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 Complex_Numbers/219558: simplify (3+2i)(2-5i)1 solutions Answer 165082 by jim_thompson5910(28595)   on 2009-09-30 13:31:19 (Show Source): You can put this solution on YOUR website! Start with the given expression. FOIL. Multiply. Replace with -1. Multiply. Combine like terms. So
 Signed-numbers/219564: Simplify: I'm lost when it comes to this problem, I just dont understand how I should simplify it.1 solutions Answer 165080 by jim_thompson5910(28595)   on 2009-09-30 13:29:10 (Show Source): You can put this solution on YOUR website!Any number divided by itself is simply 1. So this means
 Equations/219562: Can you show me how to work this problem. It's equations containing decimals. 0.24+0.18x=0.08x-0.061 solutions Answer 165078 by jim_thompson5910(28595)   on 2009-09-30 13:22:02 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by 100 to clear out the decimals. Note: this is the same as moving the decimal point 2 spots to the right on every number. 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 . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Finance/219555: what interest rate is required for an investment with continuously compounded interest to double in 6 years1 solutions Answer 165077 by jim_thompson5910(28595)   on 2009-09-30 13:20:28 (Show Source): You can put this solution on YOUR website! Start with the continuous compounding interest formula. Plug in , , and . Rearrange the terms. Divide both sides by . Divide to get . Take the natural log of both sides. Pull down the exponent using the identity . Evaluate to get . Multiply. Evaluate to get Divide both sides by to isolate 'r' Divide to get Rearrange the equation. Round to the nearest ten-thousandth. So an interest rate of about 11.55% (don't forget to multiply by 100 to convert the decimal to a percent) will make the initial investment of $250 grow to$500 in 6 years.
 Signed-numbers/219553: (10)(-9)(8)(-7)(6)(-5)0 If I try to solve this the way I think it should be the answer comes out as 0 and I'm not sure if thats correct and if I'm doing it the right way. Please help if you can, thank you.1 solutions Answer 165073 by jim_thompson5910(28595)   on 2009-09-30 13:12:04 (Show Source): You can put this solution on YOUR website!You are correct. Anything multiplied by zero is zero. So you could have a million terms multiplied here, but just multiply that whole mess by zero will get you zero (regardless of what you got beforehand).
 Trigonometry-basics/219547: express 2(cos300 dwgrees + i sin300 degrees) in rectangular form1 solutions Answer 165072 by jim_thompson5910(28595)   on 2009-09-30 13:09:00 (Show Source): You can put this solution on YOUR website!Remember that any point in polar form is basically in the form . To convert to rectangular form , just use the equations and
 Linear-equations/219545: Im not sure who will answer this question so thank you all in advance!! Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer. Create an equation of a nonlinear function and provide two inputs to evaluate. Much Appreciated.. Thank You1 solutions Answer 165069 by jim_thompson5910(28595)   on 2009-09-30 13:04:01 (Show Source): You can put this solution on YOUR website!Are all linear equations functions? No. Here's an example: Ex: The equation x=5 is linear (since it graphs a straight line) but it is a vertical line. So it fails the vertical line test which means that x=5 is NOT a function.
 Money_Word_Problems/219534: I=Prt P=740, R=6% T=1year whats the answere1 solutions Answer 165068 by jim_thompson5910(28595)   on 2009-09-30 12:50:00 (Show Source): You can put this solution on YOUR website! Start with the simple interest formula. Plug in , (note: 0.06 is the decimal equivalent of 6%), . Multiply and to get . Multiply and to get . So the simple interest is $44.40  Distributive-associative-commutative-properties/219532: Multiply (x^4 – 4x^2 – 5)(x^2 – x + 2)1 solutions Answer 165066 by jim_thompson5910(28595) on 2009-09-30 12:42:23 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Distribute. Multiply. Now combine like terms. So expands to . In other words, .  Trigonometry-basics/219521: write 3x-6y= -14 in polar form.round to the nearest degree1 solutions Answer 165061 by jim_thompson5910(28595) on 2009-09-30 12:32:36 (Show Source): You can put this solution on YOUR website!Hint: Use the identities and to find an equation in terms of 'r' and . From there, solve for 'r' and simplify.  Miscellaneous_Word_Problems/219517: When Lyle goes to the grocery store, he always leaves with 4, 5, or 6 bags of groceries. Each bag always weighs between 1 and 7 pounds. What is the difference between Lyle’s heaviest possible grocery purchase and his lightest possible grocery purchase? The answer I got is 42...I know it's incorrect...help. 1 solutions Answer 165060 by jim_thompson5910(28595) on 2009-09-30 12:28:26 (Show Source): You can put this solution on YOUR website!Worst Case (ie heaviest load): He leaves with 6 bags (the most he carries) that are 7 pounds each (the heaviest they get). How much do they weigh total? They weigh pounds total. Now compare this to the best case... Best Case (lightest load possible): He leaves with 4 bags (the smallest amount he carries) weighing 1 pound each (the lightest they get). In total, they weigh 4*1=4 pounds. The difference between the heaviest and the lightest is then: 42-4=38 So the difference between Lyle’s heaviest possible grocery purchase and his lightest possible grocery purchase is 38 pounds.  Money_Word_Problems/219513: Peter borrowed$12,000, which he paid back after 4 years at a simple interest rate of 8%. Find the total amount that Peter paid back.1 solutions Answer 165059 by jim_thompson5910(28595)   on 2009-09-30 12:22:24 (Show Source): You can put this solution on YOUR website!Recall that the simple interest formula is where 'I' is the interest, P is the balance/principal, 'r' is the interest rate, and 't' is the time in years. So let's first find out how much interest he paid: Start with the given formula. Plug in , , and Multiply So he paid $3,840 in interest alone. Now just add this to the amount he borrowed (since he has to pay that back too) to get: So Peter paid back$15,840 total.
 real-numbers/219508: Consider the system y = a and x = b where a and b are real numbers. Is this system dependent or independent? Is it consistent or inconsistent? Describe the system. If it is consistent, what is the solution?1 solutions Answer 165058 by jim_thompson5910(28595)   on 2009-09-30 12:15:30 (Show Source): You can put this solution on YOUR website!This system is consistent and independent since the solution is (b,a). Example: If x=2 and y=3 the solution is (2,3) which means that it is consistent and independent.
 Quadratic_Equations/219498: What is the answer of the following problem? 2 + (3/(2+(3/(2+(3/(2+..).))))) = Thank you for your help1 solutions Answer 165057 by jim_thompson5910(28595)   on 2009-09-30 12:07:47 (Show Source): You can put this solution on YOUR website!Let Take note how the bottom portion of the fraction is which is equal to 'y' (continue it out and you'll see it). I.e. the same expression is nested inside the larger expression. This means that Or in short Now just solve for 'y' to find the value of Note: you will get two solutions, but you're only going to focus on the positive solution.
 Inequalities/219502: 9/5c -32>-31 Please give me step by step, I just can't get this into my thick head! Thank you1 solutions Answer 165055 by jim_thompson5910(28595)   on 2009-09-30 11:55:38 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Multiply EVERY term by the LCD to clear any fractions. Multiply and simplify. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is which approximates to
Distributive-associative-commutative-properties/219494: x² - 4xy – 12y² and a² - 25a factor completely (seperate problems)

