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 Exponential-and-logarithmic-functions/332248: Suppose that $2000 is invested at a rate of 6% per year compounded continuously. What is the balance after 1 yr? After 2 yrs?1 solutions Answer 238116 by jim_thompson5910(28476) on 2010-08-16 13:08:04 (Show Source): You can put this solution on YOUR website! Recall that the formula for continuous compounding interest is where A is the return, P is the principal (amount invested), r is the interest rate (in decimal form) and t is the time in years. Since "$2000 is invested at a rate of 6% per year compounded continuously", we know that and (the decimal equivalent of 6%). Now let's compute the return when (ie find the balance after one year) Start with the continuous compounding formula. Plug in , , and . Multiply and to get . Raise 'e' (which is approximately 2.71828) to the power to get (this value is approximate). Multiply and to get . Round to the nearest hundredth (ie to the nearest penny). So after 1 year, you'll have about $2,123.67 ----------------------------------------------------------------------------- Now let's compute the return when (ie find the balance after two years) Start with the continuous compounding formula. Plug in , (the decimal equivalent of 6%), and . Multiply and to get . Raise 'e' (which is approximately 2.71828) to the power to get (this value is approximate). Multiply and to get . Round to the nearest hundredth (ie to the nearest penny). So after two years, you'll have$2,254.99
 Unit_Conversion_Word_Problems/332255: What is the cost of 33 pieces of paneling 2'-0" wide, and 5'-0" long at a cost of $.30 per square foot?1 solutions Answer 238115 by jim_thompson5910(28476) on 2010-08-16 13:03:34 (Show Source): You can put this solution on YOUR website!First find the area of one panel. Area = Length * Width = 5*2 = 10 square feet. So the area of one panel is 10 square feet. Now multiply this by 33 to find the total area of the 33 panels: 33*10 = 330 So the total area of 33 panels is 330 square feet. Now multiply this total area by the cost per square foot to get: 330*0.30 = 99.00 So the total cost is$99.00
 sets-and-operations/332254: If traingle AEF is equiangular, then m is the answer always, sometimes, or never1 solutions Answer 238114 by jim_thompson5910(28476)   on 2010-08-16 13:00:34 (Show Source): You can put this solution on YOUR website!Hint: All equiangular triangles have equal angles (it's exactly what "equiangular" means). Also, all triangles have angles which add up to 180 degrees.
Divisibility_and_Prime_Numbers/332239: factor 2x^2 -240x+5500
1 solutions

Answer 238103 by jim_thompson5910(28476)   on 2010-08-16 11:17:35 (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 :
1,2,5,10,11,22,25,50,55,110,125,250,275,550,1375,2750
-1,-2,-5,-10,-11,-22,-25,-50,-55,-110,-125,-250,-275,-550,-1375,-2750

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

These factors pair up and multiply to .
1*2750 = 2750
2*1375 = 2750
5*550 = 2750
10*275 = 2750
11*250 = 2750
22*125 = 2750
25*110 = 2750
50*55 = 2750
(-1)*(-2750) = 2750
(-2)*(-1375) = 2750
(-5)*(-550) = 2750
(-10)*(-275) = 2750
(-11)*(-250) = 2750
(-22)*(-125) = 2750
(-25)*(-110) = 2750
(-50)*(-55) = 2750

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

First NumberSecond NumberSum
127501+2750=2751
213752+1375=1377
55505+550=555
1027510+275=285
1125011+250=261
2212522+125=147
2511025+110=135
505550+55=105
-1-2750-1+(-2750)=-2751
-2-1375-2+(-1375)=-1377
-5-550-5+(-550)=-555
-10-275-10+(-275)=-285
-11-250-11+(-250)=-261
-22-125-22+(-125)=-147
-25-110-25+(-110)=-135
-50-55-50+(-55)=-105

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

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

So simply factors to

In other words, .

 Matrices-and-determiminant/332233: Can someone show me how to use the elimination method to solve this problem. The solution says it is (4y+1,y) for any real numbers. I just don't kow how they go it. Thanks 2x-8y=2 3x-12y=31 solutions Answer 238101 by jim_thompson5910(28476)   on 2010-08-16 10:53:46 (Show Source): You can put this solution on YOUR website!It turns out that this system has an infinite number of solutions. Basically one equation is just the other in a different form. So to solve this "system", we just need to solve for one variable. So what the book did was solve for 'y' (in either equation). So take and solve for x to get ----> ----> So every 'x' coordinate of the solution is simply equal to 4 times the y coordinate plus one. So recall that any solution of a system is of the form (x,y) and we know that , this means that the solution is (4y+1,y) Note: there are other ways to display the solution, but you essentially get the same thing.
 Triangles/332234: the perimeter of an isosceles triangle is 72 inches. the opposite side of the vertex is 18 inches what is the length in inches of the other two sides?1 solutions Answer 238100 by jim_thompson5910(28476)   on 2010-08-16 10:47:52 (Show Source): You can put this solution on YOUR website!Hint: Let x = length of one of the remaining sides. Since the two remaining sides are actually equal, this means that the two sides are both x inches long. So we know that . Simply solve for x to find the unknown side lengths.
 test/332162: i really need help with this three last questions to finish my last exam. please please help. 3x²=-2x+5 y=-x²+2x-1 y=x²-5x+6 thank you so much in advance!!!1 solutions Answer 238060 by jim_thompson5910(28476)   on 2010-08-15 22:48:21 (Show Source): You can put this solution on YOUR website!Please only post one problem at a time and the full instructions. Thanks.
Graphs/332134: find the x and y intercepts
3x+4y=12
1 solutions

