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# Recent problems solved by 'nerdybill'

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 Exponents/163989: A semicircular window of radius 15 inches is to be laminated with a sunblock coating that costs \$0.85 per square inch to apply. What is the total cost of coating the window, to the nearest cent? (Use p = 3.14. Hint: Area of Circle: A = pr²) 1 solutions Answer 120816 by nerdybill(6958)   on 2008-10-25 18:03:51 (Show Source): You can put this solution on YOUR website!Since it is a SEMI circle the area is: (half a circle) plugging in our values square inches (area of semicircle window) . Now, we multiply the area (above) by cost per inch: That's \$300.26 for the coating.
 Finance/163971: Please help me with this problem. Find the percent of change in price if the old selling price was \$20 and the new selling price is \$15.1 solutions Answer 120812 by nerdybill(6958)   on 2008-10-25 16:53:31 (Show Source): You can put this solution on YOUR website!Please help me with this problem. Find the percent of change in price if the old selling price was \$20 and the new selling price is \$15. . 15/20 * 100 = 0.75 * 100 = 75% . So, you could think of it as: 75% of the original price
 Exponents/163979: A rectangular light-switch plate is made according to the following dimensions. The length is 7 inches, and the width is 5.5 inches; a rectangular hole measuring 1.2 inches by 0.3 inches is left in the center. (See diagram below) (a) How many square inches in area is the light-switch plate (the shaded region)? (b) If the cost to construct the plate is \$4.27 per square inch, what is the construction cost?1 solutions Answer 120811 by nerdybill(6958)   on 2008-10-25 16:49:38 (Show Source): You can put this solution on YOUR website!Part a: "area of the entire rectangle" - "area of hole" = "area of plate" (7*5.5) - (1.2*0.3) 38.5 - 0.36 38.14 square inches . Part b: 38.14 * 4.27 = \$162.86 (sounds a little expensive to me)
 Polynomials-and-rational-expressions/163972: Hello I need to solve this and I havent done math for 5 years.could you please help me what is the equation of th eline that contains the points with ( x, y ) coordinates ( -3, 7 ) and (5,-1) thanks tha answer is y= -x + 4 can you explain why>?1 solutions Answer 120810 by nerdybill(6958)   on 2008-10-25 16:43:07 (Show Source): You can put this solution on YOUR website!If you are given two points, you can determine the slope from: m = (y2-y1)/(x2-x1) Our two points:( -3, 7 ) and (5,-1) substituting it in, we get: m = (-1-7)/(5-(-3)) m = (-8)/(5+3) m = (-8)/(8) m = -1 . Now that we know the slope (-1), we can use one of the two given points (say we use ( -3, 7 )) and plug it into the "point-slope" form of a line: y – y1 = m(x – x1) y – 7 = -1(x – (-3)) y – 7 = -1(x + 3) y – 7 = -x - 3 y = -x + 4 (this is our equation of the line)
 Travel_Word_Problems/163949: Runner A crosses the starting line of a marathon and runs at an average pace of 5.6 miles per hour. Half an hour later, Runner B crosses the starting line and runs at an average rate of 6.4 miles per hour. If the length of the marathon is 26.2 miles, which runner will finish ahead of the other?Explain.1 solutions Answer 120787 by nerdybill(6958)   on 2008-10-25 10:53:51 (Show Source): You can put this solution on YOUR website!You will need to apply the distance formula: d = rt where d is distance r is rate or speed t is time . Rearranging the formula to solve for t: t = d/r . Runner A: Time it takes for him to finish: t = 26.2/5.6 = 4.679 hours (to complete race) . Runner B: Time it takes for him to finish: t = 26.2/6.4 = 4.094 hours BUT wait, we have to account for the extra .5 hours -- the time it took for him to cross the start line. t = 4.094 + .5 = 4.594 hours . Since Runner B's time is less than Runner A's, we must conclude Runner B will finish first.
