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# Recent problems solved by 'vleith'

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 expressions/147466: a mechanic earns a salary of \$350 a week plus he gets \$10 for every oil change he carries out. a) write an eqation to represent the total weekly earnings E, when C oil changes are done. 1 solutions Answer 107845 by vleith(2825)   on 2008-07-07 15:58:56 (Show Source): You can put this solution on YOUR website! Earning is the flat 350 + \$10 for each oil change
 Inequalities/147426: How do you solve this? y<=2x+6 Y>-51 solutions Answer 107832 by vleith(2825)   on 2008-07-07 12:35:08 (Show Source): You can put this solution on YOUR website!I would plot these two. Both are lines. Then find the area between the lines that satisfies the two inequalities. Plot the line y = 2x + 6 Now draw another line at y=-5 (horizontal line). The solution is all the area between the two lines, including the top line, that lies above y=-5. So it is a 'wedge' going out from the point (-5.5, -5) toward the right. Make sense?
 Radicals/147445: 6/2-x +6/x+7=61/2-x how do i figure this out..... i have a quiz soon on questions like these and I'm not getting it..... can you please show me the steps?1 solutions Answer 107828 by vleith(2825)   on 2008-07-07 12:10:31 (Show Source): You can put this solution on YOUR website!Given In this case, the first term on the left and the one on the right have the same denominator. So we can simplify them as is Now we can 'cross multiply' to get rid of the denominators on each side Now combine like terms
 Percentage-and-ratio-word-problems/147448: Thirty-two is 7 less than 3 times a number. Find the number.1 solutions Answer 107825 by vleith(2825)   on 2008-07-07 12:03:38 (Show Source): You can put this solution on YOUR website!let x be the number. Given
 Polynomials-and-rational-expressions/147455: This question is from textbook algebra This is factoring pattern for ax^2+bx+c. The problem is 3x^2+11x+10, the answer I got was (3x+2)(x-5), Thanks for the help=)1 solutions Answer 107824 by vleith(2825)   on 2008-07-07 12:01:35 (Show Source): You can put this solution on YOUR website!Not quite. If you multiply your terms, you get 3x^2 -13x -10. Which is not what you want. You are correct in that you need 3&1 and 5&2. Now you need to find the sum of prodcuts that gives you the middle term. Notice that the sign on the constant term (10) is positive. So, the two factor must both have a + or both have a minus, in order to get a positive product. So, start with this (3x + A ) (x + B) The only choices we have that allow the product of A*B to be 10 are 2,5 and 1,10. We are trying to end up with a sum or products for the middle term that equals 11. Since there is a 3x term in one of the factors, the product can either be 3*10 + 1*1 = 31 OR 3*1 + 1*10 = 13. Neither is 11. So the other pari of factors must be the ones we want. But in which order? 3*2 + 5+1 = 11 3*5 + 2*1 = 17 So the one we want is 3*2 and 5*1 As follows: (3x+5)(x+2) Look at this URL --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic
 Expressions-with-variables/147447: This question is from textbook algebra This is dividing, the question before that I got it right, but with this dividing problem. Very difficult for me. So I have to divide 2x^2y-6xy^2+12xy/2xy, I did try to solve it and got xy+3^2-6 obviously it's wrong, So can someone please help me. Thank you=)1 solutions Answer 107821 by vleith(2825)   on 2008-07-07 11:52:32 (Show Source): You can put this solution on YOUR website!Given
 Numeric_Fractions/147359: Choose values of x, then simplify it correctly. 10x^2-30x+20/x^2-1 I did something wrong on that one, maybe someone could show me how it works. 1 solutions Answer 107762 by vleith(2825)   on 2008-07-06 19:44:59 (Show Source): You can put this solution on YOUR website!Use this --> http://www.calc101.com/webMathematica/long-divide.jsp#topdoit
 Functions/147367: find the indicated outputs for f(x)= 5x to the second power-3x. f(0)=? f(-1)=? f(2)=?1 solutions Answer 107761 by vleith(2825)   on 2008-07-06 19:43:18 (Show Source): You can put this solution on YOUR website!Given find f(0) f(-1) f(2)
 Linear_Algebra/147357: V=s^3 500=s^3 Need to know how to solve for volume when only volume is given. Need step by step instructions. Thanks.1 solutions Answer 107745 by vleith(2825)   on 2008-07-06 18:39:38 (Show Source): You can put this solution on YOUR website!Given You are given the volume of a cube and asked to find the length of one side. Take the cube rott of both sides and then simpify
 Square-cubic-other-roots/147373: This question is from textbook Beginning and Intermediate algebra I would like help solving this problem: (2 square root of 5-9) (square root of 5+7)1 solutions Answer 107744 by vleith(2825)   on 2008-07-06 18:34:18 (Show Source): You can put this solution on YOUR website!Given
 Probability-and-statistics/147378: Alan is jealous that his neighbor down the street has a very cool toy that he has been admiring for 20 years now. He decides to break in and steal it. He knows that the house is monitored by a security system that requires a 5digit pass code. He knows that it needs 2 digits and 3 letters. How many pass keys are there if no digits can be repeated?1 solutions Answer 107743 by vleith(2825)   on 2008-07-06 18:30:07 (Show Source): You can put this solution on YOUR website!Assuming the first two keys are digits and the last three are letters (that is, assuming we know in advance this is that case), then The first key is digits - so Alan has 10 choices The second key is digits, but can't be the same digit used on key 1. So 10-1=9 The third key is letters - 26 possibilities The fourth key is letters - 26 possibilities The fifth key is letters - 26 possibilities So, 10*9*26*26*26 possible permutations I never thought I would see a mathematics problem that appeals to a thief! Next question, what is the probability Alan gets caught and goes to jail? :)
Linear-systems/147355: Hi, I dont know what Im doing wrong I need help please. Here is the question: One year ago you invested \$4300 into three accounts that earn 3.25%, 4%, and 5.75% annual interest. The interest you earned after one year is \$193. You remembered you invested three times as much in the 4% account than you did the 3.25% account. How much did you invest in each type of account? This is what i have so far, I dont think its right.
x + y + Z = 4300
325x + 400Y + 575z = 19300
Y=3x
x + (3x) + Z = 4300
4x + z = 4300
325x + 400 (3x) + z =19300
1525x +575z = 19300
(-575) 4x + z = 4300 (-575)
-2300x - 575z =-2472500
1525x + 575z = 19300
-775x = -2453200
x=3165.4 then when I do 3 times x to get y it doesnt fit with the total of 4300. I dont know please help me thank you.