Answer 238038 by jim_thompson5910(28476)   on 2010-08-15 20:54:32 (Show Source):
You can put this solution on YOUR website!

#### x-intercept

To find the x-intercept, plug in and solve for x

Plug in .

Multiply and 0 to get 0.

Simplify.

Divide both sides by to isolate .

Reduce.

So the x-intercept is .

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

#### y-intercept

To find the y-intercept, plug in and solve for y

Plug in .

Multiply and 0 to get 0.

Simplify.

Divide both sides by to isolate .

Reduce.

So the y-intercept is .

 Radicals/332101: Simplify ∛512 Please show each step Thank you 1 solutions Answer 238029 by jim_thompson5910(28476)   on 2010-08-15 19:47:06 (Show Source): You can put this solution on YOUR website! which means that
 Inequalities/332085: Solve the inequality 5-3(10-7a)>4(2a+10)1 solutions Answer 238015 by jim_thompson5910(28476)   on 2010-08-15 18:11:36 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Combine like terms on the left 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 solution is
 Inequalities/332083: Solve the inequality 3-x<21 solutions Answer 238014 by jim_thompson5910(28476)   on 2010-08-15 18:10:21 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from 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 solution is
6x^2-13x-5
1 solutions

Answer 238010 by jim_thompson5910(28476)   on 2010-08-15 18:02:41 (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
1-301+(-30)=-29
2-152+(-15)=-13
3-103+(-10)=-7
5-65+(-6)=-1
-130-1+30=29
-215-2+15=13
-310-3+10=7
-56-5+6=1

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).

6x^2-11x+3
1 solutions

Answer 238009 by jim_thompson5910(28476)   on 2010-08-15 18:02:17 (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 :
1,2,3,6,9,18
-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
1181+18=19
292+9=11
363+6=9
-1-18-1+(-18)=-19
-2-9-2+(-9)=-11
-3-6-3+(-6)=-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).

 Linear-systems/332067: I need help. Find the equation of a line that is perpendicular to y=-x + 3 and passes through the point(-1, 2).1 solutions Answer 238005 by jim_thompson5910(28476)   on 2010-08-15 17:52:18 (Show Source): You can put this solution on YOUR website! We can see that the equation has a slope and a y-intercept . Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is . Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point . Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Add 2 to both sides. Combine like terms. Simplify. So the equation of the line perpendicular to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the perpendicular line (green) through the point .
 Polynomials-and-rational-expressions/332064: Simplify by removing factors of 1 n^2-1/(n+1)^21 solutions Answer 238004 by jim_thompson5910(28476)   on 2010-08-15 17:50:57 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor the numerator. Expand the denominator. Highlight the common terms. Cancel out the common terms. Simplify So simplifies to In other words, where
 Linear-systems/332066: I need help. Solve the system of equations. 4x-6y=-26 -2x+3y=13 x=?1 solutions Answer 238003 by jim_thompson5910(28476)   on 2010-08-15 17:48:20 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the second equation by 2. Distribute and multiply. So we have the new system of equations: Now 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. Simplify. Since is ALWAYS true, this means that there are an infinite number of solutions. So the system is consistent and dependent.
 Radicals/332063: I need help with this question. Solve for x. 8xy^2-2x=61 solutions Answer 238002 by jim_thompson5910(28476)   on 2010-08-15 17:47:05 (Show Source): You can put this solution on YOUR website! Start with the given equation. Factor out the GCF 2x Divide both sides by 2. Reduce. Divide both sides by . So the solution is
Polynomials-and-rational-expressions/332062: so im supposed to factor this trinomial
5x^2 - 5x - 30
but the teacher wants in in simplest factored form. my choices are
a 5(x - 2)(x + 3)
b (5x + 10)(x - 3)
c 5(x + 2)(x - 3)
or d prime polynomial.
now i notice that B and C are pretty much the same. which is factored more completely?
1 solutions

Answer 238001 by jim_thompson5910(28476)   on 2010-08-15 17:44:29 (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
-1,-2,-3,-6

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

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

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

First NumberSecond NumberSum
1-61+(-6)=-5
2-32+(-3)=-1
-16-1+6=5
-23-2+3=1

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).