 Geometry_Word_Problems/163842: The length of a rectangle is 7 units more than its width. If the width is doubled and the length is increased by 2, the area is increased by 42 square units. Use an algebraic solution to find the dimensions of the original rectangle.1 solutions Answer 120706 by nerdybill(6958)   on 2008-10-24 14:26:01 (Show Source): You can put this solution on YOUR website!Let x = width of original rectangle then x+7 = length of original rectangle . Then this: "If the width is doubled and the length is increased by 2, the area is increased by 42 square units." is translated to: (2x)(x+7+2) = x(x+7) + 42 . Now we can solve for x: (2x)(x+7+2) = x(x+7) + 42 (2x)(x+9) = x(x+7) + 42 2x^2 + 18x = x^2 +7x + 42 x^2 + 11x - 42 = 0 Factoring the left: (x+14)(x-3) = 0 So, x = {3, -14} . We can toss the negative solution leaving us with: x = 3 units (width of original rectangle) . length: x+7 = 3+7 = 10 units (length of original rectangle) . ANS: dimension of original rectangle: 3 units by 10 units
 Graphs/163860: The length of a rectangle is 3 m longer than its width. If the perimeter of the rectangle is 38 m find its area1 solutions Answer 120704 by nerdybill(6958)   on 2008-10-24 14:16:11 (Show Source): You can put this solution on YOUR website!Let x = width then because "length of a rectangle is 3 m longer than its width" x+3 = length . Perimeter of any rectangle: 2(width + length) . so: 38 = 2(x + x+3) 38 = 2(2x+3) 38 = 4x+6 32 = 4x 8 m = x (width) . length: x+3 = 8+3 = 11 m (length) . Area of any rectangle: width * length = 8 * 11 = 88 square meters (answer)
 Problems-with-consecutive-odd-even-integers/163814: find the consecutive odd numbers such that twice the sum of the first and second is one more than three times the third.1 solutions Answer 120683 by nerdybill(6958)   on 2008-10-24 08:40:57 (Show Source): You can put this solution on YOUR website!find the consecutive odd numbers such that twice the sum of the first and second is one more than three times the third. . Let x = 1st consecutive odd number then x+2 = 2nd consecutive odd number x+4 = 3rd consecutive odd number . From: "twice the sum of the first and second is one more than three times the third" we get: 2(x + x+2) = 3(x+4)+1 2(2x+2) = 3(x+4)+1 4x+4 = 3x+12+1 4x+4 = 3x+13 x+4 = 13 x = 9 (1st number) . 2nd number: x+2 = 9+2 = 11 . 3rd number: x+4 = 9+4 = 13 . Ans: 9, 11, 13
 Problems-with-consecutive-odd-even-integers/163815: The sum of two integers is fifteen. Eight times the smaller is 1 less than three times the larger. Find the numbers.1 solutions Answer 120682 by nerdybill(6958)   on 2008-10-24 08:36:55 (Show Source): You can put this solution on YOUR website!I'll use the "elmination method"... . Let x = smaller number and y = larger number . Since we have two unknowns, we'll need to find two equations. Equation 1 can be extracted from "The sum of two integers is fifteen": x + y = 15 . Equation 2 can be extracted from "Eight times the smaller is 1 less than three times the larger.": 8x = 3y -1 rearranging: 8x - 3y = -1 . The two equations now are: x + y = 15 8x - 3y = -1 . Multiplying the top equation by 3 to get: 3x + 3y = 45 8x - 3y = -1 . Adding the two equations together: 3x + 3y = 45 8x - 3y = -1 ------------- 11x = 44 dividing both sides by 11: x = 4 (smaller number) . larger number is found by substituting the above into equation 1: x + y = 15 4 + y = 15 y = 11 (larger number) . Ans: 4 and 11
 Graphs/163787: How can I find the slope of the line pasing through the points (6,7) and (2,-8).1 solutions Answer 120654 by nerdybill(6958)   on 2008-10-23 22:56:51 (Show Source): You can put this solution on YOUR website!There is a formula for the slope between two points that looks like this: . Since they gave you: (6,7) and (2,-8) . then (x[1],y[1])=(6,7) (x[2],y[2])=(2,-8) . Plugging it in:
