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# Recent problems solved by 'josmiceli'

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 Circles/297798: I am having trouble in my college geometry class. The problem is as follows: Find the circumference and area of the circle whose equation is x^2 + y^2 =36. Round to the nearest tenth.1 solutions Answer 214393 by josmiceli(9664)   on 2010-04-28 13:30:13 (Show Source): You can put this solution on YOUR website! When , and also When and So, the diameter is measured along either axis, and the radius is Just plug this into and
 Quadratic_Equations/297403: I am having trouble with writing in 50 words why the line x=4 is a vertical line. I think that x=4 is a vrtical line because it is perpindicular to the y axis.Can you help me please? I would very much appreciate it.1 solutions Answer 214204 by josmiceli(9664)   on 2010-04-27 19:16:19 (Show Source): You can put this solution on YOUR website!The thing to think about is this: No matter what this line looks like you know that every point imaginable on the line must satisfy it's equation which is whatever ends up being. The line is perpendicular to the axis at .
 Age_Word_Problems/297444: Hot chocolate sells for \$.75 and coffee sells for \$.50 at a football game. If they sold \$200 worth of hot drinks and used 295 cups, how many of each drink did they sell?1 solutions Answer 214201 by josmiceli(9664)   on 2010-04-27 19:10:27 (Show Source): You can put this solution on YOUR website!Let = number of hot chocolates sold Let = number of coffees sold given: (1) (2) Multiply both sides of (1) by and subtract from (2) and, since They sold 210 hot chocolates and 85 coffees check: (2) (2) OK
 Rational-functions/297439: After taking 3 quizzes, your average is 79 out of 100. What must your average score be on the next five quizzes to increase your average to 84?1 solutions Answer 214195 by josmiceli(9664)   on 2010-04-27 19:00:59 (Show Source): You can put this solution on YOUR website!Let = the sum of the first 3 quiz scores given: Let = the sum of the last 5 quiz scores The average score of the last 5 quizes is 87%
 Proportions/297433: a student answered 87.5% of the exam correctly. if she answered 42 problems correctly, how many questions were therer on the exam?1 solutions Answer 214189 by josmiceli(9664)   on 2010-04-27 18:50:36 (Show Source): You can put this solution on YOUR website!Let = number of questions on exam There were 48 questions on the exam
 Polynomials-and-rational-expressions/297418: A number minus twice its reciprocal is the same as the reciprocal of four times the number. find the number. I have the equation as x-2 1/x = 1/4x then i multiplied 2 by 1/x and got 2/x Then i changed the x/1-2/x into the same base so we can subtract and got (x^2-2)/x + 1/4x From there i am lost.1 solutions Answer 214184 by josmiceli(9664)   on 2010-04-27 18:39:47 (Show Source): You can put this solution on YOUR website!Let = the number Multiply both sides by Multiply both sides by Take the square root of both sides and check answer: Multiply both sides by OK
 Linear-equations/297417: How to you solve : 2x + 4y=81 solutions Answer 214182 by josmiceli(9664)   on 2010-04-27 18:29:38 (Show Source): You can put this solution on YOUR website!You can't solve this. Solving means to find the numerical values of the unknowns, x and y In order to solve, the number of unknowns must equal the number of equations. You have 2 unknowns and only 1 equation. You can make an x-y plot of the equation. It's a straight line and here it is:
 Systems-of-equations/297277: Sammy sold 700 tickets totaling \$13330. If the tickets were \$25 adi;ts amd \$15 students, how many of each ticket did Sammy sell? 1 solutions Answer 214087 by josmiceli(9664)   on 2010-04-27 14:05:40 (Show Source): You can put this solution on YOUR website!Let = number of adult tickets sold Let = number of student tickets sold given: (1) (2) ----------------------- Multiply both sides of (1) by and subtract from (2) and, since Sammy sold 283 adult and 417 student tickets check: OK
 Expressions-with-variables/297269: Tom can do a job in 4 hours, Joy can do the same job in 3 hours, How many hours will it take the two of them to do the job if they work together 1 solutions Answer 214081 by josmiceli(9664)   on 2010-04-27 13:56:55 (Show Source): You can put this solution on YOUR website!Add their rates of working to get their rate working together Tom's rate: (1 job)/(4 hrs) Joy's rate: (1 job)/(3 hrs) Multiply both sides by hrs
