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# Recent problems solved by 'nerdybill'

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 Length-and-distance/177220: i need help over distance formula i set the problem up right but now im stuck (-3-2)^2+(5-8)^2 negative 3 subtract 2 squared plus 5 subtract 8 squared equals ? then i need the square root 1 solutions Answer 132298 by nerdybill(6962)   on 2009-01-18 10:45:09 (Show Source): You can put this solution on YOUR website!You are dealing with "squaring" the term not the "square root". . (-3-2)^2+(5-8)^2 = (-5)^2+(-3)^2 = 25+9 = 34
 absolute-value/177219: This question is from textbook Factor. Write prime if the expression cannot be factored: 49^2-251 solutions Answer 132294 by nerdybill(6962)   on 2009-01-18 08:58:15 (Show Source): You can put this solution on YOUR website!Instead of: 49^2-25 I think you meant: 49x^2-25 . If so, your answer would be: (7x+5)(7x-5)
 absolute-value/177218: This question is from textbook Factor. Write prime if the expression cannot be factored: 4x^2-24x+361 solutions Answer 132293 by nerdybill(6962)   on 2009-01-18 08:56:22 (Show Source): You can put this solution on YOUR website!4x^2-24x+36 First, factor out a 4: 4(x^2-6x+9) 4(x-3)(x-3) or 4(x-3)^2
 Polynomials-and-rational-expressions/177209: 1 solutions Answer 132283 by nerdybill(6962)   on 2009-01-18 04:39:30 (Show Source): You can put this solution on YOUR website!8) Factor x^2 + 6a - 40 (x+10)(x-4) . 9) Factor 3x^2 + 2x – 5 (3x+5)(x-1)
Polynomials-and-rational-expressions/177035: Solve equations
x/3 = 4/x+1
-------------
-3/x = x/-3
1 solutions

Answer 132282 by nerdybill(6962)   on 2009-01-18 04:36:26 (Show Source):
You can put this solution on YOUR website!
x/3 = 4/x+1
Multiply both sides by 3x:
x^2 = 12+3x
Move all terms to the left:
x^2-3x-12=0
Since you can't factor, you must apply the quadratic equation. Doing so, yields:
x={5.2749, -2.2749}
Here's the details of the quadratic:
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=57 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 5.27491721763537, -2.27491721763537. Here's your graph:

-------------
-3/x = x/-3
Multiply both sides by -3x:
9 = x^2
Taking the square root of both sides:
x = {-3,3}

