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# Recent problems solved by 'oberobic'

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 Quadratic_Equations/246186: (-2)=x+41 solutions Answer 179829 by oberobic(2304)   on 2009-12-05 19:09:35 (Show Source): You can put this solution on YOUR website!(-2) = x + 4 is a linear equation, not a quadratic. . x+4 = -2 subtracting 4 from both sides x = -6
 Radicals/246171: Please solve this equation: sqrt(x - 3) => 71 solutions Answer 179822 by oberobic(2304)   on 2009-12-05 18:26:10 (Show Source): You can put this solution on YOUR website!The given inequality is sqrt(x-3) is equal to or greater than 7. . We first create the equivalent equation: sqrt(x-3) = 7 . Then we solve the equation: . Squaring both sides of the equation, we have (x-3) = 49 . Adding 3 to both sides x = 52 . Now we substitute back into the inequality: x is any real number equal to or greater than 52.
 Linear-systems/246079: at 9:00am, a car and a bus start from manila and head for the north. by 12:00noon the car, already 85km ahead of the bus, suffers a total breakdown. At what time will the bus pass by the car if the bus just maintain its speed which four-fifths that of the car?1 solutions Answer 179821 by oberobic(2304)   on 2009-12-05 18:21:38 (Show Source): You can put this solution on YOUR website!We are told the bus travels at 4/5 speed of the car. So the car travels at 5/4 speed of bus. b = 4/5*c c = 5/4*b . We are told the car drives for 3 hr at the speed c = 5/4*b. d = rt d = 5/4b*3 = 15/4b . We are told that at that time the car had traveled 85 km more than the bus. . d = 3b + 85 . If a=b and b=c, then a=c. . 15/4*b = 3b+ 85 or 15/4*b = 12/4*b + 85 . Subtract 12/4*b from both sides . 3/4b = 85 . b = (4*85)/3 = 340/3 = 113 1/3 = 113.3333333... . So at the time the car broke down, the bus had traveled d = 3*113.333 = 340 km . 340 km is 85 less than the car travelled, so the car had travelled 340+85 = 425. . The bus will cover the 85 km in t time d = rt t = d/r = 85/113.333 t = 0.75 hr = 45 min . So the bus will pass the car at 12:45 pm. . We can check this solution by checking to see if the bus can travel 425 km in 3.75 hr. 3.75*113.333333333333 = 425. . Done.
 Quadratic_Equations/246086: A rectangular compost container is to be formed in a corner of a fenced yard, with 8 ft of chicken wire completing the other two sides of the rectangle. If the chicken wire is 3 ft high, what dimensions of the base will maximize the volume of the container? 1 solutions Answer 179801 by oberobic(2304)   on 2009-12-05 17:26:31 (Show Source): You can put this solution on YOUR website!By theorem we know that to maximize the area of a quadrilateral we define a square. Given 8 ft of fencing is to enclose 2 sides, then each side will be 4 ft. The volume will be l*w*h = 4 * 4 * 3 = 48 cu ft. You can experiment with other dimensions to ensure this is the maximum.
 Linear-equations/246160: solve this system of equations by graphing. 2x+3y=12 2x-y=41 solutions Answer 179800 by oberobic(2304)   on 2009-12-05 17:21:19 (Show Source): You can put this solution on YOUR website!Given 2x + 3y = 12 2x - y = 4 . Change both in y = mx+b format . 2x + 3y = 12 3y = -2x + 12 y = -(2/3)X + 4 . 2x -y = 4 -y = -2x + 4 y = 2x - 4 . . We can see they intersect at (3,2), so they are consistent and independent. . We can check our work using x=3 and y=2. . Do these equations produce the correct answer when you substitute for x & y? 2x + 3y = 12 2(3) + 3(2) = 6 + 6 = 12 Check. . 2x - y = 4 2(3) - 2 = 6 -2 = 4 Check.
 Quadratic_Equations/246150: Solve. (y+5)(y-1)=271 solutions Answer 179798 by oberobic(2304)   on 2009-12-05 17:11:16 (Show Source): You can put this solution on YOUR website!Given the setup: . We can multiply through: . Collecting terms . Subtracting 27 from both sides . Can we factor 32 into two terms that are 4 apart? 4 * 8 = 32, so we have: . So we have to solutions: y = -8 and y = 4. . Checking , we have: Check. . Checking for , we have: Check. Done.
