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# Recent problems solved by 'Mathtut'

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 Travel_Word_Problems/171435: Having trouble finding the right formula! How do I solve? An express and local train leave Gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train. 1 solutions Answer 126567 by Mathtut(3670)   on 2008-12-04 23:30:44 (Show Source): You can put this solution on YOUR website!d=rt. we know the distance in both cases is 50. Lets call the local trains rate r and its time t. So the express's rate would be 2r and its time t-1 : 50=rt..........eq 1 50=2r(t-1).....eq 2 : lets rewrite eq 1 as t=50/r and plug that value into eq 2 : ----->---- ----> MPH-speed of the local train MPH-speed of the express :
 Graphs/171430: Graph the line with slope 3/4 and y-intercept (0,-2)1 solutions Answer 126566 by Mathtut(3670)   on 2008-12-04 23:27:19 (Show Source): You can put this solution on YOUR website!y-(-2)=3/4(x-0) : y+2=3/4x : y=3/4x-2 :
 Geometry_Word_Problems/171431: This question is from textbook Algebra 2 93. You are taking a pottery class. As an assignment, you are given a lump of clay whose volume is 200 cubic centimeters and asked to make a cylindrical pencil holder. The pencil holder should be 9 cm high and have an inner radius of 3 cm. What thickness "x" should your pencil holder have if you want to use all the clay? (hint: the volume of clay equals the difference of the volumes of two cylinders.) The answer in the back of the book is "about" 1 cm but i dont know why. Should i use completing the square? ive tried all the cylinder equations and nothing gives me 1.1 solutions Answer 126564 by Mathtut(3670)   on 2008-12-04 23:22:35 (Show Source): You can put this solution on YOUR website!ok........we know that the volume of the cylinder is so what we need is to take the outer volume and subtract out the inner volume to get the thickness volume. we know that the volume of the clay(200) will be equal to outer volume-inner volume. We also know that the outer radius which is the unknown here minus the inner radius will give the measurement of the thickness of the pencil holder. I used 3.14 as appx value of : cm...this isnt exactly 4 because of approximations cm....thickness of pencil holder
 Graphs/171422: In 2003, the federal minimum wage rate was \$5.75 per hour. In 2007, It increased to \$6.75. Find the annual rate of change in the federal minimum wage rate from 2003 to 2007.1 solutions Answer 126560 by Mathtut(3670)   on 2008-12-04 22:36:00 (Show Source): You can put this solution on YOUR website!5.75+5.75x=6.75 where x is the interest rate increase : 5.75x=1 : x=.174 or 17.4% over 4 years....so to find out an annualize rate we need to : divide by 4 : % per annum
 Age_Word_Problems/171410: Eight pennies are placed in a row on a tabletop. Every other coin is then replaced with a nickel. Every third coin is then replaced with a dime. Finally, every fourth coin is replaced with a quarter. What is the value of the eight coins now on the table? 1 solutions Answer 126557 by Mathtut(3670)   on 2008-12-04 22:29:20 (Show Source): You can put this solution on YOUR website!78 cents : 3 pennies 1 nickel 2 dimes 2 quarters
 Sequences-and-series/171411: In the following algebraic consequences, n represents the position of a term in a sequence. Find the first five terms. 5n 3n + 2 7n - 41 solutions Answer 126555 by Mathtut(3670)   on 2008-12-04 22:26:06 (Show Source): You can put this solution on YOUR website!5n:.......5,10,15,20,25 3n+2:.....5,8,11,14,17 7n-4:.....3,10,17,24,31
 Inequalities/171413: deos the shaded region of the graph of the system of inequalities y>3 x+y<5 include the points (5,-2)? how do you know?1 solutions Answer 126554 by Mathtut(3670)   on 2008-12-04 22:18:54 (Show Source): You can put this solution on YOUR website!no.....in the equation y>3 point(5,-2) -2>3 is not a true statement....the point does satisfy the x+y<5 but it has to satisfy both if you consider both equations together. If you consider them seperately it does not satisfy the first but does satisfy the 2nd
 Age_Word_Problems/171408: A fireman stood on the middle step of a ladder, shooting water into a burning building. As the smokelessened, he climbed up three steps and continued his work. The fire got worse, so he had to go down five steps. Later he climbed up the last six steps and was at th top of the ladder. How many steps were there?1 solutions Answer 126551 by Mathtut(3670)   on 2008-12-04 21:56:13 (Show Source): You can put this solution on YOUR website!well the answer is 9 : remember the middle rung can only be counted once so we need to account for that : if x is the total distance from one rung to the other : (1/2)x=3-5+6+1/2........the 1/2 is so that the middle rung is counted once : x/2=4.5 : steps
 Graphs/171407: What is the slope of a line (a) paraell, and (b) perpendicular to the line through points (5,7) and (0,3)?1 solutions Answer 126547 by Mathtut(3670)   on 2008-12-04 21:45:41 (Show Source): You can put this solution on YOUR website!ok lets find the slope first m=rise/run or change in y/change in x. : m=3-7/0-5=4/5 : so any line parallel to a line thru these two point must have the same slope of . Any line perpendicular to a line passing through these point have to have the - inverse of the slope 4/5 which is
