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 Geometry_Word_Problems/151402: Simplify: 8[a – b(3- 4a)] – 6a[2-a(3-b)] Thank you so much for your help. 1 solutions Answer 111295 by jim_thompson5910(28717)   on 2008-08-09 16:51:58 (Show Source): You can put this solution on YOUR website! 8[a – b(3- 4a)] – 6a[2-a(3-b)] = 8[a – 3b+ 4ab] – 6a[2-3a+ab] = [8a – 24b+32ab] – [12a-18a^2+6a^2b] = 8a – 24b+32ab – 12a+18a^2-6a^2b = –24b+32ab-4a+18a^2-6a^2b 
 Quadratic_Equations/151404: How would I go about writing the quadratic function, in (standard) form, which has a vertex of (-6, 2) and passes through (5, 12)? The standard form is y= a(x-h)^2+k , so i would put -6 as h and 2 as k but from there I am stuck.1 solutions Answer 111294 by jim_thompson5910(28717)   on 2008-08-09 16:45:47 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in and Rewrite as Since the quadratic passes through (5, 12), this means that if you plug in , you will get . So we can plug in and to solve for "a" Plug in and Add Square 11 to get 121 Rearrange the terms Subtract 2 from both sides. Divide both sides by 121. So the value of "a" is This means that the equation is
 expressions/151406: Multiply: ((x^2+x-12)/(x^2-x-20))X((x^2+2x-35)/(x^2+9x+14))1 solutions Answer 111293 by jim_thompson5910(28717)   on 2008-08-09 16:39:48 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where , , , or
 Trigonometry-basics/151392: tan(pi/6 + pi/4)1 solutions Answer 111290 by jim_thompson5910(28717)   on 2008-08-09 15:26:19 (Show Source): You can put this solution on YOUR website! Start with the given expression. Use the identity to expand the expression. Using the unit circle, evaluate to get and evaluate to get Multiply Combine the fractions. Multiply the first fraction by the reciprocal of the second fraction. Cancel out the common terms. Simplify. Multiply the fraction by Combine the fractions. FOIL Combine like terms Factor out the GCF Reduce So
 Miscellaneous_Word_Problems/151389: The sum of two numbers is 41 and their difference is 14. Find the numbers. not sure but 2 + x - 14 = 411 solutions Answer 111288 by jim_thompson5910(28717)   on 2008-08-09 15:12:28 (Show Source): You can put this solution on YOUR website!"The sum of two numbers is 41" translates to and "their difference is 14" translates to So we have the system of equations: Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Notice how the y terms cancel out. Simplify. Divide both sides by to isolate . ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . So our answer is and . So the two numbers are and
 Expressions-with-variables/151383: ((a/(x+y))+(m/y))/(x/(a+m))1 solutions Answer 111281 by jim_thompson5910(28717)   on 2008-08-09 13:47:37 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply every term by the LCD to clear the inner denominators. Simplify Rearrange the terms. FOIL Distribute Combine like terms. ---------------------------------------------------- Answer: So simplifies to
 Polynomials-and-rational-expressions/151353: simplify: -16x^7y5 / -4x^2y^61 solutions Answer 111279 by jim_thompson5910(28717)   on 2008-08-09 13:38:06 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Remember, and Highlight the common terms. Cancel out the common terms. Simplify. Regroup. So simplifies to . In other words, where or
 Polynomials-and-rational-expressions/151382: divide x^3-y^3 by x-y 1 solutions Answer 111278 by jim_thompson5910(28717)   on 2008-08-09 13:33:26 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to In other words, where
 Graphs/151376: Graph y=2x-11 solutions Answer 111267 by jim_thompson5910(28717)   on 2008-08-09 12:26:50 (Show Source): You can put this solution on YOUR website! In order to graph this equation, we only need two points to create a straight line --------------------------------Let's find the first point-------------------------------- Start with the given equation Plug in (you can start with any number, but zero is the easiest number to work with since anything multiplied by zero is zero) Multiply and to get Subtract So when , we have the value . This means we have the first point --------------------------------Let's find the second point-------------------------------- Start with the given equation Plug in Multiply and to get Subtract So when , we have the value . This means we have the second point ------------------------------------------------------------------------------------------------ So we have the two points: and Now plot these two points on a coordinate system Now draw a straight line through the two points. This line is the graph of Graph of through the two points and
1 solutions

Answer 111263 by jim_thompson5910(28717)   on 2008-08-09 11:39:29 (Show Source):
You can put this solution on YOUR website!
Let

So the expression goes from to

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 :
1,2,4,5,8,10,20,40
-1,-2,-4,-5,-8,-10,-20,-40

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

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

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

First NumberSecond NumberSum
1-401+(-40)=-39
2-202+(-20)=-18
4-104+(-10)=-6
5-85+(-8)=-3
-140-1+40=39
-220-2+20=18
-410-4+10=6
-58-5+8=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

Plug in

Distribute

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

So factors to .

In other words,

Note: you can check the answer by expanding to get .

