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# Recent problems solved by 'Mathtut'

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 Exponents-negative-and-fractional/180023: This question is from textbook Algebra Structure and Method book 1 hello i need help with negative exponents. what is 3 to the -4th power divided by 3 to the -3rd power? i don't understand P.S. it is on page 6521 solutions Answer 134896 by Mathtut(3670)   on 2009-02-03 19:07:09 (Show Source): You can put this solution on YOUR website! any number to the -nth power is equal to 1/number to the nth power : for instance and vise versa :
 Linear-equations/180026: Please help me with this math problem- x+y=5 i have tried to solve it by subtracting x from both sides to isolate the y variable then i came up with an equation like this y=5-x,please tell me if I did it correct if I have not could you show me what I have done wrong step by step? thank you 1 solutions Answer 134895 by Mathtut(3670)   on 2009-02-03 19:03:02 (Show Source): You can put this solution on YOUR website!if the original problem is : x+y=5 : then yes y=-x+5 or y=5-x
 Linear-equations/180027: y=-5x+41 solutions Answer 134893 by Mathtut(3670)   on 2009-02-03 19:00:09 (Show Source): You can put this solution on YOUR website!since there are no instructions with this I will graph it :
 Numbers_Word_Problems/180016: Find the two-digit number whose tens digit is 4 less than its units digit if the orignal number is 2 more than 3 times the sum of the digits.1 solutions Answer 134891 by Mathtut(3670)   on 2009-02-03 18:52:19 (Show Source): You can put this solution on YOUR website!Find the two-digit number whose tens digit is 4 less than its units digit if the orignal number is 2 more than 3 times the sum of the digits. : let the two digit number be ab--->remembering that ab = 10a+b : a=b-4............eq 1 10a+b=3(a+b)+2......eq 2 : take a's value in eq 1 and plug it into eq 2 10(b-4)+b=3(b-4)+3b+2 : 10b-40+b=3b-12+3b+2 : 5b=30 : units digit : tens unit : number is 26
 Trigonometry-basics/179996: If csc 0 is 10.2593, then sin 0 is: a. 0.0975 b. 0.0974 c. 0.0973 d. 0.09721 solutions Answer 134876 by Mathtut(3670)   on 2009-02-03 17:58:02 (Show Source): You can put this solution on YOUR website!1/10.2593=.0975 rounded off : so a is the best answer
 Linear-equations/180003: Here is the question: A line passes through the point (3,5) and the slope(m) is 2/3. Write the equation in point slope form. Would this be the right solution?: 2(x-3)= 3(y-5) I did this to get rid of the denominator from the fraction 2/3. We were taught to do it this way.1 solutions Answer 134875 by Mathtut(3670)   on 2009-02-03 17:56:14 (Show Source): You can put this solution on YOUR website!point slope form is y-k=m(x-h) ....where m is the slope and (h,k) is any point on the line : y-5=(2/3)(x-3) : y-5=(2/3)x-2 : 3y-15=2x-6......multiplied terms by 3 to get rid of fraction : 2x-3y=-9.....is the standard form : y=(2/3)x+3..is point slope intercept form : so the answer to your question is YES but answers are usually in these two forms...GOOD JOB
 Systems-of-equations/180001: Please help me solve this equation: -4(3+x)+5=4(x+3)Also thanx alot mathtut...1 solutions Answer 134873 by Mathtut(3670)   on 2009-02-03 17:50:46 (Show Source): You can put this solution on YOUR website!-4(3+x)+5=4(x+3) : -12-4x+5=4x+12.......distributed terms : -7-4x=4x+12....combined like terms on left : -8x=19........subtracted 4x and added 7 to both sides : : YOUR WELCOME : God Bless!!!!!!
