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# Recent problems solved by 'vleith'

vleith answered: 2822 problems
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 Linear_Equations_And_Systems_Word_Problems/184605: For what values of c will the system have: infinitely many solution 1) 2x - 6y = c 6x - 18y = 30 2)no solution x + 2y = 6 cx - 4y = 8 How do you do these questions? Can you explain how?1 solutions Answer 138550 by vleith(2825)   on 2009-03-02 19:19:37 (Show Source): You can put this solution on YOUR website!infinitely many solution 1) 2x - 6y = c 6x - 18y = 30 infinitely many solution means the two 'lines' are really the same line the second line above has two terms that are exactly 3 times the terms of the fisrt line (6x = 3*2x and -18y = 3 *(-6y)) so if c is 3*30, then the two lines are really the same line. 2)no solution x + 2y = 6 cx - 4y = 8 No solution occurs when the 'answer' is something that can't happen So let's double the first line to get 2x + 4y = 12 Now add the second line to it 2x + 4y = 12 cx -4y = 8 ---------- (2+c)x = 20 any c that that makes (2+x) a non-zero number will result in an x that 'works'. However, if c = -2, then we get (0*x) = 20 0 times anything is 0, so that yields 0 = 20 0=20 is impossible, so is c = -2 then ther eis no solution., make sense?
 Linear-systems/184587: Solve the system of equations by graphing x+y=8 x-y=-6 What is the solution of the system of equations?1 solutions Answer 138549 by vleith(2825)   on 2009-03-02 19:12:59 (Show Source): You can put this solution on YOUR website!See this video --> http://collabvsl.wetpaint.com/page/Solving+Systems+of+Equations The solution in this case is the point that is the intersection of the two given lines. There are several methods to solve this. We will use addition x + y = 8 x - y = -6 add these two ------------- 2x = 2 x = 1 If x =1, then y is x + y = 8 1 + y = 8 y = 7 So the solution is the point (1,7) Check your answer using the second eqaution x - y = -6 does 1 - 7 = -6 ??? yes it does !
 Probability-and-statistics/184591: I NEED Help in statistics. Could someone please help me with this. Thank you. The chair of the board of directors says, “There is a 45% chance this company will earn a profit, a 35% chance it will break even, and a 20% chance it will lose money next quarter.” a. Find the probability they will not lose money next quarter. b. Find the probability they will lose money next quarter. 1 solutions Answer 138548 by vleith(2825)   on 2009-03-02 19:08:18 (Show Source): You can put this solution on YOUR website!a. Find the probability they will not lose money next quarter. This is the sum of the probability that the company makes money and breaks even (in either of those vcases, they didn't lose money). So 45 + 35 = 80% b. Find the probability they will lose money next quarter. 20%
 Miscellaneous_Word_Problems/184603: jen is putting a fence in her rectangular garden. The length of her garden is 12 feet and the width of her garden is 14 feet. how many feet of fencing will she need?1 solutions Answer 138546 by vleith(2825)   on 2009-03-02 19:05:13 (Show Source): You can put this solution on YOUR website!what is the perimeter of a rectangle? The total length of the four sides. Each rectangle has two sets of equal length sides. So the perimeter is P= 2*lenght + 2*Width P = 2*12 + 2*14 P = 24 + 28 P = 52 feet
 Geometry_Word_Problems/184602: This question is from textbook geometry if a triangle is formed with sides having lengths what type of triangle is 6 , 8 , and 10 ? 1 solutions Answer 138545 by vleith(2825)   on 2009-03-02 19:03:18 (Show Source): You can put this solution on YOUR website!Any triangle with sides ina ratio of 3:4:5 is a right triangle. Since a^2 + b^2 = c^2 for all right triangles, you can see this one fits that.
