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 Quadratic_Equations/118654: What term in the sequence (1.6,1.2,0.8,0.4,...) is -38.4 ? I guessed 99 but was marked wrong . I don't know how to do this , please help me :)1 solutions Answer 86780 by Fombitz(13828)   on 2008-01-04 09:15:43 (Show Source): You can put this solution on YOUR website!Look at the terms and see if you can determine the pattern. First term = 1.6 Second term = 1.6-0.4 = 1.2 Third term = 1.6-0.4-0.4 = 0.8 Fourth term = 1.6-0.4-0.4-0.4 = 0.4 I think you can see the pattern. Nth term = 1.6 - 0.4*(N-1) Now that you have the formula, set it equal to the number to find N. Subtract 1.6 from both sides of the equation. Divide both sides by 0.4. Check your answer with your original formula. 101st term = 1.6 - 0.4(101-1)=1.6-40.0=-38.4. The answer checks out.
 Quadratic_Equations/118651: One number is 10 greater than the other number. Find the two numbers such that their product is a minimum. What is the product?1 solutions Answer 86779 by Fombitz(13828)   on 2008-01-04 09:06:48 (Show Source): You can put this solution on YOUR website!Let N be the first number. Then N+10 is the second number. Their product is N(N+10). To find a minimum, set the derivative of P with respect to N equal to zero. Now set it equal to zero. Graphically, the product function N(N+10) shows the same result. Here x=N and y=N(N+10). The first number is -5. The second number is 5. Their product is -25.
 Functions/118517: if x+7is a factor of f(x), then what is the value of f(-7)1 solutions Answer 86637 by Fombitz(13828)   on 2008-01-03 10:30:36 (Show Source): You can put this solution on YOUR website!If (x+7) is a factor of f(x), then where g(x) is another function of x.
 Linear_Equations_And_Systems_Word_Problems/118195: I need help bad! Find values for m and b in the following system so that the solution to the system is (-3,4), 5x + 7y = b mx + y =221 solutions Answer 86303 by Fombitz(13828)   on 2007-12-28 11:15:37 (Show Source): You can put this solution on YOUR website!If the answer is (-3,4), then substitute for x and y in your equations. First find b. Next find m.
 Rational-functions/118159: f(x)= (-2 over x+5) -1 g(x)= x-2 determine the composite function f(g(x)), and then find the inverse of that function. state domain and range. then graph the composite function and its inverse. PLEASE HELP ME THIS WILL PRACTICALLY CHANGE MY LIFE IF YOU CAN HELP ME. thank you for helping me, you are the greatest!!!!1 solutions Answer 86269 by Fombitz(13828)   on 2007-12-27 16:40:58 (Show Source): You can put this solution on YOUR website!Change your life? As long as there's no pressure. To find the composite f(g(x)), substitute (x-2) where there is an x in f(x). The domain of f(g(x)) is all points except x=-3, since the denominator goes to zero. For the range of f(x), as x gets large, either positive or negative, the term (-2)/(x+3) goes to zero and Here is the graph of f(g(x)). That was f(g(x)). Now for the inverse. To find the inverse of Reverse x and y and solve for y. Original equation of f(g(x)). Interchange x and y. Multiply both sides by (y+3). Distributive property. Simplify. Group like terms (y on left, x on right). Distributive property. Divide by (x+1). There it is. Domain of the inverse function is all numbers except x=-1. Think about the range of f(g(x)) and the domain of the inverse and you'll see why. Hint : You never reach -1 in f(g(x)) except at Range of the inverse function: as x gets large, the inverse function looks like, Again think about the range of the inverse and the domain of the f(g(x)) for reasons why. Here's the graph of the inverse.
 Rational-functions/118160: which is the range of f(x) = -(x over 3) to the power of 2? a. f(x) greater than and equal to 0 b. f(x) greater than and equal to 3 c. f(x) less than and equal to 3 d. f(x) less than and equal to 01 solutions Answer 86263 by Fombitz(13828)   on 2007-12-27 16:11:32 (Show Source): You can put this solution on YOUR website!I think this is what you mean. Since is raised to the power of two, it will always be positive. Since there is a negative sign in front of it, f(x) will always be negative. The only exception is at x=0, when it equals zero. d.)The range is (,).