 Geometry_Word_Problems/163791: A circular pool is 34 feet in diameter and has a flag stone walk around it that is 3 feet wide. Find the area of the walk. Express the answer in terms of pie.1 solutions Answer 120653 by nerdybill(6958)   on 2008-10-23 22:49:25 (Show Source): You can put this solution on YOUR website! A circular pool is 34 feet in diameter and has a flag stone walk around it that is 3 feet wide. Find the area of the walk. Express the answer in terms of pie. . Draw a picture of the situation, this will help you "see" the problem. Imagine a donut, the "hole" is the pool and the donut is the walkway. . "area of circle formed by outer edge of walkway" - "area of pool" = "area of walkway" . "area of circle formed by outer edge of walkway": radius = (34/2)+3 =17+3 = 20 feet area = (pi)r^2 area = (pi)20^2 . "area of pool": area = (pi)r^2 area = (pi)17^2 . "area of circle formed by outer edge of walkway" - "area of pool" = "area of walkway" (pi)20^2 - (pi)17^2 = "area of walkway" 400(pi) - 289(pi) = "area of walkway" 111(pi) square feet = "area of walkway"
 test/163782: a bike rental shop charges a one-time charge of \$8 plus an hourly fee to rent a bike. Dan paid \$24.50 to rent a bike for 5 1/2 hours.Find the bike shop's hourly fee dollars. i realy need help!!!!!!!!!!! 1 solutions Answer 120650 by nerdybill(6958)   on 2008-10-23 22:11:00 (Show Source): You can put this solution on YOUR website!a bike rental shop charges a one-time charge of \$8 plus an hourly fee to rent a bike. Dan paid \$24.50 to rent a bike for 5 1/2 hours.Find the bike shop's hourly fee dollars. . Let x = hourly rate then from "Dan paid \$24.50 to rent a bike for 5 1/2 hours." we get: 24.50 = 8 + 5.5x . Now, we solve for x: 24.50 = 8 + 5.5x 16.50 = 5.5x 16.50/5.5 = x 3 dollars/hour = x . Hourly fee: \$3 dollars
 Money_Word_Problems/163629: Tickets for a concert were sold to adults for \$3 and students for \$2 if the total receipts were \$824 and twice as many adult tickets as students were sold then how many of each were sold?1 solutions Answer 120532 by nerdybill(6958)   on 2008-10-23 07:20:56 (Show Source): You can put this solution on YOUR website!Let x = number of student tickets sold the because "twice as many adult tickets as students were sold" 2x = number of adult tickets sold . 2x + 3(2x) = 824 2x + 6x = 824 8x = 824 x = 103 (number of student tickets . Adult tickets: 2x = 2(103) = 206 (number of adult tickets)
 Angles/163606: The measures of one of the complementary angles of a right triangle is five times that of the other. Find the measures of the angles.1 solutions Answer 120506 by nerdybill(6958)   on 2008-10-22 20:40:48 (Show Source): You can put this solution on YOUR website! The measures of one of the complementary angles of a right triangle is five times that of the other. Find the measures of the angles. . If two angles are complementary, the sum of the two angles equal 90. . Let x = one of the complementary angles then 90-x = the other complementary angle . 5x = 90-x 6x = 90 x = 15 deg (one of two complementary angles) . "other complementary angle": 90-x = 90-15 = 75 deg . The three angles are: 90, 75, and 15 degrees