 Triangles/246102: The hypotenuse of a right triangle is 2 units longer than the longer leg which is 14 units longer than the shorter leg. Determine the lengths of the three sides. How do i begin solving this question?1 solutions Answer 179787 by oberobic(2304)   on 2009-12-05 16:33:14 (Show Source): You can put this solution on YOUR website!The Pythagorean Theorem is fundamental to the solution: , where c = hypotenuse a = longer leg b = other leg . The problem setup gives you 3 important relationships. and . So, . Of course, . Going back to the Pythagorean Theorem: . By substitution, we can cast the entire problem in terms of b, the shorter leg. . . Subtract b^2 from both sides . Subtract 32b from both sides . Subtract 256 from both sides so, . Can we factor 60 such that the factors are 4 apart? 2*30? no 3*20? no. 4*15? no. 5*12? no. 6*10? yes! . Thus we have two candidate values for b: 10 and -6. Since the leg of a triangle cannot be negative, the proposed solution is b = 10. . Substituting back into what we were told in the problem setup: . We always check our proposed solution. Here we just use the Pythagorean Theorem again. That checks, so we have the correct answer. Done.
 Quadratic_Equations/246003: Sharing Cost. The members of a flying club plan to share equally the cost of a \$200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by \$2000. How many members are currently in the club?1 solutions Answer 179693 by oberobic(2304)   on 2009-12-05 00:10:33 (Show Source): You can put this solution on YOUR website!The club has x members now, so the average cost = 200,000/x. If they add 5 members, the average cost = 200,000/(x+5) - 2000. So, we can express this as: . . Multiply through by to eliminate the denominators. . . . . Divide by 2000 . The 100x cancel, so collect terms and rearrange . Multiply by -1 . Factor . So x can = either -25 or 20. -25 members does not make sense, so x = 20 and x+5 = 25. . Checking our answer. average cost with 20 members . average cost with 25 members . So the difference in average cost is 2000, as the problem requires.
 Graphs/245815: I need help. Thank 1.Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specified variable. 2. Ellen wishes to mix candy worth \$1.80 per pound with candy worth \$2.40 per pound to form 48 pounds of a mixture worth \$2.00 per pound. How many pounds of the more expensive candy should she use? . Given the pair of linear equations in two variables: •Find the x- and y-intercepts (if any) for each line. Show your work. •Plot those intercepts, and graph the two lines. Submit your graph through the Dropbox. •Apply elimination or substitution to find the coordinates of the point of intersection (if there are no solutions or infinite solutions, state this). Show your work. 15x + 11y = -17 8x - 6y = 741 solutions Answer 179691 by oberobic(2304)   on 2009-12-04 22:36:16 (Show Source): You can put this solution on YOUR website!I will solve the candy problem. Start with what you know. x = candy @ \$1.80/lb y = candy @ \$2.40/lb . She wants to produce 48 lbs valued at \$2.00/lb. . So we have x(1.80) + y(2.40) = 48(2.00) = 96. . But with only one equation, having two unknowns is not solvable. But since we know the total, we define x in terms of y or y in terms of x. x lb = 48 lb - y lb y lb = 48 lb = x lb . Rewriting the equation we have: 1.8x + 2.4y = 96 . Substitute y = 48-x 1.8x + 2.4(48-x) = 96 . Multiply thru 1.8x + 115.2 - 2.4x = 96 . Collect terms -0.6x + 115.2 = 96 . Subtract 115.2 from both sides -0.6x = 96 - 115.2 = -19.2 . Multiply both sides by -10 6x = 192 . Divide both sides by 6 x = 32 . Looking back to our setup, we know that y = 48-x = 48-32 = 16. So we have 32 lb @ \$1.80/lb = \$57.60 And we have 16 lb @ \$2.40/lb = \$38.40 Thus we have a total of 48 lb and a total cost of \$57.60 + \$38.40 = \$96.00. 96/48 = \$2/lb. 48 lb @ \$2/lb = \$96. So our solution checks. .