 Rational-functions/118155: I know this may not be the right type of topic for the question but I guessed what i thought was close. let f(x) = -3x and g(x) = x-4. find (FoG)(-5) a. 27 b. 11 c. -135 d. -45 1 solutions Answer 86259 by Fombitz(13828)   on 2007-12-27 14:59:34 (Show Source): You can put this solution on YOUR website! a.)27
 Complex_Numbers/117518: I NEED HELP! :]1 solutions Answer 86257 by Fombitz(13828)   on 2007-12-27 13:48:26 (Show Source): You can put this solution on YOUR website!I'm assuming P(x) is of the form, a) From the properties of i, So if P(i)=0, then For P(i)=0, both the real and complex parts must equal zero. Real part Complex part b.) The assumption is d=b and c=a, so let's look at P(-i). Yes, then P(-i)=0.
 Problems-with-consecutive-odd-even-integers/118153: hI i have done this and would like to know if i am right . I took me 5 minutes to do it. Hope you help me. Tahnks TWo numbers differ by 3. the sum of teh larger and one fourth the smaller is 13. What are the numbers.1 solutions Answer 86255 by Fombitz(13828)   on 2007-12-27 13:38:31 (Show Source): You can put this solution on YOUR website!What did you get as an answer?
 Numeric_Fractions/117812: Okay..i am totally lost on this one. Help please Write the proportion 14 is to 22 as 28 is to 44.1 solutions Answer 85809 by Fombitz(13828)   on 2007-12-20 18:20:57 (Show Source):
 Linear-equations/117783: Write the equation of the L satisfying the given geometric conditions. L passes through point (-4,3) and is parallel to the line equation y=2x+11 solutions Answer 85792 by Fombitz(13828)   on 2007-12-20 16:17:10 (Show Source): You can put this solution on YOUR website!Here is the graph of your original line, y=2x+1, and the point of interest. Parallel lines have the same slope. Use the point slope form of a line.
 Numeric_Fractions/117785: Write 32 as a product of prime factors using exponents.1 solutions Answer 85783 by Fombitz(13828)   on 2007-12-20 16:10:31 (Show Source):
 Travel_Word_Problems/117631: AN ACCOUNTANT RIDES A BUS PART OF THE WAY TO WORK EVERY DAY AND WALK THE REST OF THE WAY. THE BUS AVERAGES 40MPH AND THE ACCOUNTANT WALKS AT A SPEED OF 3MPH.THE DISTANT FROM HOME TO WORK IS 22MI AND THE TOTAL TIME FOR THE TRIP IS 3 HOURS. FIND HOW FAR THE ACCOUNTANT WALKS.1 solutions Answer 85634 by Fombitz(13828)   on 2007-12-19 16:54:31 (Show Source): You can put this solution on YOUR website!Rate x Time = Distance Distance = Rate/Time Let's call Bus Time and Bus Distance, T1 and D1. Let's call walk time and walk distance, T2 and D2. 1. Total distance is 22 miles. 2. Total time is 3 hours. 3. Rate of the bus is 40 mph. 4. Rate of the accountant walking is 3 mph. From 3, 3. and from 4, 4. You can substitute these values into 1. 1. You can substitute this value for T2 into equation 2 and solve for T1. 2. From 2, From 3, From 4, So in approximate terms, the accountant rides the bus 14.1 miles for 0.35 hrs(21 minutes). Then walks 2.65 hrs (2 hrs, 39 minutes) for a distance of 7.9 miles. Total distance is 14.1+7.9 or 22 miles. Total time is 0.35+2.65 or 3 hours.
 Travel_Word_Problems/117628: AN ACCOUNTANT RIDES THE BUS PART OF THE WAYTO WORK EVERY DAY AND WALKS THE REST. THE BUS RIDES 40 MPH AND THE ACCOUNTANT WALK 3MPH. THE DISTANCE FROM WORK IS 23 MILES. THE TOTAL TIME IT TAKES THE ACCOUNTANT TO GO TO WORK IS 3HRS. HOW FAR DOES THE ACCOUNTANT WALKS?1 solutions Answer 85633 by Fombitz(13828)   on 2007-12-19 16:46:02 (Show Source): You can put this solution on YOUR website!Rate x Time = Distance Distance = Rate/Time Let's call Bus Time and Bus Distance, T1 and D1. Let's call walk time and walk distance, T2 and D2. 1. Total distance is 23 miles. 2. Total time is 3 hours. 3. Rate of the bus is 40 mph. 4. Rate of the accountant walking is 3 mph. From 3, 3. and from 4, 4. You can substitute these values into 1. 1. You can substitute this value for T2 into equation 2 and solve for T1. 2. From 2, From 3, From 4, So in approximate terms, the accountant rides the bus 15.1 miles for 0.38 hrs(22 minutes) and then walks 2.62 hrs (2 hrs, 38 minutes) for a distance of 7.9 miles.