 absolute-value/177128: This question is from textbook Factor. Write prime if the expression cannot be factored: 6f^2+5f+21 solutions Answer 132183 by nerdybill(6962)   on 2009-01-17 11:01:53 (Show Source): You can put this solution on YOUR website!6f^2+5f+2 Prime
 absolute-value/177127: This question is from textbook Factor. Write prime if the expression cannot be factored: 3a^2+9a+61 solutions Answer 132182 by nerdybill(6962)   on 2009-01-17 11:00:28 (Show Source): You can put this solution on YOUR website!3a^2+9a+6 3(a^2+3a+2) 3(a+2)(a+1)
 absolute-value/177126: This question is from textbook Factor. Write prime if the expression cannot be factored: y^2-4y-51 solutions Answer 132181 by nerdybill(6962)   on 2009-01-17 10:48:50 (Show Source): You can put this solution on YOUR website!y^2-4y-5 (y-5)(y+1)
 absolute-value/177123: This question is from textbook Factor completely: 6y^2-2yz1 solutions Answer 132180 by nerdybill(6962)   on 2009-01-17 10:48:08 (Show Source): You can put this solution on YOUR website!6y^2-2yz Pull out what's common between both of the terms: 2y(3y-z)
 absolute-value/177125: This question is from textbook Factor. Write prime if the expression cannot be factored: s^2-s-61 solutions Answer 132179 by nerdybill(6962)   on 2009-01-17 10:46:45 (Show Source): You can put this solution on YOUR website!s^2-s-6 (s-3)(s+2)
 Polynomials-and-rational-expressions/177041: Let log6=m and log7=n. Write the log as an expression in m and/or n. for log 36/71 solutions Answer 132164 by nerdybill(6962)   on 2009-01-17 07:33:53 (Show Source): You can put this solution on YOUR website!Let log6=m and log7=n . log 36/7 can be rewritten as: log 36 - log 7 log(6*6) - log 7 log 6 + log 6 - log 7 Now we can substitute: m + m - n 2m - n (this is what they're looking for) .
 Sequences-and-series/177115: This question is from textbook Elementary and Intermediate Algebra Concepts and Applications The sum of two positive integers is 108. One integer is three times as great as the other. Find the integers1 solutions Answer 132163 by nerdybill(6962)   on 2009-01-17 07:28:05 (Show Source): You can put this solution on YOUR website! The sum of two positive integers is 108. One integer is three times as great as the other. Find the integers . Let x = smaller integer and y = larger integer . x+y = 108 (equation 1) y = 3x (equation 2) . substitute the value of y from equation 2 into equation 1 and solve for x: x+y = 108 x+3x = 108 4x = 108 x = 27 . substitute the above into equation 2 and solve for y: y = 3x y = 3(27) y = 81 . The two integers are 27 and 81
 Miscellaneous_Word_Problems/177096: This question is from textbook Car rental agency A will rent a compact car for \$35 per day and an additional charge of \$0.24 per mile. Car rental agency B will charge only \$0.16 per mile but charges \$41 per day. If Adam wanted to rent a car for three days, how many miles would Adam have to drive to make car rental agency B a better bargain? 1 solutions Answer 132149 by nerdybill(6962)   on 2009-01-16 21:43:54 (Show Source): You can put this solution on YOUR website!Let y = miles driven and x = days rented . Agency A: CostA = 35x + .24y . Agency B: CostB = 41x + .16y . The problem sets x = 3 so: . Agency A: CostA = 35(3) + .24y CostA = 105 + .24y . Agency B: CostB = 41(3) + .16y CostB = 123 + .16y . Agency B would be better if: CostB < CostA 123 + .16y < 105 + .24y . Solving for y: 123 + .16y < 105 + .24y 123 < 105 + .08y 18 < .08y 18/.08 < y 225 miles < y . He has to drive MORE than 225 miles.
 Miscellaneous_Word_Problems/177093: The minute hand of a clock is 7cm long. to the nearest tenth of a centimeter, how far does the tip of the minute hand move in 25 minutes ?1 solutions Answer 132129 by nerdybill(6962)   on 2009-01-16 19:45:16 (Show Source): You can put this solution on YOUR website!In an hour, the minute hand moves 360 degrees -- full circle around the clock. The total distance in an hour is equal to the circumference: (pi)(2r) = (3.14)(2)7 = (3.14)(14) = 43.96 cm (distance if it traveled 60 minutes) . If it only moved 25 minutes: 25/60 * 43.96 = 18.317 cm
 real-numbers/177092: can someone show me how to solve this word problem Finding MSRP. What was the MSRP for a Hummer H1 that sold for \$107,272 after an 8% discount 1 solutions Answer 132124 by nerdybill(6962)   on 2009-01-16 19:39:39 (Show Source): You can put this solution on YOUR website!What was the MSRP for a Hummer H1 that sold for \$107,272 after an 8% discount . Let M = the MSRP then M - .08M = 107272 M(1 - .08) = 107272 M(.92) = 107272 M = 107272/.92 M = \$116,600
Equations/177079: I'm trying to help my granddaughter. I'm stumped
p-4/9p = -7/9
1 solutions

Answer 132103 by nerdybill(6962)   on 2009-01-16 17:20:05 (Show Source):
You can put this solution on YOUR website!
I think you mean:

multiply both sides by 9p:

divide both sides by 6:

reduce to get:

.
.
.
BUT, if you mean:

multiply both sides by 9p:

Here, you have to use the quadratic equation to solve.
Doing so will yield:
p = {0.383, -1.161}
Details are below:
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=193 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.382913554969434, -1.16069133274721. Here's your graph:

.