 Travel_Word_Problems/245998: A carpenter is building a rectangular room with a fixed perimeter of 240 ft. What dimensions would yeild the maximum area? what is the maximum area? 1 solutions Answer 179689 by oberobic(2304)   on 2009-12-04 22:01:35 (Show Source): You can put this solution on YOUR website!P = 240 = 2L + 2W A = L*W . By theorem (or from calculus), we know the maximum area is a square, so: L=W. . P = 2L + 2W = 4L = 240 L = 60 . So a 60 by 60 room is 3600 sq ft in area. . We can test the area by testing another room with dimensions close to 60 by 60 and P = 240. . Let's try 59 by 61. P = 2(59)+2(61) = 118+122 = 240. OK. A = 59 * 61 = 3599, which is less than 3600. . Let's try 58 by 62. P = 2(58) + 2(62) = 116 + 124 = 240. OK A = 58 * 63 = 3596, which is less than 3600 and less than 3599. . Let's try 57 by 63. P = 240. OK A = 57 * 63 = 3591, which is less than 3600 and less than 3599 and less than 3596. The area is decreasing as the values get further apart. . How about 1 by 119? P = 2(1) + 2(119) = 2 + 238 = 240. A = 1*119 = 119, which is way less... . Another way to look at this problem is the define the perimeter = 2C, where C = L+W. . That way L = C-W, so the area will be (C-W) * W = CW - W^2. . The maximum value of CW - W^2 is C^2/4, which occurs at W = C/2. . So, if W = C/2, and C=L+W, then L=C/2, so we have a square.
 Geometry_Word_Problems/245990: Using the existing elevation of the Big Island of Hawaii, and an assumed lava flow-rate from the hot spot of 300,000 cubic-meters per second, how long did it take to form the Big Island of Hawaii? Please show assumptions, formulas, and your calculation.1 solutions Answer 179682 by oberobic(2304)   on 2009-12-04 21:25:53 (Show Source): You can put this solution on YOUR website!What is the area of the island in square meters? Call it A. What is its average elevation in meters? Call it E. A*E = volume of the island above sea level in cubic meters. Divide by 300,000 cubic meters/second to yield the number of seconds. Convert the seconds to minutes or to hours or to days or to years.
 Miscellaneous_Word_Problems/245899: In a movie theatre line, x people are behind Darsh, who is y places in front of Anil. If there are z people in front of Anil, how many people are in the line?1 solutions Answer 179680 by oberobic(2304)   on 2009-12-04 21:18:16 (Show Source): You can put this solution on YOUR website!A sketch of the line would help a lot! . Start of Line: __________ Anil __________ Darsh ___________:Front of line . The number of people from the start of the line to Darsh is said to be: x . The number of people from Anil to Darsh is given: y . The number of people from Anil to the front of the line is given as: z . So we can separate the line into 3 segments: . Start of line to Anil = x - y . From Anil to Darsh = y . From Darsh to Front of the line = z - y . So we add the three segments and get: x-y + y + z-y = x + z - y . We can check with a concrete example. Assume 10 people in the line behind Anil, 5 between Anil and Darsh, and 5 from Darsh to the front of the line. So there are 22 people in the line: 10+5+5+Anil+Darsh. . ||||||||| Anil ||||| Darsh |||||, where each vertical bar represents a person. . x = 10 + Anil + 5 = 16 . From Anil to the front of the line is z: . z = 5 + Darsh + 5 = 11 . We know that y = 5 because that is the number of people we put between Anil and Darsh in our setup. . So, we have 16 + 11 - 5 = 22, which is the number of people we know are in the line: x + z - y.
 Radicals/245988: why dose = and not = what happens to the 6?? 1 solutions Answer 179673 by oberobic(2304)   on 2009-12-04 20:48:51 (Show Source): You can put this solution on YOUR website!When you factor you find that it = . To check, multiply through: = . We observe that: is equivalent to: . So, equals: . Note: I had to assume the original equation is as I wrote it, which has a in the middle, not .
 Average/245895: If x and y are positive numbers and the average of 4, 20, and x is equal to average of y and 16, then the ratio x:y is1 solutions Answer 179637 by oberobic(2304)   on 2009-12-04 17:58:20 (Show Source): You can put this solution on YOUR website!In the setup to the problem you are told: . So we can cross multiply . Multiplying through the numerators . . Subtracting 48 from both sides 2x = 3y . So, by inspection, the ratio x:y = 2:3 using their coefficients.
