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 Complex_Numbers/697194: If f(x) and g(x) are inverse functions what would [f(g(x)]^21 solutions Answer 429749 by jim_thompson5910(28595)   on 2012-12-28 17:55:06 (Show Source): You can put this solution on YOUR website!f(g(x)) = x if f and g are inverses, so [f(g(x))]^2 = x^2

1 solutions

Answer 429745 by jim_thompson5910(28595)   on 2012-12-28 16:59:03 (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor.

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
161+6=7
232+3=5
-1-6-1+(-6)=-7
-2-3-2+(-3)=-5

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

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

So doesn't factor at all (over the rational numbers).

So is prime.

 Money_Word_Problems/697176: How much would $500 invested at 6% interest compounded monthly be worth after 5 years? Round your answer to the nearest cent. Do not include units in your answer.1 solutions Answer 429728 by jim_thompson5910(28595) on 2012-12-28 15:27:20 (Show Source): You can put this solution on YOUR website! Start with the compound interest formula Plug in , (the decimal equivalent of 6%), and . Evaluate to get Add to to get Multiply and to get . Evaluate to get . Multiply and to get . Round to the nearest hundredth (ie to the nearest penny). So the answer is 674.43  Functions/697173: please assist me in finding the domain and range to the equation . . . 1 solutions Answer 429727 by jim_thompson5910(28595) on 2012-12-28 15:21:34 (Show Source): You can put this solution on YOUR website!You can't take the square root of a negative value. So the radicand must be non-negative (ie 0 or positive) Radicand is positive x - 1 is positive Domain: Set of all real x values such that Domain in set-builder notation: $\large \{x|x\in \mathbb{R},x \ge 1\}$ Domain in interval notation: $\large [1,\infty)$ ============================================================================= The range of in general is the set of all y values such that where 'a' is some positive number. Since k = 4, we know... Range: Set of all real y values such that Range in set-builder notation: $\large \{y|y\in \mathbb{R},y \ge 4\}$ Range in interval notation: $\large [4,\infty)$  Complex_Numbers/695823: Consider the complex number =e^(i π/3) . Write that complex number in rectangular form1 solutions Answer 429723 by jim_thompson5910(28595) on 2012-12-28 14:58:08 (Show Source): You can put this solution on YOUR website!e^(i π/3) = cis(π/3) e^(i π/3) = cos(π/3) + i*sin(π/3) e^(i π/3) = 1/2 + i*(sqrt(3)/2) e^(i π/3) = 1/2 + (sqrt(3)/2)*i Answer: e^(i π/3) = 1/2 + (sqrt(3)/2)*i  Polynomials-and-rational-expressions/697113: -22(x)^2+6(x)-51 solutions Answer 429719 by jim_thompson5910(28595) on 2012-12-28 14:46:35 (Show Source): You can put this solution on YOUR website!If you want to graph this, then use a graphing calculator to get the following  Polynomials-and-rational-expressions/697114: 9(a+1)^2-4(a-1)^21 solutions Answer 429718 by jim_thompson5910(28595) on 2012-12-28 14:45:14 (Show Source): You can put this solution on YOUR website! So simplifies to  test/697135: 2x3+6x2+5x+k1 solutions Answer 429717 by jim_thompson5910(28595) on 2012-12-28 14:43:22 (Show Source): You can put this solution on YOUR website!What do you want to do here? Please respost with the *full* instructions. Thanks.  Angles/697018: m < acb=55 the what is m < ecd1 solutions Answer 429716 by jim_thompson5910(28595) on 2012-12-28 14:42:33 (Show Source): You can put this solution on YOUR website!you're missing a lot of information (like a picture), so please repost with the full problem  Rational-functions/697089: 4/6-x + x^2/6-x=21 solutions Answer 429715 by jim_thompson5910(28595) on 2012-12-28 14:41:19 (Show Source): You can put this solution on YOUR website!4/(6-x) + x^2/(6-x)=2 (4 + x^2)/(6-x)=2 4 + x^2=2(6-x) 4 + x^2 = 12-2x 4 + x^2 + 2x - 12 = 0 x^2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x + 4 = 0 or x - 2 = 0 x = -4 or x = 2 Solutions: x = -4 or x = 2  Circles/697077: I have 100 points on a circle and connect every point with the other 99. What is the maximum number of intersection points I will have in the circle? I have figured out that I have 4950 chords. Two chords which is 4 points are needed to have an intersection. I am stuck on this. thanks Tyler1 solutions Answer 429637 by jim_thompson5910(28595) on 2012-12-27 20:51:36 (Show Source): You can put this solution on YOUR website!If you have n lines, then there will be a max of n C 2 intersections. So you will have 4950 C 2 = (4950*4949)/(2*1) = 12,248,775 intersections maximum.  