 real-numbers/117608: My problem is: 7xy (seven hundred and something) times 4z (forty something) = abcde. the variables are each a different whole number between 0 - 9 - excluding 7 and 4 which is already used. I've found a few things to narrow the problem down - such as the answer should be between 29442 (701 X 42) and 38514 (786 x 49) and that I don't thing y or z can be 0 or 1. - your help is appreciated.1 solutions Answer 85623 by Fombitz(13828)   on 2007-12-19 16:16:15 (Show Source): You can put this solution on YOUR website!I tried to look for something useful to help with this problem. I made 7xy equal to (700 + 10x + y). I made 4z equal to (40 + z). Then multiplied those together to get That didn't inspire any great thoughts. In the end I worked up a simple EXCEL spreadsheet that cycled through the available numbers until it worked. A less than elegant solution. I'm not sure of the benefit of the exercise. But here's the answer.
 Linear_Equations_And_Systems_Word_Problems/117615: This question is from textbook basic technical mathematics with calculus Solve the linear equations: A + B + C = 0 4A - 10B = 3 -10B + 5C = 61 solutions Answer 85609 by Fombitz(13828)   on 2007-12-19 15:48:17 (Show Source): You can put this solution on YOUR website!1. 2. 3. The quickest and easiest way is to use equations 2 and 3 and find expressions for A and C in terms of B and then substitute those into equation 1. You then solve for B and go back and solve for A and C. 2. 3. Now go back to equation 1. 1. Let's multiply both sides by (4*5) to get rid of the denominators. From our derivation above for A, From equation 1,
 Finance/117554: T=p(1+r)^t 9 1/2=8000(1+8%)^9 1/2 1 solutions Answer 85606 by Fombitz(13828)   on 2007-12-19 15:29:18 (Show Source): You can put this solution on YOUR website!I think you're trying to set up a Future Value problem. for a prinicipal, p, at rate, r, for t periods. The capital T and small t are not the same. Usually its written like this, where FV is the future value of an investment. Your example then becomes and simplifying So, if you invest \$8,000 at a rate of 8%, in 9 1/2 years, the investment will be worth \$16,619.41.
 Systems-of-equations/117613: f(x) = 3x + 2 Could you please explain to me how to graph this.1 solutions Answer 85601 by Fombitz(13828)   on 2007-12-19 15:06:08 (Show Source): You can put this solution on YOUR website!Make a table of value of the form (x,f(x)). Pick values. For x=0, f(x)=3(0)+2=2 For x=1, f(x)=3(1)+2=5 For x=2, f(x)=3(2)+2=8 Don't forget some negative values also. For x=-1, f(x)=3(-1)+2 = -1 For x=-2, f(x)=3(-2)+2 = -4 Then get graph paper. Draw an x-axis horizontally. Draw an f(x) or y-axis vertically. Then plot the points. (0,2) Zero units on the x, 2 units up (positive) on the y. (1,5) 1 unit to the right(positive) on the x, 5 units up on the y. (2,8)Two units on the x, 8 units up on the y. (-1,-1) One unit left (negative), one unit down (negative) on the y. (-2,-4) Then finally you connect all the points together. This function actually represents a straight line.
 Finance/117594: A member would like to borrow \$17,500 with a rate of 5.59% and the term is 60 Months. our system is calculating a monthly payment of \$333.62 and is equipped with an amortization schedule, when I use a regular calculator or an online calculator, it gives me a different amount. Could you please tell me the right formula on how to calculate the monthly payment and the interest that the member will end up paying after 60 months. Thank you.1 solutions Answer 85597 by Fombitz(13828)   on 2007-12-19 14:53:29 (Show Source): You can put this solution on YOUR website!You should get the same answer. Here's the formula. where M = monthly payment R = monthly rate (annual rate/12) N = number of months P = principal (original amount borrowed) The total interest paid would then be,
 Graphs/117484: Graph 3x + 2y = 6.1 solutions Answer 85591 by Fombitz(13828)   on 2007-12-19 13:51:10 (Show Source): You can put this solution on YOUR website!3x + 2y = 6. Simplest way is to find data pairs when x=0 and then when y=0. When x=0, First point (0,3) Next, when y=0, Second point (2,0) Then just draw a line connecting the two points.