 Linear_Equations_And_Systems_Word_Problems/245917: A store mixes Kenyan coffee worth \$10 per kilogram and Venezuelan coffee worth \$12 per kilogram. The mixture is to sell for \$11 per kilogram. Find how much of each should be used to make a 360-kilogram mixture How many kilograms of the Kenyan coffee should be in the mixture? _____ Kg1 solutions Answer 179631 by oberobic(2304)   on 2009-12-04 17:37:22 (Show Source): You can put this solution on YOUR website!You can start this problem thinking in terms of K amount of Kenyan coffee @ \$10 per kilogram + V amount of Venezuelan coffee @ \$12 per kilogram = 360 kg @ \$11/kg . The problem asks how many kg of Kenyan coffee in the mixture. Well, it can be said the amount is 360 - V. That is, the amount of Kenyan = known total - unknown amount of Venezuelan coffee. . At first, this may not seem like much help. But in fact, that is one of the key ways to reduce the number of unknown variables in algebra word problems. . K = 360 - V V = V . Substituting in the total cost equation: . 10*(360-V) + 12*(V) = 360*11 . Multiplying through: 3600-10V + 12V = 3960 . Collecting like terms 3600 + 2V = 3960 . Subtracting 3600 from both sides 2V = 360 . Dividing both sides by 2 V = 180 . So, V = 180, which means K = 360-180 = 180. . We have equal amount of K and V in the total, which makes sense because we want the mixture to cost \$11/kg and the two components cost \$10/kg and \$12/kg. \$11/kg is the average. . We can check our work by substitution back into the equation to see if our result produces the given result. 180*10 + 180*12 = 36*11 1800 + 2160 = 3960 = 36*11 . Done.
 Travel_Word_Problems/243761: How long would it take a jet flying Mach 2.3 or approx. 1,800 mph--to travel 15 miles? Thanks for your help John Davis1 solutions Answer 178563 by oberobic(2304)   on 2009-11-29 21:05:33 (Show Source): You can put this solution on YOUR website!The jet is going 1800 miles/hr. You want to know how much time it takes to go 15 miles. Looking at the units, you can see that you need to divide 15 by 1800 to end up with hours. . 15/1800 = 0.008333 hr . Since 1 hr = 60 minutes, we can multiply by 60 to get how many minutes to fly 15 miles. . 0.4999 min (or about 1/2 min) . Multiplying by 60 seconds, we will get how many seconds to fly 15 miles. . 29.9999 seconds (or about 1/2 min). . Done.
 Problems-with-consecutive-odd-even-integers/243748: Please help me in solving this word problem, any and all assistance will be forever appreciated. Word Problem: The sum of two consecutive integers is 29 less than their product.Find the integers.1 solutions Answer 178559 by oberobic(2304)   on 2009-11-29 20:50:34 (Show Source): You can put this solution on YOUR website!We always want to use the fewest unknowns, which usually means defining as many variables in terms of another variable as possible. Instead of defining two consecutive integers as x & y, define them as x and x+1. . We are told the sum (x + x+1) is 29 less than the product (x * (x+1)). . x * (x+1) = x + (x+1) + 29 . x^2 + x = 2x + 30 . Subtracting 2x from both sides x^2 - x = 30 Subtracting 30 from both sides x^2 - x - 30 = 0 . We need to determine the factors of 30 that are 1 apart to solve this without using the quadratic equation. We see 5 * 6 = 30 probably will work. . (x - 6)(x + 5) = 0 . That gives us two values of 'x' to test: x=6 and x=-5. . Testing x=6. x = 6 x+1 = 7 Product = 6*7 = 42 Sum = 6+7 = 13 Does 42 = 13 + 29? Yes. So this solution works. . Testing x=-5. x = -5 x+1 =-4 Product = -5*-4 = 20 Sum = -5 + -4 = -9 Are these 29 apart? Yes, so this checks, too. . Our solutions are: 5, 6 and -5,-4 . Done.