Expressions-with-variables/697078: Simplifying Radicals-this is the problem (16a^8b^4)^1/4 and this is what I have come up with so far (16a^8b^4)^1/4 16a^8*1/4b^4*1/4 16a^8/4b^4/4 16a^2b This problem I am completely confused I'm not sure what to do with it. (16/81)^-1/41 solutions Answer 429635 by jim_thompson5910(28595) on 2012-12-27 20:44:05 (Show Source): You can put this solution on YOUR website!You have to apply the 1/4 to the 16 to get 16^(1/4) = 4th root of 16 = 2 So (16a^8b^4)^1/4 turns into 2a^2b  Linear-equations/696986: What is the name of a system of equations with one solution1 solutions Answer 429560 by jim_thompson5910(28595) on 2012-12-27 01:48:26 (Show Source): You can put this solution on YOUR website!If the system has one solution, then the system is consistent and independent.  expressions/696854: There is a heated Facebook debate going on over the answer to this problem: 6 divided by 2(1+2) (sorry, no "divided by" symbol on this pad!) Solving the brackets first, you get 6 divided by 2(3) The question is, is 2(3) the same thing as 2x3? Should the division be done first, because it comes first in left-to-right sequence? 3x3 = 9? Or should the bracketed item be distributed first? 6/6 = 1? https://www.facebook.com/photo.php?fbid=544784552198699&set=a.499338033410018.129037.499317933412028&type=11 solutions Answer 429396 by jim_thompson5910(28595) on 2012-12-25 20:34:56 (Show Source): You can put this solution on YOUR website!6/2(1+2) 6/2(3) ... First you add the terms in the parenthesis 3(3) ... Then you divide 6 by 2 to get 3 9 ... Finally, you multiply 3 and 3 to get 9. So you start with the P in PEMDAS (for parenthesis), then you move to the D in PEMDAS because that division is to the left of the multiplication. Multiplication and division are on the same level, which means that you evaluate from left to right. Finally, you move to M in PEMDAS because that's what is left. So the answer is 9. ----------------------------------------------------------------- Note: IF the problem was 6/(2(1+2)) then the answer would be 1 because the extra set of parenthesis tell us to multiply first, then divide. But that's not the case here.  Equations/693563: 3(x-5)=91 solutions Answer 429390 by jim_thompson5910(28595) on 2012-12-25 19:06:19 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is  Equations/696125: 10=2x +121 solutions Answer 429389 by jim_thompson5910(28595) on 2012-12-25 19:05:38 (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 right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is  Linear-equations/696786: Please solve this linear equation: -7a+2a=10 1 solutions Answer 429324 by jim_thompson5910(28595) on 2012-12-25 04:03:17 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is  Linear-equations/696787: Please help me solve this equation: c+7=-11 solutions Answer 429323 by jim_thompson5910(28595) on 2012-12-25 04:02:56 (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. ---------------------------------------------------------------------- Answer: So the solution is  test/696760: In looking at the properties of the Standard Normal Distribution below: Properties of the Standard Normal Distribution:  1. The total area under the normal curve is equal to 1.  2. The distribution is mounded and symmetrical; it extends indefinitely in both directions, approaching but never touching the horizontal axis.  3. The distribution has a mean of 0 and a standard deviation of 1.  4. The mean divides the area in half0.50 on each side.  5. Nearly all the area is between z = −3.00 and z = 3.00. Which of these properties does not necessarily apply to any normal distribution? 1 solutions Answer 429285 by jim_thompson5910(28595) on 2012-12-24 16:32:09 (Show Source): You can put this solution on YOUR website!Property 5) Nearly all the area is between z = −3.00 and z = 3.00 only applies to the standard normal distribution and only this distribution. Any other normal distribution will have different values where most of the distribution lies. So the answer is property 5.  