 Word_Problems_With_Coins/163600: Warren has 40 coins (all nickels, dimes, and quarters) worth \$4.05. He has 7 more nickels than dimes. How many quarters does Warren have?1 solutions Answer 120504 by nerdybill(6958)   on 2008-10-22 20:14:25 (Show Source): You can put this solution on YOUR website! Warren has 40 coins (all nickels, dimes, and quarters) worth \$4.05. He has 7 more nickels than dimes. How many quarters does Warren have? . Let d = times then from: "He has 7 more nickels than dimes" d+7 = nickels and from: "Warren has 40 coins" 40-d -(d+7) = 33-2d = quarters . Since, he has a total of 4.05: 4.05 = .10d + .05(d+7) + .25(33-2d) 4.05 = .10d + .05d + .35 + 8.25 - .50d 4.05 = 8.60 - .35d .35d = 4.55 d = 13 (number of dimes) . quarters: 33-2d = 33-2(13) = 33-26 = 7 (number of quarters)
 Travel_Word_Problems/163603: If I drive a speed of 45mph for 6 miles how long would it take me?1 solutions Answer 120503 by nerdybill(6958)   on 2008-10-22 20:06:47 (Show Source): You can put this solution on YOUR website! If I drive a speed of 45mph for 6 miles how long would it take me? . Using the distance formula: d = rt where d is distance r is rate t is time . Solving the equation for 't': d = rt d/r = t . Plugging in the given values: d/r = t 6/45 = t 0.1334 hours = t or, multiply the above by 60 to convert to minutes: 8 minutes = t
 Complex_Numbers/163596: Factor the quadratic expression 3x²-1081 solutions Answer 120502 by nerdybill(6958)   on 2008-10-22 20:03:51 (Show Source): You can put this solution on YOUR website!3x²-108 begin by factoring out a 3 first: 3(x²-36) Then factoring the term inside the parenthesis: 3(x-6)(x+6)
 Travel_Word_Problems/163598: Noya drives to the city to buy software program at the computer store. Because of traffic she averaged only 15 miles per hour on the way there but averaged 35 miles per hour on the way home. If the total travel time was 2 hours how long does it take her to drive to the computer store.1 solutions Answer 120501 by nerdybill(6958)   on 2008-10-22 20:01:38 (Show Source): You can put this solution on YOUR website!Let x = amt of time driving to the computer store then because "total travel time was 2 hours" 2-x = amt of time driving home . Using the distance formula of d = rt where d is distance r is rate or speed t is time . "distance driving to the store" = "distance going home" 15x = 35(2-x) 15x = 70 - 35x 50x = 70 x = 70/50 x = 7/5 x = 1.4 hours or 1 hour and 24 minutes
 Mixture_Word_Problems/163455: How would I slove the following?....How many cups of pure grapefruit juice must be added to 30 cups of a punch that contains 8% grapefruit juice to obtain a punch that is 10% grapefruit juice?1 solutions Answer 120418 by nerdybill(6958)   on 2008-10-22 07:03:17 (Show Source): You can put this solution on YOUR website!Let x = cups of pure grapefruit juice added . "amt added" + "amt in original" = "desired mix" x + .08(30) = .10(30+x) x + 2.4 = 3 + .10x .90x + 2.4 = 3 .90x = 0.6 x = 0.6/.90 x = 0.6667 or x = 2/3 cups
 Radicals/163465: please simplify this radical expression: 2√6 ÷ ¼√721 solutions Answer 120417 by nerdybill(6958)   on 2008-10-22 06:57:17 (Show Source): You can put this solution on YOUR website! Start multiplying numerator and denominator by 4: Now, factor the stuff under the radical: Pull out "pairs" from underneath the radical: We can also break up the radical in the numerator thus: Canceling like-terms:
 Linear_Equations_And_Systems_Word_Problems/163266: A car rental as allocated \$1.5million to buy a fleet of cars consisting od compact, intermediate and full size cars. Compacts cost \$12000, intermediate coast 18,000 and full size cost \$24,000 each. If twice as many compacts as intermediate cars are purchased and the total number is 100 determine how many cars of each type will be purchased(assume that the entire budget will be used) I'm not sure whether my equation is right can you please help me? This is what I have: let x represent compacts, let y represent intermediate & let z represent full size. therfore, First