 Graphs/151369: graph of the line through (3, 2) with slope 1/21 solutions Answer 111261 by jim_thompson5910(28717)   on 2008-08-09 11:33:43 (Show Source): You can put this solution on YOUR website! If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Distribute Multiply and to get Add 2 to both sides to isolate y Combine like terms and to get (note: if you need help with combining fractions, check out this solver) ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line with a slope of which goes through the point (,) is: which is now in form where the slope is and the y-intercept is Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver) Graph of through the point (,) and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
 Graphs/151365: graph linear equation y = 2x - 11 solutions Answer 111258 by jim_thompson5910(28717)   on 2008-08-09 11:31:07 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 2 and the run is 1. This means that to go from point to point, we can go up 2 and over 1 So starting at , go up 2 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Graphs/151372: write the equation of y = 1/3x - 2 in standard form using only integers and a positive coefficient of x1 solutions Answer 111257 by jim_thompson5910(28717)   on 2008-08-09 11:21:26 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by 3 to eliminate the fractions. Distribute and multiply. Subtract from both sides. Rearrange the terms. Multiply both sides by -1. This will make the x coefficient positive. Distribute and multiply. So the equation is now in standard form where , and
 Graphs/151371: 4. Find the slope of the line that contains the points (-11,5) and (5,-8) 1 solutions Answer 111256 by jim_thompson5910(28717)   on 2008-08-09 11:16:01 (Show Source): You can put this solution on YOUR website! Start with the slope formula. Plug in , , , , , Subtract from to get Subtract from to get So the slope of the line that goes through the points and is
 Radicals/151325: 5 square root of x + 1 = 3 2/3 = 2 - 5x-3 over x-1 solve algebraically thanks 1 solutions Answer 111241 by jim_thompson5910(28717)   on 2008-08-08 21:53:58 (Show Source): You can put this solution on YOUR website!I'll do the first one to get you started. Start with the given equation. Divide both sides by 5. Square both sides. Square to get Subtract 1 from both sides. Combine the fractions. So the solution is which approximates to
 Matrices-and-determiminant/151324: I am lost with this assignment, HELP! I do not understand hwo these are answered! 4. A group of students decides to sell pizzas to help raise money for their senior class trip. They sold pepperoni for $12, sausage for$10, and cheese for $8. At the end of their sales the class sold a total of 600 pizzas and made$5900. The students sold 175 more cheese pizzas than sausage pizzas. Set up a system of three equations and three unknowns, use an augmented matrix to solve, and show all work to receive full credit. A. What are the three unknowns? B. Write a separate equation representing each of the first three sentences. C. Determine the augmented matrix that represents the three equations. D. Solve for the matrix. Show all work to receive full credit. E. How many of each type of pizza were sold? 1 solutions Answer 111240 by jim_thompson5910(28717)   on 2008-08-08 21:50:26 (Show Source): You can put this solution on YOUR website!a) Let x=# of pepperoni sold, y=# of sausage sold, and z=# of cheese sold b) Since there are 3 unknowns, we need 3 equations: Equation #1: First, since they sold "pepperoni for $12, sausage for$10, and cheese for $8" and collected$5,900, this means that Equation #2: Also, we know that the students sold 600 pizzas total. So this means that the sum of all of the pizzas sold was 600. So this translates to . Equation #3: Finally, since they sold "175 more cheese pizzas than sausage pizzas", this makes the equation Getting all of the variables to one side for equation 3 gives us: So we have the system c) This means that we have the augmented matrix matrix d) Solution was generated by the Linear Algebra Toolkit ============================================================= Answer: So the solutions are , , and (these values form the right hand column of the augmented matrix). So this means that they sold 225 pepperoni pizzas, 100 sausage pizzas, and 275 cheese pizzas.
 Linear-systems/151320: Hello may someone please elp me with this question im very confused! The length of a rectangle is 3 in. more than the width. The perimeter of the rectangle is 24 in. I THINK THAT I AHVE FOUND THE VARIABLES LENGTH=3iN. WIDTH=24iN.(AM I RIGHT???) What is the expression for the length in terms of the width? What is the length of the rectangle? 1 solutions Answer 111236 by jim_thompson5910(28717)   on 2008-08-08 21:26:58 (Show Source): You can put this solution on YOUR website!Let x=width and y=length Since the "length of a rectangle is 3 in. more than the width", this means that . Also, because the "perimeter of the rectangle is 24 in", this tells us that Start with the formula for the perimeter of a rectangle Plug in and Distribute Subtract 6 from both sides. Combine like terms. Divide both sides by 4. Reduce. So the first part of the answer is or . This means that the width is 4.5 inches. Go back to the first equation Plug in Combine the fractions. So the second part of the answer is or . This means that the length is 7.5 inches. ======================================================= Answer: So the width is 4.5 inches and the length is 7.5 inches
 Quadratic-relations-and-conic-sections/151316: Please help me divide and simplify: (3x^4 - 2x^3 + 16x - 192) / (x^2 - 8)1 solutions Answer 111234 by jim_thompson5910(28717)   on 2008-08-08 21:18:08 (Show Source): You can put this solution on YOUR website!This solution was generated from the Long Division Calculator So
 Distributive-associative-commutative-properties/151323: how would you... A.) use the distributive property to solve and create a binomial to set up the FOIL method B.) Solve with the FOIL method could you break it down step by step? 4x(x^2-2x+5)1 solutions Answer 111233 by jim_thompson5910(28717)   on 2008-08-08 21:13:22 (Show Source): You can put this solution on YOUR website!This problem does not involve FOILing, but involves distribution (you use FOIL when you have two binomials). So I would double check the problem. Anyways, here's how you would simplify the problem. Start with the given expression. Distribute. Multiply and to get Multiply and to get Multiply and to get So distributes and simplifies to In other words,
 Exponential-and-logarithmic-functions/151295: - How many months does it take for $1000 to grow to$1500 in an account paying 12% compounded monthly?1 solutions Answer 111196 by jim_thompson5910(28717)   on 2008-08-08 13:52:24 (Show Source): You can put this solution on YOUR website! Start with the compound interest formula. Plug in , , (note: 12%=0.12) and Divide both sides by 1000. Reduce Divide to get 0.01 Add 1 to 0.01 to get 1.01 Take the log of both sides. Rewrite the right side using the identity Divide both sides by . So the answer is which approximates to So it takes about 3.4 years (or 40.8 months) to go from $1,000 to$1,500