 Problems-with-consecutive-odd-even-integers/243740: Please help me to figure out this problem: THis is how the word problem is written in the book: Find three consecutive even intergers such that the square of the largest exceeds the sum of the squares of the other two by 12.1 solutions Answer 178554 by oberobic(2304)   on 2009-11-29 20:41:16 (Show Source): You can put this solution on YOUR website!For most problems like this, your best interest is served by using as few variables as possible. For example, the setup says "3 consecutive EVEN integers," which is a temptation to call x, y, and z. But from what we know about consecutive numbers, they're just 1 apart. Consecutive EVEN integers are 2 apart. So we can define the 3 unknown numbers in terms of x. a = x b = x+2 c = x+4 . We're all told the square of the largest number is 12 more than the sum of the squares of the other two numbers. We can write this fact as: . Combining we have: . . Resolving the squares. . Collecting like terms Subtract x^2 from both sides Subtracting 8x from both sides Subtracting 16 from both sides . We can factor an 'x' from the left-hand. . So we have two possible solutions: x=0 x=4 . Testing x=0. 0^2 = 0 2^2 = 4 4^2 = 16 Is 4^2 equal to the sum of the other two squares + 12? Yes. . Testing x=4. 4^2 = 16 6^2 = 36 8^2 = 64 Is 8^2 equal to the sum of the other two squares + 12? 16+36=52, with is 12 less than 64. So this works, too. . The EVEN consecutive digits are: 0, 2 & 4 and 4, 6 & 8 . Done.
 Miscellaneous_Word_Problems/243737: The area of a rectangle is 80 square feet. The length is 2 feet longer than the width. Find the measure of each.1 solutions Answer 178542 by oberobic(2304)   on 2009-11-29 20:19:53 (Show Source): You can put this solution on YOUR website!We know the area of a rectangle is width times the length. . We are told A = 80 . We also are told L is 2 feet longer than the width. or You pick. . Substituting what we know: Multiplying through the right-hand: Equal things are equal, so we can rewrite: Subracting 80 from both sides . We now consider whether it can be factored. The factors of 80 are 2*40, 4*20, 5*18, 8*10... We have to have different signs to get them to multiply to -80. And we need them to be 2 apart to have the solve the L term. 8 & 10 is the way to go. . . So we have two candidate solutions: L=10 and L=-8. Since we are talking about the area of a rectangle, a length of -8 is not reasonable. So we'll test 10. . Looking back at the equations we established: . So we propose the L=10 and W=8. . Checking the Area, we test: . That checks. So we're done.
 Linear-systems/243718: how do i find out if a graph on an equation will be parallel or perpendicular if only given the points? EX. (3,1) (5,3) is the graph of the equation parallel, perpendicular or neither?1 solutions Answer 178528 by oberobic(2304)   on 2009-11-29 19:53:47 (Show Source): You can put this solution on YOUR website!Given the two points, you can draw a line. But any line will be perpendicular to any other line that has a slope = negative inverse of the first line; and it will be parallel to any line that has the same slope. So you need to give us more information in your problem statement. . With two points, you can determine the slope = change in y divided by change in x, which is also known as the rise over the run. . (x1,y1) = (3,1) (x2,y2) = (6,3) . m = slope = (y2 - y1) / (x2 - x1) m = (3-1) / (6-3) m = 2/3 . The slope-intercept formula for a line is: y = mx + b. We only have a value for m, so we cannot determine the y-intercept (that is, where it crosses the y-axis when x=0). . We can 'assume' b = 0 to be able to draw a line to show you what the line looks like. . y = 2/3x + 0. Graph: . As I mentioned above, a line with negative inverse slope will be perpendicular. Given y = 2/3x, then the perpendicular line will be y = -3/2x. Graph: . A parallel line will have the same slope, but a different y-intercept. So, we'll 'assume' the second intercept is 3 so that the graph will show the parallel. y = 2/3x + 3 Graph: . To finish this lesson, we can plot a line parallel to the first perpendicular. Let's assume a y-intercept of -4, so y = -3/2x - 4. Graph:
 Triangles/243712: If the measures of the angles of a triangle are in the ratio 1:3:5, the number of degrees in the measure of the smallest angle is1 solutions Answer 178517 by oberobic(2304)   on 2009-11-29 19:38:47 (Show Source): You can put this solution on YOUR website!This problem hinges on your remembering that the sum of the angles in a triangle is always 180. . In this case we have 3 unknown angles: a, b, and c. However, we are told they have a specific relationship: 1 to 3 to 5. So the second angle is 3 times the first and the third angle is 5 times the first. . a = a b = 3a c = 5a . a + b + c = 180 Substituting, a + 3a + 5a = 180 9a = 180 Divide both sides by 9 a = 20 . Substituting back into the formulas we defined. a = 20 b = 3a = 3(20) = 60 c = 5a = 5(20) = 100 . Check the work. Does 20 + 60 + 100 = 180? Yes. . Done.
