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# Recent problems solved by 'chitra'

chitra answered: 358 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359, >>Next

 Linear-equations/130972: Can you help me solve for x: 4/3 = 8/x I'm not sure where to begin....1 solutions Answer 95605 by chitra(359)   on 2008-03-07 21:35:24 (Show Source): You can put this solution on YOUR website!The given expression is: cross multiply now we get : 4 * x = 8 * 3 ==> 4x = 24 divide by 4 on both sides ==> ==> x = 6 thus the solution
 Polynomials-and-rational-expressions/129592: If P(x)is a third degree polynomial and Q(x) is a fourth degree polynomial what can be said about the degree of P(x)+ Q(x). What I need here is an examples of polynomials that support this. thank you1 solutions Answer 94616 by chitra(359)   on 2008-02-27 23:25:02 (Show Source): You can put this solution on YOUR website!Here goes the examples. Let P(x) be a third degree polynomial as per the data given by you. So P(x) = and Q(x) be a fourth degree polynomial. Q(x) = So the addition of these would result in the following Adding like terms we get: P(x) + Q(x) = thus the degree of the resulting polynomial would be equal to 4 Thus the solution Regards
 Quadratic_Equations/129582: How's it going? I was wondering if you would be able to assist me please, as I am stuck as to how to go about this question. Thank you. The question is as follows: With the use of a graphics calculator, sketch the following y=5x^2-3x+2 Your help with this one is greatly appreciated. Thank you. Cheers D.1 solutions Answer 94615 by chitra(359)   on 2008-02-27 23:14:23 (Show Source): You can put this solution on YOUR website!The given equation represents a parabola since the term x is in terms of a quadratic and it is a parabola facing above(opening upwards) . So on a graphing Calculator, just go and plug in the equation and say plot(graph) The graph of the given curve looks as shown below. Regards
 Polynomials-and-rational-expressions/129562: This question is from textbook algebra 2 find all of the other roots of the polynomial equation x^5-x^3-8x^2+8=01 solutions Answer 94607 by chitra(359)   on 2008-02-27 22:02:15 (Show Source): You can put this solution on YOUR website! by observing the graph we cn find that -1 and +1 are the first twoo roots. The other 3 roots are repeated roots and it would be 2. This can be factorised by the method of trail and error method and then by synthetic division method. by the trail and error method we find that 1 is the first factor Then the second equation is agin siplified here we find that x + 1 is a factor. So will be the next eqn. So the last eqn will be can be factored and thus we get repeated roots hence, the roots are x = 1, -1, 2, 2, 2 (x - 1)(x + 1)(x- 2)(x - 2)(x - 2) Are the roots of the eqn Thus the solution Regards Chitra
 Miscellaneous_Word_Problems/128350: The length of a rectangular sign is 3feet longer than the width. If the sign has a area of 40 square feet for advertising , find its length and its width.1 solutions Answer 93962 by chitra(359)   on 2008-02-22 03:57:03 (Show Source): You can put this solution on YOUR website!Let "x" ft be the width of the rectangle So lenght will be "3 + x" ft Given area = 40 ft^2 We know that the area of the rectangle is given by lenght times breadth 40 = x * (x + 3) 40 = x^2 + 3x ==> x^2 + 3x - 40 = 0 ==> by the method of factoring we find ==> x^2 + 8x - 5x - 40 = 0 ==> x(x + 8) - 5(x + 8) = 0 ==> x = 5 Or x = -8 We dont consider the negative values of x. Therfore x = 5 ft will be the width and x + 3 = 5 + 3 = 8ft will be the lenght of the rectangle thus the solution
 Graphs/128351: Given the parabola y=x^2-6x-7, answer the following questions: what is its x-intercept? Find its y-intercept. Graph the parabola.1 solutions Answer 93960 by chitra(359)   on 2008-02-22 00:25:19 (Show Source): You can put this solution on YOUR website!The given conic is: To find the x-intercept put y = 0 (x + 1)(x - 7) = 0 ==> x = -1 or x = 7 these are 2 x - intercepts To find the y- intercept put x = 0 ==> y = 0 - 6(0) - 7 ==> y = -7 This is the one y intercept. Graph looks this way:
 Travel_Word_Problems/128132: John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time? 1 solutions Answer 93823 by chitra(359)   on 2008-02-21 03:05:29 (Show Source): You can put this solution on YOUR website!Here by the data that is given - Distance = 28 miles time taken is 30 mins Let us convert the time in minutes to hours 1 hr = 60 mins x hr = 30 mins ==> x = 1/2 hr ==> x = 0.5 hr We have to calculate the speed. Speed = Distance traveled / time taken Speed = 28/0.5 Speed = 56 miles/hour
 Inverses/128137: -15+8x=-311 solutions Answer 93822 by chitra(359)   on 2008-02-21 02:58:00 (Show Source): You can put this solution on YOUR website!I assume that you have to solve for the given question. If that is not the instruction given in your question then revert .. I'll help you The given equation is: -15 + 8x = -31 ==> 8x = -31 + 15 ==> 8x = -16 ==> x = - 2
 Linear_Algebra/128140: 2a+5+5=201 solutions Answer 93821 by chitra(359)   on 2008-02-21 02:51:56 (Show Source): You can put this solution on YOUR website!The given expression is: ==> 2a + 10 = 20 ==> 2a = 20 - 10 ==> 2a = 10 ==> ==> a = 5 thus the solution.