 logarithm/297262: log(3,1/81)1 solutions Answer 214080 by josmiceli(9664)   on 2010-04-27 13:51:02 (Show Source): You can put this solution on YOUR website! Let this expression equal Rewrite this as:
 Finance/297266: What are the algebraic formulas for this (in a collection of nickels, dimes, and quarters, there are twice as many dimes as nickels and 3 fewer quarters than dimes. if the total value is \$4.50 how many of each coin are there)1 solutions Answer 214077 by josmiceli(9664)   on 2010-04-27 13:43:33 (Show Source): You can put this solution on YOUR website!Let = number of nickels Let = number of dimes Let = number of quarters given: (in cents) -------------------------- This is 3 equations and 3 unknowns, so it's solvable By substitutions: And, substituting again: and, since and There are 14 dimes, 11 quarters, and 7 nickels check: OK
 Travel_Word_Problems/297242: If i ride my bike 8 miles and then walk 4 miles it takes me 3hrs. If i walk 1/4 the rate that i ride, how fast did i ride my bike?1 solutions Answer 214073 by josmiceli(9664)   on 2010-04-27 13:27:35 (Show Source): You can put this solution on YOUR website!Let = your speed riding your bike Then, your speed walking is In words: (time spent walking and biking) = (distance biking/biking speed) + (distance walking/walking speed) Multiply both sides by The speed biking is 8 mi/hr check: OK
 Linear_Equations_And_Systems_Word_Problems/297255: 8.25 months = how many days1 solutions Answer 214059 by josmiceli(9664)   on 2010-04-27 13:17:00 (Show Source): You can put this solution on YOUR website!This is a problem of converting units. First of all, forget about any numbers. Just write an expression with units only. Units are hours, yards, dollars, days, miles/hours, etc. In this problem, (months)*(days/month) = days All months don't have 30 days, but it's a common estimate Now write it with numbers: months x days/month = days
 Travel_Word_Problems/297107: A dog is walking along a train track on e day, and traceled along that track onto a train bridge. When the dog was 1/4 of the way across the bridge, he heard a train whistle from an oncoming train that was coming in the same direction the dog had already come. The dog bounded away form the train, and made it to the end of the bridge at exactly the same time as the train. What the dog didn't know, but what was also true, was that the dog could have bounded toward th train and made it to the "start" of the bridge at exactly the same time as the traing. The train was traceling at a speed of 30 mph. How fast was the dog traveling?1 solutions Answer 213973 by josmiceli(9664)   on 2010-04-27 03:36:04 (Show Source): You can put this solution on YOUR website!Let = the dog's speed running Let = the time for the train to just reach the bridge Let = the length of the bridge in miles ------------------------- In words: (dog's speed) x (time for train to reach bridge + time for train to cross bridge) = (3/4)x(the length of the bridge) As an equation: (1) --------------------------- In words: (dog's speed) x (time for train to reach bridge) = (1/4)*(length of bridge) As an equation: (2) --------------------------- In words: (train's speed plus dog's speed) x (time for train to reach bridge) = (distance train travels to reach bridge plus distance dog runs) As an equation: (3) ---------------------------- This is 3 equations and 3 unknowns, so it's solvable (1) (1) (1) and (2) and (3) (3) (3) I can substitute (2) in (1) (1) (1) (1) (1) The dog was running 15 mi/hr check answer: (2) (2) (2) Substitute in (3) (3) (3) (3) OK
 Finance/297117: how many liters of 40% solution has to be added to 10 leiters of 80% to make 60%? I need linier equations with 2 viariables to solve1 solutions Answer 213970 by josmiceli(9664)   on 2010-04-27 02:25:06 (Show Source): You can put this solution on YOUR website!Let = liters of 40% solution needed Let = liters of 60% solution you end up with given: (1) (2) ------------------------------------- from (2), (2) ----------------------- and answers -------------------------- check answers: and, since (2) (2) OK