 Graphs/171406: Graph the function F(x) = 1-xsquared1 solutions Answer 126543 by Mathtut(3670)   on 2008-12-04 21:41:40 (Show Source):
 Graphs/171402: Can a straight line pass through (2,4) , (-6,3), and (-3,1)?1 solutions Answer 126541 by Mathtut(3670)   on 2008-12-04 21:38:16 (Show Source): You can put this solution on YOUR website!take any two point and write an equation find slope first....I will use the first two points change in y /change in x is the slope. 3-4/-6-2=1/8 is the slope. now take one of the points(of the two we just used to find the slope), and plug it into point slope formula(I am using the first point) : y-4=(1/8)(x-2) : we dont need to re write this we just take the third point (-3,1) and check and see if it works in the equation ....if it does it is on the same line...if not then a straight line doesn not pass thru these 3 points. : 1-4=(1/8)(-3-2) : -3=1/8(-5) : -3=-5/8.......which is not a true statement therefore they do not all lie on the same line.
 Complex_Numbers/171398: Write the expression as a complex number in standard form. -(3+i)(7-3i)1 solutions Answer 126540 by Mathtut(3670)   on 2008-12-04 21:29:08 (Show Source): You can put this solution on YOUR website!given : multiplying factors : combining like terms : multiplication by a negative 1
 Polynomials-and-rational-expressions/171397: solve by factoring first 1 solutions Answer 126538 by Mathtut(3670)   on 2008-12-04 21:22:56 (Show Source): You can put this solution on YOUR website! : factoring out a 27 : combining terms :
 Linear-equations/171390: A movie theater sells tickets for \$7.00 each. Senior citizens receive a discount of \$2.00. One evening the theater sold 400 tickets and took in \$2600.00 in revenue. How many tickets were sold to senior citizens? How many were sold to non-senior citizens? 1 solutions Answer 126535 by Mathtut(3670)   on 2008-12-04 21:17:53 (Show Source): You can put this solution on YOUR website!let the number of tickets sold to non seniors and seniors , be n and s respectively : n+s=400.........eq 1 7n+5s=2600......eq 2 : lets rewrite eq 1 to s=400-n and place that value into eq 2. : : distribution : combining terms : number of non senior ticket sold
 Systems-of-equations/171392: This question is from textbook if bx-2=k, then x equals...1 solutions Answer 126532 by Mathtut(3670)   on 2008-12-04 21:12:03 (Show Source): You can put this solution on YOUR website!bx-2=k........first add 2 to both sides of the equation : bx=k+2......next we divide both sides by b :
 Linear-equations/171382: what is the graph for y=2x+11 solutions Answer 126528 by Mathtut(3670)   on 2008-12-04 20:55:08 (Show Source):
 Exponential-and-logarithmic-functions/171323: The cost of attending college has been rising at an average increase of 7% for the past ten years. How much will college that now costs \$10,368 for room, board, tuition and fees cost two yearsfrom now?1 solutions Answer 126493 by Mathtut(3670)   on 2008-12-04 19:49:33 (Show Source): You can put this solution on YOUR website!10368(.07)=725.76 round and add this to the original amount : 10368+726=11094 : 11094(.07)=776.58 round and add to new amount : costs of college in 2 years
 Systems-of-equations/171332: How to solve each system of equations by elimination?1 solutions Answer 126486 by Mathtut(3670)   on 2008-12-04 19:29:33 (Show Source): You can put this solution on YOUR website!you are simply adding or subtracting one equation from another trying to eliminate one of the variables. Sometimes you have to manipulate one equation or the other or both to accomplish the elimination. : 2x+y=5 x-y=7------. these two equation need no help add one to the other and y-y=0 and your left with 2x+x=7+5 and you can solve for x. once you solve for x you can plug its value back into either original equations and solve for y : 3x+3y=9...eq 1 x-y=10....eq 2----in this case if you multiply all terms in eq 2 by 3 you will get 3x-3y=30........as you can see if you now add the two equations together the y's will again be eliminated because 3y-3y=0 and your left with 3x+3x=9+30 and again you follow the same procedure. hope that helps
 Functions/171337: Find f(1) given f(x) = 3x to the third power - x to the second power + 231 solutions Answer 126481 by Mathtut(3670)   on 2008-12-04 19:22:03 (Show Source): You can put this solution on YOUR website!just plug the numbers in where ever there is an x replace it with 1 : : : is answer to f(1)
 Exponential-and-logarithmic-functions/171325: My Toyota Avalon was purchased for \$27,500 in 1997. It has been decreasing in value at an average rate of 15% annually since then. When is its approximate value now?1 solutions Answer 126474 by Mathtut(3670)   on 2008-12-04 19:07:12 (Show Source): You can put this solution on YOUR website!well if you figure it to be 11 years formula is total amount(27,500) times n being the number of years of depreciation. In general depreciation equals where T is the Total being depreciated, x is the rate of depreciation, and n is the number of years. : gives us a percentage of .167 : multiply that by 27500 and the appx value is dollars