 Functions/179959: -3(2s-1)-3=-2(9s+4)-31 solutions Answer 134872 by Mathtut(3670)   on 2009-02-03 17:46:49 (Show Source): You can put this solution on YOUR website!-3(2s-1)-3=-2(9s+4)-3 : -6s+3-3=-18s-8-3....distributed terms : -6s=-18s-11.....collected like terms : 12s=-11.....added 18s and subtracted 3 from both sides :
 Signed-numbers/179998: if m=4 what is 3m?1 solutions Answer 134871 by Mathtut(3670)   on 2009-02-03 17:39:13 (Show Source): You can put this solution on YOUR website!take the given value and plug it into the variable : m=4 : 3m is 3(4)=12
 Systems-of-equations/180000: Please help me solve this equation: 4(-3x+1)=-10(x-4)-14x1 solutions Answer 134870 by Mathtut(3670)   on 2009-02-03 17:38:21 (Show Source): You can put this solution on YOUR website!4(-3x+1)=-10(x-4)-14x : -12x+4=-10x+40-14x.........distributed terms : -12x+4=-24x+40....collected like terms on each side : 12x=36......added 24x and subtracted 4 from each side :
 Linear_Equations_And_Systems_Word_Problems/179976: Car rental company charges \$39.99 per day. The first 50 miles are free, but there there is a charge of \$0.28 per mile after 50 miles. I need to write an inequality to determine the greatest number of miles that you can drive for \$55 or less. I don't know how to begin to write this inequality. Can you help me? Thanks1 solutions Answer 134869 by Mathtut(3670)   on 2009-02-03 17:35:57 (Show Source): You can put this solution on YOUR website!Car rental company charges \$39.99 per day. The first 50 miles are free, but there there is a charge of \$0.28 per mile after 50 miles. I need to write an inequality to determine the greatest number of miles that you can drive for \$55 or less. I don't know how to begin to write this inequality. Can you help me? : C(m)=39.99+.28(m-50) where m is the miles and m>50 miles : : : : miles ......so miles have to be less than or equal to 103.6 in order to spend no more than 55 dollars
 Systems-of-equations/179991: Please help me solve this equation: 2b+11=15-6b1 solutions Answer 134868 by Mathtut(3670)   on 2009-02-03 17:28:08 (Show Source): You can put this solution on YOUR website!2b+11=15-6b : 8b=4......added 6b and subtracted -11 from both sides :
 expressions/179981: If a tree is 6 feet tall and grows 2 feet a year, what is the expression for the growth of the tree in y years?1 solutions Answer 134864 by Mathtut(3670)   on 2009-02-03 17:11:48 (Show Source): You can put this solution on YOUR website!g(y)=2y+6
 Trigonometry-basics/179984: The measures of all the angles in standard position which are coterminal with an angle whose measure is 400 degrees are given by the expression. a. 400+360 b. 40 c. 40 + n360,neI d. 40 + n 180, neI1 solutions Answer 134862 by Mathtut(3670)   on 2009-02-03 17:10:36 (Show Source): You can put this solution on YOUR website!c is your answer
 Systems-of-equations/179985: Please help me solve this equation: m-30=6-2m1 solutions Answer 134860 by Mathtut(3670)   on 2009-02-03 17:07:32 (Show Source): You can put this solution on YOUR website!m-30=6-2m : 3m=36........added 2m and 30 to both sides :
 test/179963: This question is from textbook Business Mathematics What is the net cost of 200 stocks at \$42.125 a) \$8,425 b) \$42.13 c) \$4212.5 d) none of these1 solutions Answer 134859 by Mathtut(3670)   on 2009-02-03 17:06:16 (Show Source): You can put this solution on YOUR website!200(42.125)=8425 : a) is the answer
 Equations/179971: rearranging formula T=20W+30 (FIND W) A=LxB (FIND B) N=6P+2 (FIND P) K=8(M/5) (FIND M)1 solutions Answer 134852 by Mathtut(3670)   on 2009-02-03 16:19:33 (Show Source): You can put this solution on YOUR website!T=20W+30 (FIND W) A=LxB (FIND B) N=6P+2 (FIND P) K=8(M/5) (FIND M) : T=20W+30 : 20W=t-30....subtracted 30 from both sides : ......divided both sides by 20 : A=LxB : .....divided both sides by L : N=6P+2 : 6P=N-2....subtracted 2 from both sides : .....divide both sides by 6 : K=8(M/5) : K=8M/5 : 5K=8M.....multiplied both sides by 5 : ......divided both sides by 8