 Equations/177070: please help me solve this quadratic equation in vertex form. y=x^2+12x-4 thank you very much 1 solutions Answer 132096 by nerdybill(6962)   on 2009-01-16 15:58:22 (Show Source): You can put this solution on YOUR website!The vertex form is: y= a(x-h)^2+k . This involves "completing the square". For reference see: http://www.purplemath.com/modules/sqrvertx.htm . y=x^2+12x-4 y+4 = x^2+12x y+4+36 = x^2+12x+36 y+40 = (x+6)^2 y = (x+6)^2 - 40 y = (x-(-6))^2 + (-40) . Now, we see that: (h,k) = (-6,-40)
 Geometric_formulas/176985: if the length of a rectangle is increased by 120%and its width is decreased by 20%,what is the resulting percentage increase or decrease in the area?1 solutions Answer 132047 by nerdybill(6962)   on 2009-01-16 08:10:24 (Show Source): You can put this solution on YOUR website!if the length of a rectangle is increased by 120%and its width is decreased by 20%,what is the resulting percentage increase or decrease in the area? . Let x = width of original rectangle and y = length of original rectangle . "original area" = xy . New dimensions: x-.20x = .80x = width of new rectangle y+1.20y = 2.20y = length of new rectangle . "new area" = (.80x)(2.20y) = 1.76xy . Therefore, the percentage increase is 176%
 Rational-functions/176975: How would you write the following expression with a rational denominator and in simplest form?: I have a test tomorrow and myself and most of the people in my algebra class are still extremely confused. Please, please, please, help me with this and explain in full detail if possible! You're help would be very much appreciated! 1 solutions Answer 132026 by nerdybill(6962)   on 2009-01-15 22:03:36 (Show Source): You can put this solution on YOUR website!When they are asking you to write it in "rational" form, they do not want to see any radicals (square root symbols) in the denominator. . . Multiply by the above by: . . . . . or,
 Problems-with-consecutive-odd-even-integers/176949: fIND tHREE CONSECUTIVE EVEN INTERGERS SUCH THAT THE SUM OF THE FIRST AND THIRD IS 90 MORE THAN THE SECOND1 solutions Answer 131997 by nerdybill(6962)   on 2009-01-15 20:43:01 (Show Source): You can put this solution on YOUR website! fIND tHREE CONSECUTIVE EVEN INTERGERS SUCH THAT THE SUM OF THE FIRST AND THIRD IS 90 MORE THAN THE SECOND . Let x = first consecutive even integer x+2 = second consecutive even integer x+4 = third consecutive even integer . x + (x+4) = (x+2) + 90 2x + 4 = x + 92 x + 4 = 92 x = 88 . The three consecutive even integers are: 88, 90 and 92
 Exponential-and-logarithmic-functions/176950: This question is from textbook Algebra & Trigonometry Solve the logarithmic equation algebraically approximately 3 decimal places Ln x-Ln(x+1)=2 Thank you!1 solutions Answer 131995 by nerdybill(6962)   on 2009-01-15 20:39:50 (Show Source): You can put this solution on YOUR website!Ln x-Ln(x+1)=2 Ln x/(x+1)=2 x/(x+1)=e^2 x=e^2(x+1) x=xe^2+e^2 x-xe^2=e^2 x(1-e^2)=e^2 x = e^2/(1-e^2) x = -1.157
 Polynomials-and-rational-expressions/176925: A circular pool is surrounded by a brick walkway 3 m wide. Find the radius of the pool if the area of the walkway is 198 m^21 solutions Answer 131993 by nerdybill(6962)   on 2009-01-15 20:35:21 (Show Source): You can put this solution on YOUR website!Draw a picture of the situation -- it'll help you visualize the problem. . "area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway" . Let R = radius of pool . "area of the circle bounded by the outside edge of the walkway" is: (pi)(R+3)^2 . "area of the pool" is: (pi)R^2 . Our equation is: (pi)(R+3)^2 - (pi)R^2 = 198 factoring the left: (pi)((R+3)^2 - R^2) = 198 expanding: (pi)(R^2+6R+9 - R^2) = 198 (pi)(6R+9) = 198 6R+9 = 198/(pi) 6R = 198/(pi) - 9 R = (198/(pi) - 9)/6 R = (198/(3.14) - 9)/6 R = (63.057 - 9)/6 R = 54.057/6 R = 9.01 meters