 Equations/171327: About two twenty fifth of the male population in the world cannot distinguish red from green. If there are fourteen boys in the ninth grade that cannot distinguish red from green, about how many ninth grade boys are there in all. write and solve an equation to find the answer.1 solutions Answer 126472 by Mathtut(3670)   on 2008-12-04 18:48:52 (Show Source): You can put this solution on YOUR website!if the ratio of the world is the same for these 9th grade boys then 2/5 of the 9th graders(we will call the total t) will not be able to distinguish red from green. number that cannot distinguish red from green we will call c and we have the number that fit this category as 14 : equation would be .4(t)=c : .4t=14 : ninth graders
 Numbers_Word_Problems/171304: i am a three digit number less than 200. i am divisible by 9 and 12 .my units digit is less than my ten digit .what am I1 solutions Answer 126466 by Mathtut(3670)   on 2008-12-04 18:14:51 (Show Source): You can put this solution on YOUR website!to be divisible by 9 the digits added together must be divisible by 9 and to be divisible by 12 it must be even. along with units digit being < tens digit....let see if we can come up with something. ones unit must be 0,2,4,6,or 8. if 0 then tens unit can be 1-9 case1 if 2 then tens unit can be 3-9 case2 if 4 then tens unit can be 5-9 case3 if 6 then tens unit can be 7-9 case4 if 8 then tens unit can be 9 case5 : 108 is covered in case1 because 0<8 : lets work backwards : case5: 98----9+8=17 to be divisible by 9 hunderds unit has to be 1 and 198 is not divisible by 12 : case4:96,86,76...96---9+6=16 to be div by 9 100's unit has to be 3 and that is more than 200. 86 ...8+6=14 to be div by 9 100's unit has to be 4....to big same problem with 76 : case3:94,84,74,64,54...9+4, 8+4,7+4,6+4,5+4 all present problems with #'s larger than 200 : case2:92,82,72,62,52,42,32 ...92,82,and 72 all get throw out because #'s larger than 200. 62 is 6+2=8..to be divisble by 9 100's unit must be 1...162..not divisible by 12 take 52,42,32 end up with being over 200 : case1:90,80,70,60,50,40,30,20,10... 90 larger than 200...80 is 8+0=8 in order to be divisible by 9 100's unit has to be 1. 180.......guess what this number is divisible by 9 and 12 and is less than 200 applying divisibility rules for the rest of the numbers in this case make all the numbers to large >200 : SO WE HAVE GONE THROUGH ALL THE CASES AND 180 is the only one that qualified there could be a simpler way but I will have to think on that
 Geometry_proofs/171290: This question is from textbook Geometry Concepts and Skills if line ab is congruent to line ae and angle acb is congruent to angle ade angle b is congruent to angle e1 solutions Answer 126450 by Mathtut(3670)   on 2008-12-04 17:45:09 (Show Source): You can put this solution on YOUR website!no not necessarily you can make two 90 degree angles with acb and ade and get very different angles for b and e. In the drawing below you can see that AB and AE are congruent and ACB congrent to ADE both at 90 degrees. but angle B and E are clearly not congruent
 Miscellaneous_Word_Problems/171282: Express the following statement as a formula: w varies jointly with square root of y and z squared and inversely as x cubed.1 solutions Answer 126437 by Mathtut(3670)   on 2008-12-04 16:52:12 (Show Source): You can put this solution on YOUR website!jointly simply means directly with 2 or more variables. Any direct variations take the form a/b=k and any inverse proportions take on the form ab=k : so where k is the constant of variation
 Expressions-with-variables/171280: This question is from textbook algebra 1 x-5=141 solutions Answer 126429 by Mathtut(3670)   on 2008-12-04 16:26:53 (Show Source): You can put this solution on YOUR website!given : added 5 to each side
 Expressions-with-variables/171274: Can u please help me evaluate the expression for the given value of the variable 5y over32-y to the third power when y equals three?1 solutions Answer 126428 by Mathtut(3670)   on 2008-12-04 16:25:41 (Show Source): You can put this solution on YOUR website! for y =3 : : : : for y=3 now if this reads all terms to the 3rd power..because the way you wrote it was unclear. =.138 for y=3
 Polynomials-and-rational-expressions/171270: This is from a Factoring Polynomials Section i need help finding the diffrent solutions to y(2y+7)=151 solutions Answer 126426 by Mathtut(3670)   on 2008-12-04 16:18:32 (Show Source): You can put this solution on YOUR website! given : distribute : subtract 15 from both sides : factor : 2y-3=0--->add 3 to each side--->2y=3--->divide by 2 on each side y=3/2 y+5=0--->subract 5 from each side--->y=-5 :
Polynomials-and-rational-expressions/171269: Factoring Polynomials using the quadratic formula...
X^2-4x=0
1 solutions