Distributive-associative-commutative-properties/696723: 7x+4=5x+161 solutions Answer 429283 by jim_thompson5910(28595) on 2012-12-24 16:29:32 (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  Word_Problems_With_Coins/696720: find two consecutive even integers whose product is 2881 solutions Answer 429252 by jim_thompson5910(28595) on 2012-12-24 02:17:52 (Show Source): You can put this solution on YOUR website!x*(x+2) = 288 x^2 + 2x = 288 x^2 + 2x - 288 = 0 (x+18)*(x-16) = 0 x+18 = 0 or x-16 = 0 x = -18 or x = 16 So the two numbers are 16 and 18.  Linear_Algebra/696682: 4(2x-3)-3(3x-10)=11 find x.1 solutions Answer 429231 by jim_thompson5910(28595) on 2012-12-23 19:59:09 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. 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. ---------------------------------------------------------------------- Answer: So the solution is  Travel_Word_Problems/696681: use the formula d=rt to find the value of the missing variable. d=88 feet, t=22 seconds1 solutions Answer 429230 by jim_thompson5910(28595) on 2012-12-23 19:57:57 (Show Source): You can put this solution on YOUR website!d = rt 88 = r*22 88/22 = r 4 = r r = 4 ft/sec  Linear_Algebra/696679: 3(x+2)-2(3x-5)=10 find x.1 solutions Answer 429226 by jim_thompson5910(28595) on 2012-12-23 19:39:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. 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. ---------------------------------------------------------------------- Answer: So the solution is  Rational-functions/696678: Whats the vertical asymptote of g(X)=1/X+31 solutions Answer 429225 by jim_thompson5910(28595) on 2012-12-23 19:37:20 (Show Source): You can put this solution on YOUR website!Set the denominator equal to zero and solve for x x+3 = 0 x = -3 So the vertical asymptote is x = -3  decimal-numbers/696676: When the cost of a car is multiplied by 0.06 the result is$1720 find the cost of the car and show work1 solutions Answer 429222 by jim_thompson5910(28595)   on 2012-12-23 19:28:26 (Show Source): You can put this solution on YOUR website!x * 0.06 = 1720 x = 1720/0.06 x = 28,666.6666666667 x = 28,666.67 So the cost of the car is \$28,666.67
 Linear-systems/696675: I don't understand Linear Equations. My teacher does the notes too fast in class and I can't keep up with the lesson and then I don't understand it. What I do not understand is how you get the linear equation for two given points. How do you get the linear equation for "Write a linear equation for the line going through the points (-3, 105) and (6, -3"? 1 solutions Answer 429218 by jim_thompson5910(28595)   on 2012-12-23 19:15:03 (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 Reduce 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 Distribute Multiply Add 105 to both sides. Combine like terms. So the equation that goes through the points and is
 Linear-equations/696670: Find the slope of the line passing through the points (1980, 18000) and (2000, 42000). 1 solutions Answer 429214 by jim_thompson5910(28595)   on 2012-12-23 19:00:57 (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 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
 Equations/696672: y-11=1/2(x+2)for y 1 solutions Answer 429210 by jim_thompson5910(28595)   on 2012-12-23 18:42:45 (Show Source): You can put this solution on YOUR website!y-11=1/2(x+2) y = 1/2(x+2)+11 y = 1/2x+1/2(2)+11 y = 1/2x+2/2+11 y = 1/2x+1+11 y = 1/2x+12
 Linear_Algebra/696660: x-2(x-1)-x/2+11 solutions Answer 429207 by jim_thompson5910(28595)   on 2012-12-23 18:01:34 (Show Source): You can put this solution on YOUR website! Answer:
 test/696661: Solve algebraically for x: so there's a radical sign over 3x+1 and then +1 which is not included in the radical sign=x 3x+1+1=x *Radical sign is over 3x+1 Please help and thank you very much. I really appreciate it!1 solutions Answer 429206 by jim_thompson5910(28595)   on 2012-12-23 17:47:27 (Show Source): You can put this solution on YOUR website! or or ------------------------------------------------------- So the two *possible* answers are or However, only one of these solutions actually work (ie are actually solutions). You have to check to see if they work (which is something I leave for you to do)