equation is 12000x +18000+ 24000 = 1.500000 Second equation is x= 2y + 100 1 solutions Answer 120314 by nerdybill(6958)   on 2008-10-21 06:58:37 (Show Source): You can put this solution on YOUR website!First, you need to define your variables: Let x = number of intermediate cars purchased then because "twice as many compacts as intermediate cars are purchased": 2x = number of compacts purchased and finally because "a total of 100 cars" were purchased: 100-3x = full size cars purchased . Now, we can derive our equation: 12000(2x) +18000x+ 24000(100-3x) = 1500000 24000x + 18000x+ 2400000 - 72000x = 1500000 24x + 18x+ 2400 - 72x = 1500 2400 - 30x = 1500 2400 = 30x+1500 900 = 30x 30 = x (number of intermediate cars) . number of compacts: 2x = 2(30) = 60 . number of full-sized cars: 100-3x = 100-3(30) = 100-90 = 10
 Age_Word_Problems/163279: Susan is six years older than Mary. She is twicw as old as Mary. How old is each now?1 solutions Answer 120312 by nerdybill(6958)   on 2008-10-21 06:45:11 (Show Source): You can put this solution on YOUR website!Let M = Mary's age then because "Susan is six years older than Mary." M+6 = Susan's age . From:"She is twicw as old as Mary" M+6 = 2M Solve for M by subtracting M from both sides: M+6-M = 2M-M 6 years old = M (Mary's age) . Susan's age: M+6 = 6+6 = 12 years old (Susan's age)
 Square-cubic-other-roots/163070: (4+ square root 5 ) (10-3 square root 5)1 solutions Answer 120165 by nerdybill(6958)   on 2008-10-20 07:09:15 (Show Source): You can put this solution on YOUR website! . Performing FOIL:
 Quadratic_Equations/162905: This question is from textbook Solve: x = 2+ sqrt2-x I have: (x-2)^2 = (sqrt2 - x)^2 x^2 - 4x + 4 = 2 - 1x x^2 - 3x + 2 = 0 (x-1) (x -2)answer Please let me know what you think? correct or no.1 solutions Answer 120058 by nerdybill(6958)   on 2008-10-19 11:52:59 (Show Source): You can put this solution on YOUR website!When you got here: x^2 - 3x + 2 = 0 You factored to get: (x-1)(x-2) = 0 . Two solutions are possible: solution 1: (x-1) = 0 x-1 = 0 x = 1 solution 2: (x-2) = 0 x-2 = 0 x = 2 . Conclusion: x = {1,2}
 Equations/162904: The length of a rectangle is 3 in. more than its width. The perimeter is 30 in. Write and solve the equation to find the width of the rectangle. Formula is P=2 x length + 2 x width Please show all work. Thanks1 solutions Answer 120057 by nerdybill(6958)   on 2008-10-19 11:32:11 (Show Source): You can put this solution on YOUR website!Let w = width of rectangle then because "length of a rectangle is 3 in. more than its width" we have w+3 = length of rectangle . Plugging all the information into: P=2 x length + 2 x width we get 30 = 2(w+3) + 2x dividing both sides by 2: 15 = w+ 3 + x 15 = 2w + 3 12 = 2w 6 inches = w (width)
 Problems-with-consecutive-odd-even-integers/162874: Find the smallest angle in which the sum of the measures of the angle, three times its complement, and four times its supplement is at most 480 degrees. I have been struggling with this problem for a while. please help1 solutions Answer 120049 by nerdybill(6958)   on 2008-10-19 10:42:51 (Show Source): You can put this solution on YOUR website!Remember, if two angles are "supplementary" then the sum of the two angles is 180. And, if two angles are "complementary" then the sum of the two angles is 90. . Let x = "the angle" then 180-x = the supplement 90-x = the complement . From: "sum of the measures of the angle, three times its complement, and four times its supplement is at most 480 degrees." we get x + 4(180-x) + 3(90-x) <= 480 x + 720 - 4x + 270 - 3x <= 480 990 - 6x <= 480 -6x <= -510 x >= 85 degrees . Since they asked for the "smallest" angle, it would then be 85 degrees.