 Graphs/179956: Calculate the shortest distance from the given line and point povided. 2x-y=3 (2,3) I subtracted 2 from 2x-y=3 and got -y=-2+3, I made them postitive and got y=1 I plugged 2 in for x then got seven, I put 2(1)-7=3 and recieved 5. I was told this is incorrect but i dont know any other way to do it...any help would be helpful.1 solutions Answer 134847 by Mathtut(3670)   on 2009-02-03 14:43:54 (Show Source): You can put this solution on YOUR website!find the equation of the line that passes thru (2,3) and is perpendicular to the given line : the slope of the perpendicular line will have a negative reciprical to the given line. 2x-y=3 --->y=2x-3 so m= for this line is 2. the slope for the perpendicular line is -1/2 : y-3=(-1/2)(x-2) : y-3=(-1/2)x+1--->y=(-1/2)x+4--->x+2y=8 : now we have to find the intersection of these two lines : 2x-y=3....eq 1 x+2y=8...eq 2 : multiply eq 1 by 2 and add all terms of the equations together. : 4x-2y=6....eq 1 revised x+2y=8....eq 2 : y terms are eliminated becaue -2y+2y=0. We are left with 4x+x=14 : 5x=14 : x=14/5 : plug this value back into eq 1 or 2. I chose eq 2 : (14/5)+2y=8 : 2y=26/5: y=26/10=13/5 : Now we can use the distance formula: we have point (2,3) and point (14/5,13/5) : : : : : distance between point (2,3) and line 2x-y=3 is :
 Linear-systems/179943: 5x+4y=22 3x + 4y=101 solutions Answer 134846 by Mathtut(3670)   on 2009-02-03 14:29:09 (Show Source): You can put this solution on YOUR website!5x+4y=22.......eq 1 3x+4y=10.......eq 2 : subtract equation 1 from equation 2 : y terms are eliminated because 4y-4y=0. We are left with 5x-3x=22-10 : 2x=12 : : take the found value of x and plug it back into either equation : 3(6)+4y=10--->18+4y=10--->4y=-8 :
 Word_Problems_With_Coins/179953: A child's coin bank contains \$2.58 in pennies and nickels. If the number of pennies is 36 less than 2 times the number of nickels, how many pennies are in the bank?1 solutions Answer 134845 by Mathtut(3670)   on 2009-02-03 14:24:58 (Show Source): You can put this solution on YOUR website!A child's coin bank contains \$2.58 in pennies and nickels. If the number of pennies is 36 less than 2 times the number of nickels, how many pennies are in the bank? :lets call the number of pennies and nickels ,p and n respectively : .01p+.05n=2.58.........eq 1 p=2n-36................eq 2 : take p's value of 2n-36 in eq 2 and plug it into eq 1 : .01(2n-36)+.05n=2.58 : .02n-.36+.05n=2.58 : .07n=2.94 : number of nickels : number of pennies
 Radicals/179954: 4. A container with curved sides is 10 ft tall. When water is in the container to a depth of h ft, the number of cubic feet of water can be approximated by using the formula V = 0.95h2.9. Find the amount of water in the container when the depth of the water is 7.5 ft. Round to the nearest hundredth. 1 solutions Answer 134844 by Mathtut(3670)   on 2009-02-03 14:20:16 (Show Source): You can put this solution on YOUR website! : : cu ft
 Quadratic_Equations/179941: Joe has a collection of nickels and dimes that is worth \$6.05. If the number of dimes is doubled and the number of nickels was decreased by 10, the value of the coins would be \$9.85. How many dimes do we have?1 solutions Answer 134843 by Mathtut(3670)   on 2009-02-03 14:16:13 (Show Source): You can put this solution on YOUR website!Joe has a collection of nickels and dimes that is worth \$6.05. If the number of dimes is doubled and the number of nickels was decreased by 10, the value of the coins would be \$9.85. How many dimes do we have? : let the number of nickels and dimes be n and d respectively : .05n+.1d=6.05.........eq 1 .05(2n)+.1(d-10)=9.85.....eq 2 : rewrite eq 1 to .05n=6.05-.1d--->n=121-2d and plug the value of n which is 121-d into eq 2 : .1(121-2d)+.1(d-10)=9.85 : 12.1-.2d+.1d-1=9.85 : -.1d=1.25 : d=12.5 : something is wrong with this problem. One of the amounts in the equation is off. there is no way to get a whole number for dimes in this scenario. Email me the correct numbers. thanks Mathtut