1 solutions

Answer 165053 by jim_thompson5910(28595)   on 2009-09-30 11:53:44 (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -12 respectively.

Now multiply the first coefficient 1 and the last coefficient -12 to get -12. Now what two numbers multiply to -12 and add to the middle coefficient -4? Let's list all of the factors of -12:

Factors of -12:
1,2,3,4,6,12

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

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

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

Now which of these pairs add to -4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -4

First NumberSecond NumberSum
1-121+(-12)=-11
2-62+(-6)=-4
3-43+(-4)=-1
-112-1+12=11
-26-2+6=4
-34-3+4=1

From this list we can see that 2 and -6 add up to -4 and multiply to -12

Now looking at the expression , replace with (notice combines back 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

 Money_Word_Problems/219496: How long does it take your money in your savings account to double at 8% interest rate using the formula A=Pe^rt ? 1 solutions Answer 165051 by jim_thompson5910(28595)   on 2009-09-30 11:44:34 (Show Source): You can put this solution on YOUR website! Start with the continuous compounding interest formula. Plug in (since we want to double our investment), and (note: 0.08 is the decimal equivalent of 8%). Divide both sides by . Reduce. Take the natural log of both sides. Pull down the exponent using the identity . Evaluate to get . Multiply. Evaluate to get Divide both sides by to isolate 't' Divide to get Rearrange the equation. Round to the nearest hundredth. So it will take about 8.66 years for an initial investment to double if it is compounded continuously at an interest rate of 8%.
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 Miscellaneous_Word_Problems/219159: How could you order (mixed nums) 3 1/4, 3 1/3, 3 2/7, and 3 1/8 from least to greatest without writing them as improper fractions? Explain your reasoning. Then order the mixed numbers from least to greatest. I like math but i hate mixed numbers mostly in word problems... word problems is my weak spot.... thanks! -CaMiLLe-1 solutions Answer 164868 by jim_thompson5910(28595)   on 2009-09-29 18:56:28 (Show Source): You can put this solution on YOUR website!Hint: Since they all have whole parts of 3, just compare the fraction parts. For example, instead of comparing and (to see which one is bigger), just compare and . Do this with all possible pairs. Does this make sense? If not, just ask me or repost.
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 Numbers_Word_Problems/219152: if five is subtracted from twice a number and this difference is tripled, the result is one more than four times the number. find the number. Domain:{8, 9, 10} I tried to set the problem up as: 2x-5+3(2x-5)=1+4x where the first number is 2x-5 and the 2ns number is 3(2x-5) what did I do wrong?1 solutions Answer 164862 by jim_thompson5910(28595)   on 2009-09-29 18:46:07 (Show Source): You can put this solution on YOUR website!The equation should be . We're not looking for two numbers. We just want to find that one unknown value of 'x'. Start with the given equation. Distribute. 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 which means that the unknown number is 8.
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 Graphs/219079: identify the slope and intercepts of 2x-6y=181 solutions Answer 164825 by jim_thompson5910(28595)   on 2009-09-29 17:34:56 (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. So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point
Probability-and-statistics/219077: Write this fraction in lowest terms? 110/100
1 solutions

Answer 164824 by jim_thompson5910(28595)   on 2009-09-29 17:34:08 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Reducing Fractions Calculator In order to reduce , the numerator and denominator must share a common factor. This common number must evenly divide into both of them without any remainder or decimal. In order to completely reduce the fraction, you must divide the numerator and the denominator by the greatest common factor (GCF). The GCF of and is (note: click here if you need help with finding the GCF). So divide both the numerator and denominator by In other words, to reduce the fraction you do this Plug in the numerator, denominator, and the GCF Now divide 110 by 10 to get 11. This is now the new numerator. Now divide 100 by 10 to get 10. This is now the new denominator. So This means that reduces to In other words,