 Numeric_Fractions/126415: Can you please help with the question. If you drove 100 miles on 5 gallons of gas, how many miles can you drive on 12 gallons?1 solutions Answer 92626 by chitra(359)   on 2008-02-12 00:40:31 (Show Source): You can put this solution on YOUR website!Given that 5 gallons of gas runs for 100 miles So therfore 12 gallons runs for -- miles 5 -----> 100 12 -------> x ? x = (12 * 100)/5 x = 12 * 20 x = 240 thus the solution.
 Radicals/125373: I was wanting to know if the was a easy way to simplify radicles. Im in geometry but we are working with radicals and my teacher hasnt done a very good job explaing how to simplify radicals. ex. sqrt 52. I know thats not a perfect square but im somewhat confused on how to simplify them.1 solutions Answer 91873 by chitra(359)   on 2008-02-06 21:11:26 (Show Source): You can put this solution on YOUR website!Hey hello.. Get back to me with the sums.. I'll surely help you with the solutions.. You can avail a free demo too on this Chapter.. Regs Math Tutor
 Expressions-with-variables/124972: i need to be shown the work to get the answer to this problem. what is the value of this rational expression when x = 3? x-1 _____ (x+1)(x-5) 1 solutions Answer 91611 by chitra(359)   on 2008-02-05 02:45:13 (Show Source): You can put this solution on YOUR website!The given expression is: When x = 3, just plugin the above equation. ==> Thus the solution.
 expressions/124973: how step by step I can simplify this example (2a)(5a)(6a)1 solutions Answer 91610 by chitra(359)   on 2008-02-05 02:38:10 (Show Source): You can put this solution on YOUR website!The given expresion is: (2a)(5a)(6a) ==> (2 * 5 * 6) * (a * a * a) ==> (60) * ==> Thus the solution
 Linear-equations/124954: I am confused can someone help? I need to solve each system by the substitution method and determine if they are independent, dependent, or inconsistent. first line thanks1 solutions Answer 91609 by chitra(359)   on 2008-02-05 01:49:46 (Show Source): You can put this solution on YOUR website!The given equations are: 2y = x + 6 ---------------(1) -3x + 2y = -2 --------------(2) Substituting (1) in (2) we get: -3x + x + 6 = - 2 -2x = -2 - 6 -2x = -8 x = 4 By back substitution we get the "y" value: 2y = 10 ==> y = 5 So we observe that the line intersects at (4,5) for both the graphs. Hence the given system of equations are Consistent & Dependent Thus the solution. Here are the notes that will help you determine the category under which they fall. If the two equations describe the same line, and thus lines that intersect an infinite number of times, the system is dependent and consistent. If the two equations describe lines that intersect once, the system is independent and consistent. If the two equations describe parallel lines, and thus lines that do not intersect, the system is independent and inconsistent.
 Graphs/124965: g(x) = 5x/2^2+11 solutions Answer 91608 by chitra(359)   on 2008-02-05 01:08:55 (Show Source): You can put this solution on YOUR website!The graph is as follows:
 Miscellaneous_Word_Problems/124939: Kesha has collected the autographs of 9 more television celebrities than she has of movie stars. each tv celebrity autograph is worth \$75 and each movie star autograph is worth \$250. her colection is valued at \$2,300. how many Tv celebrity autographs does she have? how many of movie star autographs does she have?1 solutions Answer 91607 by chitra(359)   on 2008-02-05 01:02:00 (Show Source): You can put this solution on YOUR website!Let "x" represent the autograph of the movie stars and "y" represent the autograph of the tv celebrities. So according to the given data, she has 9 more autographs of the tv celebs than the movie stars. So y = x + 9 Now let us wirte the equation 250x + 75y = 2300 Substitute for "y" we get: 250x + 75(x + 9) = 2300 250x + 75x + 675 = 2300 325x = 1625 x = 5 Pluggin back we get the value of y. y = x + 9 y = 5 + 9 y = 14 Thus, the solution.