1 solutions

Answer 107729 by vleith(2825)   on 2008-07-06 15:44:06 (Show Source):
You can put this solution on YOUR website!
x + w + y = 4300
0.0325x + 0.04w + 0.0575y = 193
3.25x + 4(3x) + 05.75y = 19300
4x + y = 4300
15.25x + 5.75y = 19300
Using substitution:
 Solved by pluggable solver: Solving a linear system of equations by subsitution Lets start with the given system of linear equations Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y. Solve for y for the first equation Subtract from both sides Divide both sides by 1. Which breaks down and reduces to Now we've fully isolated y Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x. Replace y with . Since this eliminates y, we can now solve for x. Distribute 5.75 to Multiply Reduce any fractions Subtract from both sides Combine the terms on the right side Now combine the terms on the left side. Multiply both sides by . This will cancel out and isolate x So when we multiply and (and simplify) we get <---------------------------------One answer Now that we know that , lets substitute that in for x to solve for y Plug in into the 2nd equation Multiply Subtract from both sides Combine the terms on the right side Multiply both sides by . This will cancel out 5.75 on the left side. Multiply the terms on the right side Reduce So this is the other answer <---------------------------------Other answer So our solution is and which can also look like (,) Notice if we graph the equations (if you need help with graphing, check out this solver) we get graph of (red) and (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle. and we can see that the two equations intersect at (,). This verifies our answer. ----------------------------------------------------------------------------------------------- Check: Plug in (,) into the system of equations Let and . Now plug those values into the equation Plug in and Multiply Add Reduce. Since this equation is true the solution works. So the solution (,) satisfies Let and . Now plug those values into the equation Plug in and Multiply Add Reduce. Since this equation is true the solution works. So the solution (,) satisfies Since the solution (,) satisfies the system of equations this verifies our answer.