 Geometry_Word_Problems/162875: This question is from textbook mathemathical ideas Trouble setting this up. Half the supplement of the angle is 12 degrees less than twice the complement of the angle. Find the measure of the angle. Thank You in advance for your help. George 1 solutions Answer 120045 by nerdybill(6958)   on 2008-10-19 10:33:44 (Show Source): You can put this solution on YOUR website!Remember, if two angles are "supplementary" then the sum of the two angles is 180. And, if two angles are "complementary" then the sum of the two angles is 90. . Let x = "the angle" then 180-x = the supplement 90-x = the complement . From: "Half the supplement of the angle is 12 degrees less than twice the complement of the angle." . (1/2)(180-x) = 2(90-x) - 12 180-x = 4(90-x) - 24 180-x = 360 -4x - 24 180-x = 336 -4x 180+3x = 336 3x = 156 x = 52 degrees
 Polynomials-and-rational-expressions/162817: This question is from textbook algebra tools for a changing world Please help me with this 5=-1/3y + 2/7 I tried subtracting by 2/7 and multiplied by 3 Thanks!1 solutions Answer 120039 by nerdybill(6958)   on 2008-10-19 06:07:48 (Show Source): You can put this solution on YOUR website!5=-1/3y + 2/7 . To attack this problem you're better off by: 1. find a common denominator (say, 21) 2. multiply BOTH sides by the common denominator . (21)5 = (21)(-1/3y + 2/7) (21)5 = (21)(-1/3y + 2/7) 105 = -7/y + 6 99 = -7/y 99y = -7 y = -7/99
 Radicals/162831: Please help me solve the following equation: (2x-5)(x+8)=0 This is as far as I have gotten: 2x^2+16x-5x-40=0 2x^2+11x-40=0 2x^2+11x=40 1 solutions Answer 120018 by nerdybill(6958)   on 2008-10-18 22:01:49 (Show Source): You can put this solution on YOUR website!You did not need to expand it. This, is enough: (2x-5)(x+8)=0 . Notice that if EITHER then contents of the left parenthesis or the right parenthesis, is zero, then the ENTIRE left side is zero. . Therefore, the solutions are found by setting the two term on the left to zero. Solution 1: (2x-5)=0 2x = 5 x = 5/2 . Solution 2: (x+8)=0 x = -8 . Therefore, x = {-8, 5/2}
 Rational-functions/162833: Please help me solve the following: For the graph of the function f(x)=2x^2-12x+20 Find the vertex; state whether this is a maximum or minimum value and find the value; and find the range. I have no idea where to begin to solve this. Any assistance you can provide is greatly appreciated! 1 solutions Answer 120017 by nerdybill(6958)   on 2008-10-18 21:48:29 (Show Source): You can put this solution on YOUR website!This site gives some insight into parabolas: http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php . Standard vertex form is: y= a(x-h)^2+k where (h,k) is the vertex Minimum or maximum is determined by the 'a'. If a is POSITIVE (think happy face -- smile -- U) -- opens upwards -- will be a minimum. If a is NEGATIVE (think sad face -- upside down U) -- opens downwards -- will be a maximum. . Idea is to get your equation into that form. f(x)=2x^2-12x+20 Group terms: f(x)=(2x^2-12x)+20 Factor: f(x)=2(x^2-6x)+20 Complete the square: f(x)=2(x^2-6x+9)+20-18 f(x)=2(x-3)^2+2 . Vertex is then (3,2) Since 'a' is POSITIVE, it is a MINIMUM.