 Distributive-associative-commutative-properties/124947: How would you factor out the greatest common factor in this problem? 21b^4-14b^21 solutions Answer 91587 by chitra(359)   on 2008-02-04 22:44:29 (Show Source): You can put this solution on YOUR website!The given expression is: Here we observe that b^2 is the highest factor among the variables. Then among the numbers both are multiples of 7. so take out 7 as a common factor. Thus the solution.
 Linear_Equations_And_Systems_Word_Problems/124940: One number exceeds three times a second number by 7. The sum of twice the larger number and four times the smaller nu mber is 44. What are the numbers?1 solutions Answer 91586 by chitra(359)   on 2008-02-04 22:40:08 (Show Source): You can put this solution on YOUR website!Let the numbers be x & y. According to the data given we write "x" in terms of "y". x = 3y + 7 Given that: 2(3y + 7) + 4y = 44 6y + 14 + 4y = 44 10y = 44 - 14 10y = 30 y = y = 3 By back substitution, we get: x = 3(y) + 7 x = 3(3) + 7 x = 9 + 7 x = 16 Thus the values are x = 16 & y = 3 Hence, the solution.
 Travel_Word_Problems/124932: An airplane travels 750 miles against the wind in 7.5 hours, and makes the return trip with the same wind in 3 hours. Find the rate of the wind. (Make sure to answer the question.)((This is exactly how the problem reads.)) Thank you!1 solutions Answer 91572 by chitra(359)   on 2008-02-04 22:07:14 (Show Source): You can put this solution on YOUR website!The given data is: Distance traveled = 750 miles and Time taken = 7.5 hours Here lets find the speed of the plane. Speed = distance traveled/ time taken S = 750/7.5 S = 100 miles per hour Now we shall calculate for the rest of the data. Distance remains the same 750 miles but time taken = 3 hours Therfore Speed = dist/time Speed = 750/3 Speed = 250 miles Thus the solution.
 Graphs/124901: x+y=1 2x+y=4 1 solutions Answer 91553 by chitra(359)   on 2008-02-04 21:34:37 (Show Source): You can put this solution on YOUR website!The given equations can be written as: y = 1 - x y = 4 - 2x They can be graphed as:
 Expressions-with-variables/124193: Please simplify and solve: (-x-y) + (x^2 + y^2)/(x-y)1 solutions Answer 91018 by chitra(359)   on 2008-02-01 05:18:04 (Show Source): You can put this solution on YOUR website!The given expression is: This can be written as: Taking LCM, we get: Thus, the solution.
 Proportions/124185: Question: Solve for x 2x+5/2x+3 = x+3/x-1 Thanks in advance1 solutions Answer 91016 by chitra(359)   on 2008-02-01 04:20:17 (Show Source): You can put this solution on YOUR website!The given expression is: = By cross multiplying we get: (2x + 5)(x - 1) = (x + 3)(2x + 3) Simplifying the above equation using the distributive property, we get: = Grouping all the terms we get: 3x - 5 - 9x - 9 = 0 -6x - 14 = 0 6x + 14 = 0 6x = -14 x = -14/6 x = -7/3 Thus, the solution. regs
 Miscellaneous_Word_Problems/124115: Apples are collected in a basket for six people. One-third, one-fourth, one-eighth and one-fifth are given to four people, respectively. The fifth person gets ten apples with one apple remaining for the sixth person. Find the original number of apples in the basket. 1 solutions Answer 91015 by chitra(359)   on 2008-02-01 03:48:20 (Show Source): You can put this solution on YOUR website!Let the total number of apples that the basket contains = "x" Lets write the data as given in the problem. + 10 + 1 = x Adding all the like terms we get: + 11 = x ==> + 11 = x ==> 11 = x - ==> 11 = ==> 11 = ==> x = 120 Hence there are 120 apples in the basket. Thus the solution Regards