 Miscellaneous_Word_Problems/179951: Disregarding wind resistance, the distance a body falls from rest varies directly as the square of the time it falls. If a skydiver falls 64ft in 2 seconds, how far will he fall in 10 seconds?1 solutions Answer 134841 by Mathtut(3670)   on 2009-02-03 13:54:03 (Show Source): You can put this solution on YOUR website!d/t=k : 64/2=32=k : d/10=32 : d=320 ft
 Functions/179950: This question is from textbook algebra 1 how solve problem1 solutions Answer 134840 by Mathtut(3670)   on 2009-02-03 13:46:53 (Show Source): You can put this solution on YOUR website!we need the problem to solve it..thanks Mathtut
 Mixture_Word_Problems/179947: Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which method works the best? Why? What circumstances would cause one to use a different method?1 solutions Answer 134839 by Mathtut(3670)   on 2009-02-03 13:46:22 (Show Source): You can put this solution on YOUR website!it all depends upon the equations in question: if equations are VERY straight forward then the graphing method can work well. It has the advantage of visualation. In other words, you can see the behaviour of the system. Main drawback to graphing is it isnt very accurate for solutions. : For other short and simple equations substitution can work well. The advantage to substitution is when one of the variables is already isolated in one of the equations. Even then you must look closely at the other equation to see how complicated the substitution method could be. A few drawbacks to substitution is there can be alot of division and finding LCM. : I would say the elimination method is the most popular and in my opinion is the best .Many times you can even do calculations in your mind, and so it is much faster. Elimination seems to be more useful when coefficients are larger, whereas substitution is useful when coefficients are smaller and when it is easy to islate a variable. Elimination works for any system of linear equations. After one or two steps you have a one-step equation to solve and you have half of your solution. Con can be Sloppy calculations can lead to incorrect solutions If I need a rough idea of the solution, I graph. If one of the equations is already solved for y or for x, I use substitution. If neither of the above is true, I use elimination.
 Mixture_Word_Problems/179935: How many pounds of walnuts at 84 cents Lb should be mixed with 20lb of pecans at \$1.20/lb to give a mixture worth \$1.04/lb.1 solutions Answer 134837 by Mathtut(3670)   on 2009-02-03 13:17:22 (Show Source): You can put this solution on YOUR website!let x and y be the amount of walnuts and pecans respectively : x+y=20................eq 1 .84x+1.2y=1.04(20)....eq 2 : rewrite eq 1 to x=20-y and plug that value into eq 2 : .84(20-y)+1.2y=20.8 : 16.8-.84y+1.2y=20.8 : .36y=4 : pounds of pecans : pounds of walnuts
 Square-cubic-other-roots/179945: This question is from textbook AGS Algebra powers and roots1 solutions Answer 134836 by Mathtut(3670)   on 2009-02-03 13:11:08 (Show Source): You can put this solution on YOUR website!we have no access to the problems . please re submit with a problem...thanks Mathtut
 absolute-value/179932: This question is from textbook [b+2]<-11 solutions Answer 134835 by Mathtut(3670)   on 2009-02-03 12:55:53 (Show Source):
 absolute-value/179926: This question is from textbook Solve:[k-2]=41 solutions Answer 134834 by Mathtut(3670)   on 2009-02-03 12:51:35 (Show Source): You can put this solution on YOUR website! : k-2=4 and -(k-2)=4 : k=6 and -k=2 : k=6 and k=-2 :
 Quadratic_Equations/179942: Write 3 quadratic equations with a,b,c (coefficients of x^2,x and the constant) as: 1. integers 2. rational numbers 3. irrational numbers1 solutions Answer 134833 by Mathtut(3670)   on 2009-02-03 12:45:03 (Show Source): You can put this solution on YOUR website!a) : b) : c)
 Expressions-with-variables/179933: This question is from textbook To divide 7/x+2 by x-2/14, you can multiply 7/x+2 by:1 solutions Answer 134832 by Mathtut(3670)   on 2009-02-03 12:42:35 (Show Source): You can put this solution on YOUR website!To divide 7/x+2 by x-2/14, you can multiply 7/x+2 by : so you take the bottom fraction and invert it and then multiply : so you can multiply 7/(x+2) by 14/(x-2)