So x = \$700
w = 3x = \$2100
y = \$1500

 Polynomials-and-rational-expressions/147354: I'm really lost and I need to know how to get this done. I have no other real examples that are showing me the way. Find all positive values for k for which each of the following can be factored. x^2-kx+171 solutions Answer 107726 by vleith(2825)   on 2008-07-06 15:31:21 (Show Source): You can put this solution on YOUR website!It is hard to tell from this problem to know 'where in algebra' you are. If you are just starting out, I suspect they are asking you to find the value(s) for k that allow simple factoring to work. In that case, you will be looking for combinations of numbers whose product is 17 (since the coefficient of the x^2 term is 1). In that case, since 17 is prime, only 1 and 17 are possible factors. (x-17)(x-1) = x^2 -18x + 17 (x+17)(x+1) = x^2 +18 +17 So the only positive k would be 18 However, if you are farther along in algebra, then what you are being asked is "what vaues of k make the determinant of the solution to the quadratic equation greater than or equal to 0". If the term determinant is something you are learning or know, then use that to find the values of k. There are an infinite number; so use an inequality based on the the determinant being >= 0
 Linear-equations/147321: change each equation to slope intercept form and state the slope and y intercept: 6y-4x+8=01 solutions Answer 107706 by vleith(2825)   on 2008-07-06 11:51:15 (Show Source): You can put this solution on YOUR website!Slope intercept form is y = mx + b Given Assuming this is a not mistyped, slope is undefined there is no y intercept I figure you had a typo. Let's assume you meant slope is 2/3 y intercept is -4/3
 Proportions/147305: solve for the indicated letter: a=5b, for b. b=?1 solutions Answer 107679 by vleith(2825)   on 2008-07-06 07:26:02 (Show Source): You can put this solution on YOUR website! divide both sides by 5 to find b Use this tool to help check your answers --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=equations&s2=solve&s3=basic
 Money_Word_Problems/147304: media services charges \$20 for a phone and 30/month for it's economy plan. the equation C=30t+20 describes the total cost, c, of operatinga media services phone for t months. the total cost for 2 mos service is? if a customer only has \$90 available,how many mos can she recieve?1 solutions Answer 107676 by vleith(2825)   on 2008-07-06 07:23:31 (Show Source): You can put this solution on YOUR website! is the given equation. What is the cost at 2 months? That is asking, what is C(2)? dollars Is the client has \$90, she can only get 2 months of service. Keep the other \$10 for something else.
 Triangles/147274: If ABC is any triangle, and TAC is one of its exterior angles, then what can be said about the size of angle TAC, in relation to the other angles of the figure? thanks !!!!!1 solutions Answer 107655 by vleith(2825)   on 2008-07-05 21:33:14 (Show Source): You can put this solution on YOUR website!The sum of the interior angles of a triangle is 180 degrees. TAC + CAB = 180 a well since those angles are supplementary (the form a straight angle). Thus TAC = the sum of the other two angles in ABC TAC = ABC + BCA
 Triangles/147277: Ive tried this problem 6 different times, and cannot seem to find the answer. Given triangle ABC with AB = AC, extend segment AB to a point P so that B is between A and P and BP = BC. In the resulting triangle APC, show that angle ACP is exactly three times the size of angle APC. (By the way, notice that extending segment AB does NOT mean the same thing as extending segment BA.) thnx!!!1 solutions Answer 107653 by vleith(2825)   on 2008-07-05 21:26:29 (Show Source): You can put this solution on YOUR website!Let the angle at BAC = a. Triangle ABC is isosceles, so its base angles are equal. Call those angles b. We have a+b+b = 180 By extending B to P, with a length equal to BC, we create a second isosceles triangle BPC. The angle at PBC is the supplement of the angle CBA. That angle is b (from above). So angle PBC = 180-b Since the second triangle also has base angles equal, we know that angle BPC and BCP are the same. Call that angle c. Then PBC + 2c = 180. PBC = 180 - 2c From above PBC = 180-b, so 180-b = 180 - 2c b/2 = c The angle at CPB = c = b/2 The angle PCA = c + b = b/2 + b = 3b/2 Which is 3 times CPB
 Geometry_proofs/147218: what are the examples of basic postulate?1 solutions Answer 107586 by vleith(2825)   on 2008-07-05 05:24:24 (Show Source): You can put this solution on YOUR website!See this --> http://library.thinkquest.org/2647/algebra/post.htm Then substitute in 'numbers' or other combinations of letters to create examples. For instance: Transitive Property of Equality: if a = b and b = c, then a = c example If 12 = (9+3) and (9+3) = (13-1) then 12 = (13-1) OR if x = y and y = 2z then x = 2z
 Quadratic_Equations/147220: hwo many methods to solve quadratic equation1 solutions Answer 107584 by vleith(2825)   on 2008-07-05 05:18:52 (Show Source): You can put this solution on YOUR website!I know of 6. Perhaps there are more 1) solving by substitution 2) solving by elimination 3) solving by completing the square 4) solving graphically 5) solving using the quadratic equation 6) factoring See here for some more words --> http://www.purplemath.com/modules/solvquad.htm
 Linear-equations/147219: is 1/-4 is equal to -4? please answer this......1 solutions Answer 107583 by vleith(2825)   on 2008-07-05 05:12:17 (Show Source): You can put this solution on YOUR website!No. = = is not equal to
 Geometric_formulas/146741: what is the formula will i use if i want to get the area in square meter of an octagon?1 solutions Answer 107166 by vleith(2825)   on 2008-06-29 08:32:26 (Show Source): You can put this solution on YOUR website!Is the polygon regular? see --> http://www.mathwords.com/a/area_regular_polygon.htm If not, then chop it into triangles and solve that way
 Polynomials-and-rational-expressions/146465: I need help with some math problems Please factor the following polynomials 24x^3y -8xy^2 16x^2-24xy+9y^2 5r^3-5 (36x^2-49y^2) Thanks alot for your help!!!!! 1 solutions Answer 107070 by vleith(2825)   on 2008-06-27 16:53:29 (Show Source): You can put this solution on YOUR website!Use this --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic
 Radicals/146621: perform indicated operations: 3sqrt[3]+2sqrt[27]-sqrt[12]1 solutions Answer 107068 by vleith(2825)   on 2008-06-27 16:44:00 (Show Source):
Graphs/146623: Plot the points and find the slope of the line passing through the points (-4,0),(-4,3)
1 solutions