 Quadratic_Equations/176813: The length of a rectangle is 3in. more than twice its width. If the perimeter of the rectange is 30in., find the dimensions of the rectangle. Choose the answer with the correct equations used to solve this problem. 1 solutions Answer 131886 by nerdybill(6962)   on 2009-01-15 06:50:42 (Show Source): You can put this solution on YOUR website!Let w = width of rectangle then 2w+3 = length of rectangle . 2(w + 2w+3) = 30 2(3w+3) = 30 6w+6 = 30 w+1 = 5 w = 4 inches (width) . length: 2w+3 = 2(4)+3 = 8+3 = 11 inches (length)
 Bodies-in-space/176762: Find the cubic volume of a cylinder which has a diameter of 14 feet and is 12 feet high.1 solutions Answer 131833 by nerdybill(6962)   on 2009-01-14 21:41:23 (Show Source): You can put this solution on YOUR website!Vol = "area of the base" * "height" . Vol = (pi)7^2 * 12 Vol = (3.14)7^2 * 12 Vol = (3.14)(49) * 12 Vol = 153.86 * 12 Vol = 1846.32 cubic feet
 Bodies-in-space/176764: A 10 foot ladder is leaning against a vertical wall. The base of the ladder is 3 feet from the wall. How high is the point where the ladder touches the wall?1 solutions Answer 131831 by nerdybill(6962)   on 2009-01-14 21:37:45 (Show Source): You can put this solution on YOUR website!Apply Pythagorean theorem: Length of the ladder is the hypotenuse. . Let x = height where the ladder touches the wall 3^2 + x^2 = 10^2 9 + x^2 = 100 x^2 = 91 x = 9.54 feet
 Bodies-in-space/176767: What is 22% of 83%?1 solutions Answer 131829 by nerdybill(6962)   on 2009-01-14 21:34:44 (Show Source): You can put this solution on YOUR website!That's 22/100 * 83 .22 * 83 18.26%
 Inequalities/176660: A car rents for \$35 per day plus 21 cents per mile. You are on a daily budger of \$98. What milage will allow you to stay within your budget?_1 solutions Answer 131814 by nerdybill(6962)   on 2009-01-14 20:25:37 (Show Source): You can put this solution on YOUR website!Let x = mileage 98 >= 35 + .21x Solving for x: 98 >= 35 + .21x 63 >= .21x 300 >= x . This says that if the total mileage is 300 miles or less he will be within his budget.
 Systems-of-equations/176232: please help me solve in interval noation. thanks x+3 over 2+ 5 = 3x over 4. 1 solutions Answer 131335 by nerdybill(6962)   on 2009-01-12 18:44:38 (Show Source): You can put this solution on YOUR website!x+3 over 2+ 5 = 3x over 4 . I think you mean: . If so, start by multiplying both sides by 4:
 percentage/176223: If I bought an item for \$100 and I want to make a 35% profit margin when I sell it, what price do I sell it for? What is the difference between percent profit and percent profit margin, or is there a diference?1 solutions Answer 131331 by nerdybill(6962)   on 2009-01-12 18:31:52 (Show Source): You can put this solution on YOUR website! If I bought an item for \$100 and I want to make a 35% profit margin when I sell it, what price do I sell it for? . selling price =100 + .35(100) selling price =100 + 35 selling price = \$135 . What is the difference between percent profit and percent profit margin, or is there a difference?.. . "percent profit" is how much is made by selling the item (calculated above). "percent profit margin" is how much is made by selling the item (calculated above) MINUS any expenses associated with the sale -- an example might be cost of packaging, shipping, handling, etc -- these must be deducted from "profit". .
 Linear-systems/176227: i couldnt figure out how to work this problem. im in 9th grade in algebra 1. what is y=4x-8 y=2x+10 1 solutions Answer 131325 by nerdybill(6962)   on 2009-01-12 18:19:44 (Show Source): You can put this solution on YOUR website!y=4x-8 (equation 1) y=2x+10 (equation 2) . Plug in the value of 'y' from equation 1 into equation 2 and solve for 'x': y=2x+10 4x-8=2x+10 2x-8 = 10 2x = 18 x = 9 (solution for x) . Plug the above into equation 1 and solve for 'y': y=4x-8 y=4(9)-8 y=36-8 y=28 (solution for y)
 Linear-equations/176228: This question is from textbook A right triangle has legs of lengths 10 and 24. What is the length of the hypotenuse? Round to the nearest tenths.1 solutions Answer 131321 by nerdybill(6962)   on 2009-01-12 18:16:18 (Show Source): You can put this solution on YOUR website!Let h = length of the hypothenuse then 10^2 + 24^2 = h^2 100 + 576 = h^2 676 = h^2 26 = h