 Linear-equations/243703: How do you convert a linear equation to standard form? Having problems with positive and negative signs1 solutions Answer 178516 by oberobic(2304)   on 2009-11-29 19:31:41 (Show Source): You can put this solution on YOUR website!A linear equation in standard form is: Ax + By = C The A, B, and C are numeric values. Traditionally, A is a + number. . The other common form is slope-intercept form: y = mx + b I use slope-intercept to solve most problems. . You will need to be more specific about what your problem with positive and negative numbers.
 Functions/243708: Solve using the substitution method. 4m+n=23 m-4n=101 solutions Answer 178512 by oberobic(2304)   on 2009-11-29 19:23:51 (Show Source): You can put this solution on YOUR website!With the substitution method, you isolate one unknown and then substitute it into the other equation to find a solution. The equations are: EQ1: 4m + n = 23 EQ2: m - 4n= 10 . Working with EQ2. Add 4n to both sides. m = 4n + 10 . Now we can substitute it back into EQ1. 4(4n+10) + n = 23 Multiply through the left-hand pararentheses 16n + 40 + n = 23 Collect like terms 17n + 40 = 23 Subtract 40 from both sides 17n = - 17 Divide both sides by 17 n = -1 . Now we take that value and substitute back into EQ2. m = 4(-1) + 10 m = 6 . So our proposed solution is: n = -1 m = 6 . We can check by putting these values back into the equations. 4(6) + (-1) = 24 - 1 = 23. Check. 6 - 4(-1) = 6 + 4 = 10. Check.
 Triangles/243639: The perimeter of a triangle is 110cm. one side is twice the second side. the third side is 30cm more than the second side. find the length of each side1 solutions Answer 178479 by oberobic(2304)   on 2009-11-29 18:01:18 (Show Source): You can put this solution on YOUR website!The perimeter of a triangle = a + b + c. where a = first side b = second side c = third side . We are told P = 110. . To solve word problems, it usually is best to define these variables in terms of one another, which the problem tells you how to do so. For example, . a = a b = 2a c = b+30 = 2a+30 . 110 = a + b + c Substituting for 'b' and 'c' defined in terms of 'a'. 110 = a + 2a + 2a+30 Collecting terms 110 = 5a + 30 Subtract 30 from both sides 80 = 5a Equals are equal, so 5a = 80 Divide both sides by 5 a = 16 . Substituting back into the formulas we set up above. b = 2a = 2(16) = 32 c = b + 30 = 32 + 30 = 62 . Checking our work: a + b + c = 16 + 32 + 62 = 110 Done.
 Triangles/243641: the perimeter of an isoceles triangle is 54ft. let s be the length of one of the two equal sides . is it possible for s to be 30ft.1 solutions Answer 178473 by oberobic(2304)   on 2009-11-29 17:44:34 (Show Source): You can put this solution on YOUR website!Given the perimeter of any triangle is a + b + c. Given your triangle is an isosceles, it's perimeter will be 2*sides + base. So, given P = 54, then s cannot be 30.
 Expressions-with-variables/243631: an ad for a special baseball card that was posted on the internet cloaims that the value of the card "doubles every year." Jerome buys the card for \$40 at the end of the year 2001. If the value of the card does indeed double every year, in what year will the value of the card first reach \$5000? Thank you1 solutions Answer 178468 by oberobic(2304)   on 2009-11-29 17:38:52 (Show Source): You can put this solution on YOUR website!To say that a value doubles every year means that it will go up in value by 2, 4, 8, 16, 32, etc. Notice that those are 2 raised to the 't', where 't' = years numbered 1, 2, 3, 4, 5, etc. . f(x) = future value P = present value = \$40 t = year - 2001, which means t will take on values 0, 1, 2, 3, 4, 5, etc. Note that an exponent of 0 means the value is 1. . f(t) = P*2^t . year...t...f(t) 2001...0...40 2002...1...80 2003...2...160 2004...3...320 2005...4...640 2006...5...1280 2007...6...2560 2008...7...5120 . So the card first reaches \$5000 value in 2008.
 Unit_Conversion_Word_Problems/243605: jake can rake the lawn in 2hrs 22mintues.Jill can rake the same lawn 27 mintues quicker .how long does it tak ejill to rake the lawn1 solutions Answer 178452 by oberobic(2304)   on 2009-11-29 17:01:24 (Show Source): You can put this solution on YOUR website!Convert Jake's total time into minutes: 2*60 + 22 = 120 + 22 = 144 . We are told Jill can do the job 27 minutes quicker, so her speed is 144-27 = 117.