 test/117582: Pls Help!!with full explaination : A cylindrical wax candle of radius 5cm and height 28cm, is melted and the wax is poured into a rectangular prism whose cross section is a square of side 8 cm. Calculate the height of the wax in the rectangular prism. (take pi- 22/7)1 solutions Answer 85589 by Fombitz(13828)   on 2007-12-19 13:38:07 (Show Source): You can put this solution on YOUR website!The candle is modeled as a cylinder of radius, r, and height, h. The volume of a cylinder is given by the formula, There is 2200 sq.cm. of wax that gets poured into the prism. The volume of the rectangular prism is given by where A is the cross sectional area. The cross section of the prism is a square with 8 cm sides. The area of a square is given by, } } Putting that back into our prism volume equation, We set this equal to the volume of wax and solve for L. The height of the wax in the prism is 34 3/8 cm.
 Probability-and-statistics/117479: Hi, I am stuck in the middle of a probability and stats assignment and could use some insight. My question is that is it true that if I flip a coin 1,000 times, I will get heads 500 of those flips and I need to explain. If its true than I dont understand what an explanation is needed for. I appreciate any help. B.Cook1 solutions Answer 85473 by Fombitz(13828)   on 2007-12-18 16:54:01 (Show Source): You can put this solution on YOUR website!No, you could flip the coin 1,000 times and get 1,000 heads. You could also get 1,000 tails. It's within the realm of possibility. Most likely, most probably, you will get a value that's close to 500. In the limit, if you did it an infinite amount of times it would go towards 50/50. But your arm would be tired by then. Probability does not give you an actual value. It gives you the likelihood of the expected value. A statistician will never say "Here's the exact value you're going to get.". More likely she'll say "You should probably get a value near x plus or minus this much".
 Surface-area/117465: hI1 please help me with this. I have done so many questions before but this one just doesnt give the right answer?? any help would be apreciated The volume of a library is 20000 m (cubed) We have to minimize the Surface area to ignore the heat loss.Dtermine the dimensions of the building that will best give us teh minimum Surface area.?? thanks for any help coming this way.1 solutions Answer 85472 by Fombitz(13828)   on 2007-12-18 16:49:17 (Show Source): You can put this solution on YOUR website!For a cylindrical room, h is height, r is the radius. Volume of the cylinder Surface area of top and bottom plus unrolled side You can rearrange the equation to solve for h as a function of r. Then substitute that back into the surface area equation, Plot S using various values of r and look for a minimum. 8.1, 5350. 9.1, 4915. 10.1, 4601. 11.1, 4377. 12.1, 4225. 13.1, 4131. 14.1, 4085. 15.1, 4080. 16.1, 4112. 17.1, 4175. 18.1, 4267. 19.1, 4385. 20.1, 4527. Looks like a minimum at r=15.1. Now that you have r, go back to your equation for h and solve. Make sure to check your answer. Close enough. r=15.1 m, h=27.9 m
 Travel_Word_Problems/117476: I am traveling from Kansas city, mo to Flagstaff arizona. I want to know if I am traveling at speed of 55 mph going a distance of 1117.5 miles and stopping for 45 minutes for breaks. How many hours will I be traveling to get to my destination. Also if I have to slow down to 10 mph for about 30 miles many more hours will that add to my trip. How would I put this in an equation form. 1 solutions Answer 85471 by Fombitz(13828)   on 2007-12-18 16:38:57 (Show Source): You can put this solution on YOUR website!Rate x Time = Distance Time = Distance/Rate Transfer all of the rates and distances into time. Total Time = Drive Time + Break Time Total Time = 1175 miles/55 mph + 45/60 hours Total Time = 21.36 hours + 0.75 hours Total Time = 22.11 hours or 22 hours 7 minutes. Remember to watch the units, all distances should be the same units (miles). All times should be in the same units (hours). If you have to slow down, that changes the distance and rate Total Time = (1175-30)/55 + 30/10 + 45/60 Total Time = 20.82 + 3.0 + 0.75 Total Time = 24 hours 34 minutes. It adds 2 hours, 27 minutes minutes to slow down for the 30 miles at 10 mph.
 Reduction-of-unit-multipliers/117472: if someone can throw a ball 40 feet in 32/100 of a second, how many miles per hour does this convert to?1 solutions Answer 85468 by Fombitz(13828)   on 2007-12-18 16:28:35 (Show Source): You can put this solution on YOUR website!40 ft x 1 mile/5280 ft = 7.58E-3 miles 32/100 second x 1 hr/3600 seconds = 8.89E-5 hours 40 ft/(.32 sec) = 7.58E-3/8.88E-5 mph = 85.3 mph.