Answer 126425 by Mathtut(3670)   on 2008-12-04 16:12:19 (Show Source):
You can put this solution on YOUR website!

:
 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) 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=16 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, 0. Here's your graph:

Mixture_Word_Problems/171217: Without drawing the given ewuation, determine
A)how many x-intercepts the parabola has
B)whether its vertex lies above or on below or on the x-axis. Show your work.
y=-x^2-5x+6
y=-x^2+2x-1
1 solutions

Answer 126423 by Mathtut(3670)   on 2008-12-04 16:10:36 (Show Source):
You can put this solution on YOUR website!
given....... x intercepts are found when y is 0
:
so x intercepts are 2 and 3.
:
vertex (-B/2A , C - B^2/4A) (5/2(1),6-(25/4)...(5/2,-1/4)
so the vertex is below the x axis
:

vertex for x is -2/2(-1)=1 plug that into equation to find y
:
=0....so vertex is at (1,0) which is on the x axis meaning there is no x intercepts
there is one x intercept at x=1
:
 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) 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=0 is zero! That means that there is only one solution: . Expression can be factored: Again, the answer is: 1, 1. Here's your graph:

 Geometry_proofs/171263: This question is from textbook Geometry I have tried many approaches. Still i cant find the answer. Your help is greatly appreciated. THANK YOU1 solutions Answer 126418 by Mathtut(3670)   on 2008-12-04 15:47:48 (Show Source): You can put this solution on YOUR website!we need a problem before we can answer
 Miscellaneous_Word_Problems/171260: Solve for x: y=mx+b Would the answer be m+b/y?? 1 solutions Answer 126417 by Mathtut(3670)   on 2008-12-04 15:46:29 (Show Source): You can put this solution on YOUR website!y=mx+b....first subtract b from both sides : y-b=mx...next divide by m :