Answer 107067 by vleith(2825)   on 2008-06-27 16:41:04 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Finding the slope Slope of the line through the points (-4, 0) and (-4, 3) Since you CANNOT divide by 0, this means that the slope of the line is undefined. Answer: The slope of the line is undefined.

 Quadratic_Equations/146624: I need to solve 8x+x(x-6)=0 and find the x-intercepts. Thank you so much! 1 solutions Answer 107066 by vleith(2825)   on 2008-06-27 16:37:56 (Show Source): You can put this solution on YOUR website! Using products of zero rule x = 0 x = -2
 Exponents-negative-and-fractional/146155: { 36x^5y^-1 }^-1/2 _________ { 91x^-3y^-5 } After I simplify I get, [4/9]^-1/2 x^-4 y^-2 I don't know how to simplify the 4/9, any help I would greatly appreciate it.1 solutions Answer 106713 by vleith(2825)   on 2008-06-23 18:42:25 (Show Source): You can put this solution on YOUR website!Not sure what the original equation really is. Look here for a tool --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=simplify&s3=basic
 test/146158: I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected?1 solutions Answer 106712 by vleith(2825)   on 2008-06-23 18:36:02 (Show Source): You can put this solution on YOUR website!Use a combination. See http://www.mathagonyaunt.co.uk/STATISTICS/ESP/Perms_combs.html 15P6 = 15!/((15-6)! * 6!) = (15*14*13*12*11*10)/ (6*5*4*3*2*1) = (14*13*11*10)/4 = 7*13*11*5 = 5005
 Probability-and-statistics/146168: find the probability of pulling out a heart and then a dimond from a standard 52 card deck with a) replacement and b) with out replacement1 solutions Answer 106711 by vleith(2825)   on 2008-06-23 18:30:26 (Show Source): You can put this solution on YOUR website!a) Hearts are 13/52 or 1/4. With replacement, diamonds are 13/52 = 1/4 so 1/4* 1/4 = 1/16 b) without replacement hearts is still the same (13 of 52). But diamonds is then 13/51. 1/4 * 13/51 = 13/204