So the answer is C (the order of the factors doesn't matter)

The difference between B and C is that if you factor 5 from 5x+10, you get 5(x+2)

Functions/332057: I have a problem that says make an input output table for the function. Use 0,1,2, and 3 as the domain.
The problem is y=3x+2
Can anyone help me figure this out and explain how you did it?
1 solutions

Answer 237999 by jim_thompson5910(28476)   on 2010-08-15 17:29:35 (Show Source):
You can put this solution on YOUR website!
When ,

When ,

When ,

When ,

So we have the table

Input(x)Output(y)
02
15
28
311

 Functions/332054: By looking at an input and output chart with numbers how can you tell if it is a function or not?1 solutions Answer 237996 by jim_thompson5910(28476)   on 2010-08-15 17:12:58 (Show Source): You can put this solution on YOUR website!If one input generates more than one output, then the relation is NOT a function.
 Linear-equations/332041: graph y=4 and x=01 solutions Answer 237987 by jim_thompson5910(28476)   on 2010-08-15 16:41:56 (Show Source): You can put this solution on YOUR website!Simply graph the horizontal line at y=4 (green line) and a vertical line at x=0 (ie over the y axis) (blue line)
 Length-and-distance/332042: (b,4) (2,-1) distance = 5 i need the steps for distance when the distance is given with a variable 1 solutions Answer 237986 by jim_thompson5910(28476)   on 2010-08-15 16:38:58 (Show Source): You can put this solution on YOUR website!Hint: The distance formula is So plug in the given info to get and solve this equation for 'b'.
 Graphs/332029: graph: y=x2-31 solutions Answer 237973 by jim_thompson5910(28476)   on 2010-08-15 16:05:46 (Show Source): You can put this solution on YOUR website!Start with the graph of Now move it down 3 units to graph (new graph shown in green) So the graph of is
 Inequalities/332016: -3<2x+1<51 solutions Answer 237972 by jim_thompson5910(28476)   on 2010-08-15 16:03:59 (Show Source): You can put this solution on YOUR website! Start with the given compound inequality. Subtract from all sides. Combine like terms on the left side. Combine like terms on the right side. Divide all sides by 2. Reduce. So our answer is
 Equations/332026: 3-6t=5t-191 solutions Answer 237971 by jim_thompson5910(28476)   on 2010-08-15 16:02:29 (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
 Distributive-associative-commutative-properties/330439: i am in algebra 3-4 and its my first day and the question is identify the property shown and the problem is 24x1=24 i dont understand what there asking for 1 solutions Answer 236842 by jim_thompson5910(28476)   on 2010-08-09 23:59:25 (Show Source): You can put this solution on YOUR website!This is the multiplicative identity property. Ie, it says that if you multiply any number by 1, the result is that same number.
 Radicals/330436: Hello, Need to find the exact and approximate solutions to three decimal places for the following: (x-6)^2=20. I am unable to solve, and have even tried using Algebrator, but cannot interpret. Thanks!1 solutions Answer 236837 by jim_thompson5910(28476)   on 2010-08-09 23:31:26 (Show Source): You can put this solution on YOUR website! Start with the given equation. Take the square root of both sides. or Break up the "plus/minus" to form two equations. or Simplify the square root. or Add to both sides. -------------------------------------- Answer: So the solutions are or . and they approximate to or
 Complex_Numbers/330420: Can I get more assistance with this problem, thanks! Find the quotient and remainder when x3 + 3x2 – x – 7 is divided by x – 21 solutions Answer 236827 by jim_thompson5910(28476)   on 2010-08-09 22:26:43 (Show Source): You can put this solution on YOUR website!Perform polynomial long division to get So we can see that the quotient is and the remainder is
 Quadratic_Equations/330417: begin with ax2+bx+c=0 and derive the quadractic formula by completing the square1 solutions Answer 236822 by jim_thompson5910(28476)   on 2010-08-09 22:04:25 (Show Source): You can put this solution on YOUR website!See this page and this page for explanations (you'll have to scroll down a bit).
 Functions/330410: i was studying for the ACT compass test and i am having problems with functions. the question was: if f(4)=0 and f(6)=6 then which of the following could represent f(x)? The answer is 3x-12, but i do not understand how to get to that answer, what does the 4 and 6 have to do with it? thank you ahead of time1 solutions Answer 236814 by jim_thompson5910(28476)   on 2010-08-09 21:45:46 (Show Source): You can put this solution on YOUR website!Hint: If f(4)=0, then we have the point (4,0). Recall that f(x) is really 'y'. So if f(4)=0, then x=4 and y=0. Similarly, if f(6)=6, then we have the second point (6,6)