 Problems-with-consecutive-odd-even-integers/297121: One-fifth of sum of two consecutive integers is 22 less than the smaller integer. Find the smaller of the two integers. 1 solutions Answer 213967 by josmiceli(9664)   on 2010-04-27 02:06:15 (Show Source): You can put this solution on YOUR website!Call the consecutive integers and given: Multiply both sides by answer check: OK
 Travel_Word_Problems/296684: A jet fighter cruises at 1.5 times the speed of sound. The speed of sound is 1.24x10^3 km/hr. How many hours does it take for the jet to fly the 5.8x10^3 from new york to paris. Demonstrate the use of scientific method.1 solutions Answer 213755 by josmiceli(9664)   on 2010-04-26 11:59:21 (Show Source): You can put this solution on YOUR website!The speed of the jet is km/hr hr or, about 3 hrs and 7 min
 Travel_Word_Problems/296377: Two trains are coming at each other at sixty miles an hour, one from Chicago, one from Los Angeles. Given an East South East wind of 15 mph in Eastern Colorado, which train uses more fuel to reach its destination?1 solutions Answer 213580 by josmiceli(9664)   on 2010-04-25 17:59:31 (Show Source): You can put this solution on YOUR website!I'm guessing a little, but I believe the wind is OUT OF the ESE direction, so the train from Chicago will have a tailwind (helping), and the train from LA will have a headwind (slowing it) So, the train from Chicago should use less fuel. (assuming they both have the same, or nearly the same, fuel efficiency)
 Travel_Word_Problems/296366: The average speed of a plane is 480 kilometers per hour. How long does it take the plane to travel 140?1 solutions Answer 213578 by josmiceli(9664)   on 2010-04-25 17:52:50 (Show Source): You can put this solution on YOUR website! hr In minutes this is: min min
 Functions/296402: The gas mileage, m, of a specific car is a linear function of the speed, s, at which the car is driven,for 60 less that or equal to s less than or equal to 30. if the car is driven at a rate of 30MPH, the cars gas mileage is 35MPG. If the car is driven at 60MPH the cars gas mileage is 20MPG. I need to use this data (s,m) to write an equation for the gas mileage m. I have know idea how to do this!1 solutions Answer 213576 by josmiceli(9664)   on 2010-04-25 17:47:28 (Show Source): You can put this solution on YOUR website!You need to plot this the same way you plot Plot gas milage, (m) on the vertical axis and speed, (s) on the horizontal axis. This is . You are told that it's a straight line between and . Essentially what you are given is two points, (s,m) on this line (30,35) and (60,20) Now you need the point-slope formula which looks like: Multiply both sides by This is gas milage as a function of speed Here's a plot: Remember that the plot is only good between and
 Finance/296384: FIND THE VERTEX THE LINE OF SYMMETRY THE MAXIMUM OR MINIMUM VALUES OF THE QUADRATIC FUNCTION F(X)=-X^2+10X+5 1 solutions Answer 213568 by josmiceli(9664)   on 2010-04-25 17:22:32 (Show Source): You can put this solution on YOUR website! When the sign of the squared term is minus, the curve has a max and not a min. The x co-ordinate of the max is always at Now I need maximum The line of symmetry is simply the x-value Here's a plot:
 Radicals/296388: Please help me solve this radical equation. Thank you. 1 solutions Answer 213565 by josmiceli(9664)   on 2010-04-25 17:10:13 (Show Source): You can put this solution on YOUR website! This is the same as: Take the cube root of both sides square both sides answer check: close enough
 Triangles/296392: what would the missing side be to a right triangle with the sides of 15 and 9? 1 solutions Answer 213564 by josmiceli(9664)   on 2010-04-25 16:55:10 (Show Source): You can put this solution on YOUR website!The missing side is either a leg or the hypotenuse. If it is a leg, then: The missing side is a leg, and it equals 12
 Geometry_Word_Problems/293223: The perimeter of a rectangle is 60 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 144 square feet.1 solutions Answer 211679 by josmiceli(9664)   on 2010-04-17 12:57:31 (Show Source): You can put this solution on YOUR website!Let the width = Let the length = Let the perimeter = Let the area = It is given that ft2 I'll take a guess I'll try I'll try OK Next, I deduce that and Either side must be less than or equal to 6 or greater than or equal to 24