 Graphs/184558: I'm not sure about this. Graph the linear equation by finding and plotting its intercepts. y=-5x Thanks1 solutions Answer 138534 by vleith(2825)   on 2009-03-02 17:28:43 (Show Source): You can put this solution on YOUR website!Intercepts are points that are on the axis. So one or the other coordinate of the point must be 0. So (0,y) and (x,0). Solve for them as follows. Assume x =0, using y=-5x y = -5*0 = 0 So the x intercept is (0,0) Assume y=0. Using y = -5x 0 = -5x 0 = x So the y intercept is (0,0) What you have are 'two points that are the same point'. So you cannot plot the line using just the intercepts, since this line passes thru the origin.
 Inequalities/184554: The problem 7x+3<=7(x+1)has got me! My best solution. 7x+3<=7(x+1) = 7x+3<=7x+7 = -3 -3 = 7x<=7x+4 =-7x -7x = 0<=4 This is so frustrating. Thank you for any answers. 1 solutions Answer 138531 by vleith(2825)   on 2009-03-02 17:24:42 (Show Source): You can put this solution on YOUR website!Dont get frustrated. You got to the point where the 'solution' is 0<=4 Your frustration is 'that cant be'. Guess what, you're right. It can't be. When the 'solution' ends up being something that is not possible, then that means 'there is no solution to this problem'. Thus, it is not possible for 7x+3<=7(x+1)
 Graphs/184559: I need help please. Complete each ordered pair so that it is a solution of the given linear equation. x-2y=-5;( ,-3),(-9, ) The first ordered pair is ( ,-3) The second ordered pair is (-9, ) Thank u!1 solutions Answer 138530 by vleith(2825)   on 2009-03-02 17:21:18 (Show Source): You can put this solution on YOUR website!Plug in the given half of the point ans then solve for the other one. x-2y=-5;( ,-3),(-9, ) plug in -3 for y and solve for x x - 2*(-3) = -5 x + 6 = -5 x = -11 (-11,-3) Second point, plug in -9 for x and solve for y -9 - 2y = -5 -2y = 4 y = -2 (-9,-2)
 Polynomials-and-rational-expressions/184194: This question is from textbook saxon algebra 2 Identify all real roots of x^3+x^2-34x+56=0 I worked it out to: 2, -3+ square root 11 and -3- square root 11. Am I correct?1 solutions Answer 138253 by vleith(2825)   on 2009-02-28 15:31:19 (Show Source): You can put this solution on YOUR website!2 is correct. The others are not. See the URLS below for tools to factor http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic http://www.calc101.com/webMathematica/long-divide.jsp#topdoit
 Exponents-negative-and-fractional/184220: why can't you leave a negative number in the denominator? I know you mult. the top and bottom by -1 to keep the neg. out, I just need to know why is that the rule. trying to explain to a student/1 solutions Answer 138251 by vleith(2825)   on 2009-02-28 15:24:04 (Show Source): You can put this solution on YOUR website!It is just convention. There is 'no good reason' why the negative sign is usually associated with the numerator or even placed 'in front of' the fraction. It is just 'good practice'.
 Polynomials-and-rational-expressions/184221: This question is from textbook Algebra 1(Concepts and Skills) How do you factor a trinomial?1 solutions Answer 138250 by vleith(2825)   on 2009-02-28 15:16:30 (Show Source): You can put this solution on YOUR website!See this video for a discussion on factoring. Two fo the 4 examples are trinomials http://www.teachertube.com/view_video.php?viewkey=e178941e511e7a36475c
 Quadratic_Equations/184167: solve for x x^2-7=01 solutions Answer 138192 by vleith(2825)   on 2009-02-28 05:09:32 (Show Source): You can put this solution on YOUR website! AND
Surface-area/184114: A square field has 5m added to its length and 2m added to its width.The field then had an area of 130m^2.Find the length of the side of the original field.
1 solutions