 Divisibility_and_Prime_Numbers/124120: What are the prime numbers? 1 solutions Answer 91014 by chitra(359)   on 2008-02-01 03:00:56 (Show Source): You can put this solution on YOUR website!A number (n > 1) which is divisible by 1 and itself is called a prime number These are the list of prime numbers between 1 and 100 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 regs
 Evaluation_Word_Problems/123753: Tom's father is 3 times as old as Tom. 4 years ago, he was 4 times older. How old is Tom?1 solutions Answer 91012 by chitra(359)   on 2008-02-01 00:49:59 (Show Source): You can put this solution on YOUR website!Let the age of Tom be "x" yrs. Therefore, the age of Tom's father is 3x yrs. Given that 4 yrs ago, he was 4 times as old as tom. Therfore the equations are: 3x - 4 = 4(x - 4) 3x - 4 = 4x - 16 16 - 4 = 4x - 3x 12 = x Therfore, Tom is 12 yrs old Hence his father would be 3 times as tom. that is equal to 3(12) = 36 yrs Hence the solution regs
 Linear_Equations_And_Systems_Word_Problems/124146: Use two variable and the methods for solving word problems to solve: The sum of two number is 40, one number is 8 more than the other. Find the numbers1 solutions Answer 91011 by chitra(359)   on 2008-02-01 00:32:38 (Show Source): You can put this solution on YOUR website!Let x and y be 2 numbers. Givent hat their sum is equal to 40. x + y = 40 Also given that one number(x) is 8 more than the other (y) Therfore x = 8 + y Now by back substituion we get: (8 + y) + y = 40 2y = 40 - 8 2y = 32 y = 16 Now by back substituion we get: x = 8 + y x = 8 + 16 x = 24 Thus the solution.
 Linear-systems/124092: what is the solution to y=-2x+4 and y=1x+21 solutions Answer 91009 by chitra(359)   on 2008-01-31 23:43:46 (Show Source): You can put this solution on YOUR website!The given equation is: y = -2x + 4 and y = 1x + 2 Subtracting both the equations we get: -3x + 2 = 0 -3x = - 2 3x = 2 x = Now by back substitution in one of the equations we get: y = 1(2/3) + 2 y = 2/3 + 2 Taking LCM, we get: y = 8/3 ==> y = 8/3 Thus, the solution. regs
 Square-cubic-other-roots/124116: The base of a ladder is 11 feet away from the wall. The top of the ladder is 11 feet from the floor. Find the length of the ladder to the nearest thousandth.1 solutions Answer 91008 by chitra(359)   on 2008-01-31 23:31:58 (Show Source): You can put this solution on YOUR website!The given problem can be stated like this: The base of the triangle is 11 ft and the altitude is 11 ft. So we are supposed to measure the height of the ladder which forms the hypotenuse of the ladder. We therefore use the pythagoras theorem to find the height of the ladder. let the height be "x" feet x = 15.5563 So to the nearest thousandth is 15.6000 ft
 Money_Word_Problems/124117: You earn \$15 an hour mowing lawns an \$10 an hour washing windows. You want to make \$400 in one week. An Alkgebraic model for your earnings is 15x + 10y = 400. where x is the number of hours mowing lawns and y is the number of hours washing windows. Solve the equation for y? Sketch a grapg of the equation?1 solutions Answer 91004 by chitra(359)   on 2008-01-31 22:41:25 (Show Source): You can put this solution on YOUR website!The equation for y can be written as: 15x + 10y = 400 ==> 10y = 400 + 15x ==> y = (400/10) + (15/10)x ==> y = 40 + 1.5x The graph of the above equation is:
 Circles/124049: I need help with truth tables. See question below. The symbol -> is an arrow for if...then. Construct a truth table for (~q^p)->~q1 solutions Answer 91002 by chitra(359)   on 2008-01-31 22:29:38 (Show Source): You can put this solution on YOUR website!THE TRUTH TABLE FOR THE GIVEN COMPUND PROPOSITION IS AS FOLLOWS: p Q ~Q (~Q ^ P) (~Q ^ P) --> ~Q T T F F T T F T T T F T F F T F F T F T OR THIS CAN ALSO BE WRITEN IN THE FORM OF 0'S ADN 1'S THAT IS REPLACE T BY 1 AND F BY 0 THUS WE FIND THAT THE GIVEN PROPOSITION IS A TAUTOLOGY REVERT TO ME IF YOU STIL HAVE MANY DOUBTS ABOUT THE DISCRETE MATH REGS