 Geometry_Word_Problems/293198: A circle of radius 2 rolls completely around the inside perimeter of a square of side 10. what distance is covered by the centre of the circle ? a 16 b 24 c 32 d 401 solutions Answer 211675 by josmiceli(9664)   on 2010-04-17 12:32:51 (Show Source): You can put this solution on YOUR website!It will trace out a square who's sides are 1 radius away from the outside square The outside square's sides are units apart. The inside square's sides are smaller, so The perimeter of a square with sides = 6 is units The answer is (b)
 logarithm/293221: CAN YOU PLS TELL ME HOW TO SOLVE LOG 0.3 to the base 9..?? The answer should be 1/2. 1 solutions Answer 211674 by josmiceli(9664)   on 2010-04-17 12:23:08 (Show Source): You can put this solution on YOUR website!The main thing to remember is: LOGS ARE EXPONENTS The other main thing is: You have to know how to read this: First of all, it's telling you that is an exponent, since it says "y = log(something)" Then it tells you that when you raise the base to the exponent , the result is Putting all that together: You can also express as The rule for this is to multiply the exponents You can solve this on a calculator, or take the log to the base of both sides ----------------- Actually, and, as I showed,
 Linear-equations/293220: Find and equation of the line containing the given pair of points (-4,0) and (0,1)1 solutions Answer 211673 by josmiceli(9664)   on 2010-04-17 12:01:05 (Show Source): You can put this solution on YOUR website!The formula to use is where , = (-4,0) and , = (0,1) Plugging these values into the formula: Multiply both sides by answer check: does it pass through the given points? (-4,0) and (0,1) OK
 Average/293200: A week ago, Sandy’s seasonal Little League batting average was 360. After five more at bats this week, Sandy’s batting average is up to 400. What is the smallest number of hits that Sandy could have had this season?1 solutions Answer 211659 by josmiceli(9664)   on 2010-04-17 10:41:33 (Show Source): You can put this solution on YOUR website!The batting average is (hits)/(number of times at bat) x 1000 Let = times at bat last week Let = number of hits last week Let = number of hits this week (1) and after this week: (2) ------------------------------ This is 2 equations and 3 unknowns, so it isn't directly solvable, but it can be analyzed From (1): (1) and from (2) I know that Suppose ends up being (-), so that doesn't work Suppose . Then , and that can't be Suppose From (1) and from (2): (2) (2) The smallest number of hits Sandy could have got this season is , or 12 hits OK
 Travel_Word_Problems/293156: a car driving in fog passed a man walking at 3km\hr in a same direction. he could see the car for 4 minute and up to a distance 100 meter .what was speed of the car?1 solutions Answer 211652 by josmiceli(9664)   on 2010-04-17 10:10:52 (Show Source): You can put this solution on YOUR website!I think that their relative speed is km/hr where is the speed of the car. The car looks like it's going km/min or km/min x min/hr = km/hr The speed of the car is 4.5 km/hr Hope I got it right
 Travel_Word_Problems/292740: An airplne flew for 4 hours with a 20 km/hour tail wind. The return flight against the same wind took 5 hours. Find the speed of the plane in still air. I am having trouble finding the distance flown to figure out the answer.1 solutions Answer 211390 by josmiceli(9664)   on 2010-04-15 20:30:36 (Show Source): You can put this solution on YOUR website!Let = wind speed Let = speed of plane in still air = speed of plane flying with the wind = speed of plane flying against the wind -------------------- Flying with the wind: km (1) km Flying against the wind: km (2) km Since is the same in (1) and (2), they are equal to eachother The plane's speed in still air is 180 km/hr
 Pythagorean-theorem/292741: The base path of a baseball diamond forms a square. If it is 90 ft. from home to first, how far does the catcher have to throw to catch someone stealing second base? Give your answer as a radical expresion in simplest form and then stimate the lenght to the nearest tenth of a foot.1 solutions Answer 211378 by josmiceli(9664)   on 2010-04-15 20:10:26 (Show Source): You can put this solution on YOUR website!It is telling you that ft is one side of the square, and it is asking you for the distance between opposite corners. The sides are all equal to ft and, for a square, the diagonal and a side are in the ratio to , so I can say Multiply both sides by ft (rounded to nearest 1/10 th)