Word_Problems/167790: we are using this formula...S=C+rC and/or S=R-rR computer retailer uses a markup of 22%. Find the selling price of a computer game that costs the retailer $40.001 solutions Answer 123690 by jim_thompson5910(28595) on 2008-11-15 22:27:04 (Show Source): You can put this solution on YOUR website!Note: 22% = In this case, the cost to the retailer is and the percentage rate is . Start with the markup cost formula. Note: the other formula is used for discounts Plug in and . Multiply Add So if the cost to the retailer is$40.00 and they use a markup of 22%, then the selling price is \$48.80