Answer 138136 by vleith(2825)   on 2009-02-27 16:11:18 (Show Source):
You can put this solution on YOUR website!
Let the original field's sides be x.
The new field has length (x+5) and width (x+2)
Area of a rectangle is given as

Use quadratic equation to solve
 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=529 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 8, -15. Here's your graph:

or factor as

Either way, the possible original sides are 8 or -15. Since the original field cannot have a negative length side, the answer must be 8meters on each side

 Expressions-with-variables/184115: 1-3(5b-2)=4-(7b+3) What is b? I'd really like to know HOW to solve this.1 solutions Answer 138135 by vleith(2825)   on 2009-02-27 16:04:47 (Show Source): You can put this solution on YOUR website!use the same rules you use for arithmetic. first use distribution collect like terms now isolate the terms with variables simplify now solve for b simplify Check your answer by plugging 3/4 in for b and verifying that boths sides are the same
 Triangles/184063: hi, Please help me my problem.If a shape that has three sides and three angles,can we call that a triangle?If the sides of the triangles are unsraight lines ,how can we call that?How can I know its angles and sides by computing? please ..please..help me...thank you very much for yor answer.Thank you very much!! ! ! 1 solutions Answer 138134 by vleith(2825)   on 2009-02-27 15:59:34 (Show Source): You can put this solution on YOUR website!If a shape that has three sides and three angles,can we call that a triangle? Generally speaking - no. In order to be a 'euclidean triangle' the sides must be line segments. (that is, they cannot be curved). See http://www.mathopenref.com/triangle.html If the sides of the triangles are unstraight lines ,how can we call that? A 3 sided polygon. How can I know its angles and sides by computing? I'll assume you mean on a triangle. Use the law of sines --> http://en.wikipedia.org/wiki/Law_of_sines
 Proportions/184073: I would like help with the following problem Solve by using a proportion. If the answer does not come out evenly, round it to the nearest hundredth. You read 500 words in 3 minutes. At that rate, how many words would you read in 20 minutes? All correct answers are greatly appreciated.Thank You:)1 solutions Answer 138133 by vleith(2825)   on 2009-02-27 15:53:25 (Show Source): You can put this solution on YOUR website!Same idea here. use ratios
 Proportions/184075: I would like help with the following problem A flagpole is 12.5 m tall. It casts a 17.5-m shadow. How tall is a nearby radio tower that casts a 61.25-m shadow? All help with my problem is greatly appreciated.Thank You:)1 solutions Answer 138132 by vleith(2825)   on 2009-02-27 15:51:41 (Show Source): You can put this solution on YOUR website!Use ratios
 Equations/184103: graph the following linear equation f(x)= 3/4x + 21 solutions Answer 138131 by vleith(2825)   on 2009-02-27 15:48:01 (Show Source):
 Exponential-and-logarithmic-functions/184111: log 3 (5x+1)=21 solutions Answer 138130 by vleith(2825)   on 2009-02-27 15:46:40 (Show Source): You can put this solution on YOUR website!Convert to log 10 http://www.mathwords.com/c/change_of_base_formula.htm Now that it is converted, solve
 Quadratic_Equations/184112: Aki's Bycycle Designs has determined that when x hundred bicycles are built, the average cost per bycycle is given cy C(x)=0.7x^2-1.3x+10.679, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle? I don't know where to begin with this problem, can someone please help me with it? I would really appreciate it.1 solutions Answer 138129 by vleith(2825)   on 2009-02-27 15:35:33 (Show Source): You can put this solution on YOUR website!If you know calculus, take the derivative, set that to 0 and solve for x. If you don't know that yet, find the minimum of the parabola. Here is a URl with the formula on it --> http://www.tpub.com/math1/17e.htm
 Exponents/184113: What is the answer to r to the negitive 5th s to the 4th t divided by rs to the negitive 2nd t to the negitive 5th 1 solutions Answer 138128 by vleith(2825)   on 2009-02-27 15:21:49 (Show Source): You can put this solution on YOUR website!You mean this ?
 Polynomials-and-rational-expressions/184104: please help me solve this problem Reduce an expression to lowest terms. -2b2-6b-4/b2-1 1 solutions Answer 138126 by vleith(2825)   on 2009-02-27 15:15:53 (Show Source): You can put this solution on YOUR website! You might find this URL handy --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic
 Miscellaneous_Word_Problems/184108: What is the population density of a city with 425,000 people in 1,872 square miles? express each ratio as a fractionin simplist form. If we completed correctly, we came up with 53125/234 - is this the correct answer?1 solutions Answer 138125 by vleith(2825)   on 2009-02-27 15:09:47 (Show Source): You can put this solution on YOUR website!That's what I got.
 Polynomials-and-rational-expressions/184109: please help me solve this problem on factor out the GCF in the expression 6x3+18x2+24x1 solutions Answer 138124 by vleith(2825)   on 2009-02-27 15:05:35 (Show Source): You can put this solution on YOUR website! So the GCF is 6x
 Triangles/184083: Not sure if this question goes here, but I am having a horrible time trying to figure this out, so any help is greatly appreciated. Thank you. The perimeter of a triangular dog pen has one side represented by 3x, another side represented by x +19 and the third side represented by 2x + 6. Find the algebraic expression for the perimeter. Find the numerical perimeter if the value of x is 5 feet.1 solutions Answer 138091 by vleith(2825)   on 2009-02-27 09:34:09 (Show Source): You can put this solution on YOUR website!The perimeter is the sum of the triangles sides. If x = 5, then feet
The equation of the line that goes through the point ( 7 ,2 ) and is parallel to the line 5 x + 3 y = 5 can be written in the form y = mx+b where m is:
and where b is:

1 solutions

Answer 138090 by vleith(2825)   on 2009-02-27 09:31:28 (Show Source):
You can put this solution on YOUR website!
Get the original equation in the form

 Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line Since any two parallel lines have the same slope we know the slope of the unknown line is (its from the slope of which is also ). Also since the unknown line goes through (7,2), we can find the equation by plugging in this info into the point-slope formula Point-Slope Formula: where m is the slope and (,) is the given point Plug in , , and Distribute Multiply Add to both sides to isolate y Make into equivalent fractions with equal denominators Combine the fractions Reduce any fractions So the equation of the line that is parallel to and goes through (,) is So here are the graphs of the equations and graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)

 Polynomials-and-rational-expressions/183359: Suppose that you square two consecutive whole numbers and subtract the smaller square from the larger. Is it possible that the difference is an even number provide an example please 1 solutions Answer 137681 by vleith(2825)   on 2009-02-23 14:01:24 (Show Source): You can put this solution on YOUR website!Let one number be x. Then the other one is (x+1) 2x will always be even. So 2x+1 is always odd 4 , 5 25-16 = 9 which is odd
 Miscellaneous_Word_Problems/183377: One pump fills a tank 4 times as fast as another pump. If the pumps work together, they fill the tank in 28 minutes. How long does it take for each pump to fill the tank? It takes the faster pump ______ minutes to fill the tank when working alone and it takes the slower pump ______ minutes.1 solutions Answer 137680 by vleith(2825)   on 2009-02-23 13:57:17 (Show Source): You can put this solution on YOUR website!Let the slow pump rate be X. Then the fast pump rate is 4X Together they can pump at X+4X = 5X The slow pump will be 1/5 as fast. So it will take 28*5 minutes The faster pump will be 4/5 as fast. So it will take (28*5)/4 minutes
 Equations/183376: How to reach the end results for x/2+1=3, 3x/2+1=4 and 2x/3+1=5. break these down please1 solutions Answer 137679 by vleith(2825)   on 2009-02-23 13:54:11 (Show Source): You can put this solution on YOUR website!Use the following process for each. We'll do the first one, then you cna use the same idea to do the other two. Isolate the term with x by subtracting the constant on the left (sub 1 from both sides). To get Now get x 'by itself'. In this case, multiply both sides by 2 For the next one Isolate the term with x Now get x 'by itself'. Multiply by 2/3 You can do the last one
 Average/183337: x(x-6) = 7 If I solve it: x^2-6x = 7 how do i continue from here? It is solving an equation but how do i reach x= ?1 solutions Answer 137660 by vleith(2825)   on 2009-02-23 10:09:53 (Show Source): You can put this solution on YOUR website! Now you can factor it or use the quadratic equation. Let;s factor this one so x = 7 or x= -1 Check using this URL --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic
 Mixture_Word_Problems/183339: One thrid of a number is 5 less than half of the same number. What is the number? ISNB -13 978-0-395-97722-4 ISBN-10 0-395-97722-31 solutions Answer 137659 by vleith(2825)   on 2009-02-23 10:05:15 (Show Source): You can put this solution on YOUR website!Let x be the number. You are told multiply thru by 6 Is 10 five less than 15?