 Quadratic_Equations/243590: I am struggling on a few word problems on my homework, please help me, it is due tomorrow! You have 280 feet of fencing. Do you have enough to fence a rectangular region with an area of 4850 sq. ft. ? and... In 1987, your uncle opened a neighborhood grocery store. for 1987-2007 his annual sales, S(in millions of dollars) could be modeled by S= -0.035t^2 + 0.8t + 0.5 where t=0 represents 1987. During which years of operation were his annual sales 3 million dollars?1 solutions Answer 178448 by oberobic(2304)   on 2009-11-29 16:49:10 (Show Source): You can put this solution on YOUR website!(1) Since I don't know the dimensions of the rectangle, I will assume it is a square. Given the area = 4850, then the sides are the square root of 4850, which = 69.64. Since the perimeter of a square is simply 4s, s = length of a side, then YES your 280 ft of fencing can do the job. . (2) This one requires you to set up the given equation and then substitute the values of t, where ```year t 1987 0 1988 1 1989 2 1990 3 etc. ``` . The equation is . Using Excel, I created the following table for the years 1987-2007. Notice that the sales go up for a while and then start back down. ```yr t Sales 1987 0 0.500 1988 1 1.265 1989 2 1.960 1990 3 2.585 1991 4 3.140 1992 5 3.625 1993 6 4.040 1994 7 4.385 1995 8 4.660 1996 9 4.865 1997 10 5.000 1998 11 5.065 1999 12 5.060 2000 13 4.985 2001 14 4.840 2002 15 4.625 2003 16 4.340 2004 17 3.985 2005 18 3.560 2006 19 3.065 2007 20 2.500 ```
 Numeric_Fractions/243593: Help! 2/x+3/y divided by 3/x-2/y seems simple but I can't figure it out. I would think that you would simplify the the numerator by multiplying it by the LCD xy then the same for the denominator but it doesnt work out. 1 solutions Answer 178438 by oberobic(2304)   on 2009-11-29 16:24:22 (Show Source): You can put this solution on YOUR website! . . The division can be replaced by multiplication by the inverse. So instead of: . we can substitute: . . The 'xy' terms will cancel, so we have: .
 Linear-equations/243571: Find the slope and the y-intercept of the line Write fractional answers in lowest terms 6y+9x+4=16+9x The slope is ? And the y-intercept is (0,?) can anyone help me with this please? Thanks1 solutions Answer 178429 by oberobic(2304)   on 2009-11-29 15:50:58 (Show Source): You can put this solution on YOUR website!First, get the equation into y = mx + b format. . 6y + 9x + 4 = 16 + 9x Subtract 4 from both sides 6y + 9x = 12 + 9x = 9x + 12 Subtract 9x from both sides 6y = 12 Divide both sides by 6 y = 12/6 = 2 . Note that the 'x' term seems to have 'disappeared.' Of course, the x-axis exists, so it cannot 'disappear.' So logically it has to be there, but with a coefficient = 0. . y = 0m + 2 . So, the slope = m = 0, which means it is a horizontal line. . When x = 0, y = 2. (Of course, when x=anything, y=2.) . Graph: . Done.
 Rectangles/243566: The perimeter of a rectangle is 800 feet, and length of it is 50 feet less than half the width. What are it's dimensions?1 solutions Answer 178424 by oberobic(2304)   on 2009-11-29 15:41:51 (Show Source): You can put this solution on YOUR website!CORRECTION! I read the problem too fast the first time. (sorry) . The perimeter of a rectangle = 2L + 2W, where L=length and W=width. We are told L is 50 ft less than HALF the W, so L = .5W -50. We are told the perimeter = 800. . Substituting we have: 800 = 2L + 2W 800 = 2(.5W-50) + 2W Multiplying the factor 800 = W - 100 + 2W Collecting like terms 800 = 3W - 100 Adding 100 to both sides 900 = 3W 3W = 900 Dividing both sides by 3 W = 900/3 = 300 . Looking back, we know L = .5W-50, so L = 150 - 50 = 100. . Check the perimeter. 2W + 2L = 2(300) + 2(100) = 800. This is what it's supposed to be. Done.