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# Recent problems solved by 'mathslover'

mathslover answered: 135 problems
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 Geometry_Word_Problems/613984: to make 8 flags it takes 6 meters of cloth. how many meters would you need to make 20 flags 1 solutions Answer 386348 by mathslover(135)   on 2012-05-23 03:49:26 (Show Source): You can put this solution on YOUR website!To make 8 flags it requires 6 meters of cloth => to make 1 flag it requires 6/8 meters of cloth => to make 20 flags it would require of cloth =120/8 =15 meters of cloth
 Linear_Equations_And_Systems_Word_Problems/613980: the difference of squares of two numbers is 88.If the larger number is 5 less than twicw the smaller one ,then find the two nubers? 1 solutions Answer 386346 by mathslover(135)   on 2012-05-23 03:36:35 (Show Source): You can put this solution on YOUR website!Let the smaller number be x Now the larger number = 5 less thann 2 times the smaller number = 2x -5 Difference of the sqaures of the 2 numbers is 88 =88 =>=88 =>=0 Grouping the common terms together => => => =>and =>and => Therefore the smaller number is 9 and the bigger number is 2*9-5= 13 Ignoring the negative -7/3 as 2 times this number - 5 that is (-14/3 -5 =-29/5),gives a smaller number and not a larger number as in the problem statement
 Angles/330199: if the degree measures of 2 comlementary angles are in the ratio 2:13, what is the measure of the smaller angle?1 solutions Answer 236642 by mathslover(135)   on 2010-08-09 12:29:15 (Show Source): You can put this solution on YOUR website!Sum of the complementary angles is 90 degress. If one of the angles is 2x , the other angle is 13x (from the given condition that their ratios are 2:13) => 2x + 13x = 90 => 15x = 90 => x=6 Measure of the smaller angle is 2x = 2* 6 =12 degrees
 Travel_Word_Problems/330147: Professor Ortiz leaves campus on her bike, heading west at 6mph. Professor Wilson leaves campus at the same time and walk south at 2.5mph. how far apart are they after 4hrs? include check 1 solutions Answer 236625 by mathslover(135)   on 2010-08-09 11:05:25 (Show Source): You can put this solution on YOUR website! In 4 Hours , Prof Ortiz would have travelled 4* 6 = 24 miles west In 4 Hours ,Wilson would have travelled 4* 2.5 = 10 miles south B | | | 0--------A The distance between them is the distance AB as depicted in the figure. Note that they form 2 sides of a right angled triangle. Using the Pyathogrean theorem,
 Triangles/330002: The base of a traingle is 1/3 as long as its height. If the area is 24 square meters, how long is its base?1 solutions Answer 236492 by mathslover(135)   on 2010-08-08 20:56:38 (Show Source): You can put this solution on YOUR website!Let the height be x So the base is x/3 (One third of the height ) Area of a triangle =1/2 * base * height According to the given condition 1/2 * x/3 * x = 24 x^2/6 = 24 Multiplying both sides by 6 x^2 = 24*6 x^2=144 x=sqrt(144) therefore x=12 and x/3 = 4 Base is 4 and height is 12
 Quadratic-relations-and-conic-sections/329976: Prove that tan x (cot x + tan x) = sec^2x1 solutions Answer 236484 by mathslover(135)   on 2010-08-08 20:32:31 (Show Source): You can put this solution on YOUR website!Prove that tan x (cot x + tan x) = sec^2x LHS (Left hand side) tan x (cot x + tan x) =tan x * cot x + (tan x)(tan x) =1+ tan^2 x =1 + sin^2 x/cos ^ x =(cos ^ 2 x + sin ^ x)/cos ^2 x =1/cos^2 x =sec ^2 x = RHS (right hand side)
 real-numbers/330001: Simplify "(5 + 3i)(5 - 3i)." Is the result real, complex, or both? Explain.1 solutions Answer 236482 by mathslover(135)   on 2010-08-08 20:24:34 (Show Source): You can put this solution on YOUR website!Simplify "(5 + 3i)(5 - 3i)." Is the result real, complex, or both? Note the expression is of the form (A+B)(A-B)= A^2 - B^2 therefore we can write 5 + 3i)(5 - 3i) as 5^2 - (3i)^2 =25 - 9i^2 =25 -9(-1) as i^2 = -1 =25+9 =34 which is real number.
 Polynomials-and-rational-expressions/324557: factor completely (x+3)^2-10(x+3)+24 write a quadratic equation and answer the following: the shortest leg of a right triangle is two less than the hypotenuse. the hypotenuse is one longer than the longest leg. thank you1 solutions Answer 232292 by mathslover(135)   on 2010-07-21 22:25:01 (Show Source): You can put this solution on YOUR website!(x+3)^2-10(x+3)+24 Let's replace x+3 by A So, the given expression would transform to A^2 -10A + 24 Rewriting it as A^2 - 6A -4A + 24 A(A-6) -4(A-6) Taking A-6 as the common factor, (A-6)(A-4) Substituting A=x+3 back into the expression we get (x+3-6)(x+3-4) (x-3)(x-1) is the required factor. ========================================================================== write a quadratic equation and answer the following: the shortest leg of a right triangle is two less than the hypotenuse. the hypotenuse is one longer than the longest leg. Let the longest leg be x So the hypotenuse is (x+1) {the hypotenuse is one longer than the longest leg} And the shortest leg is (x+1)-2=x-1 {the shortest leg of a right triangle is two less than the hypotenuse} Using Pythagoras's theorem, hypotenuse^2 = shorter leg^2 + longer leg^2 we get (x+1)^2 = (x-1)^2 + x^2 Expanding the LHS and the RHS x^2 + 2x+ 1 = x^2 -2x+1 + x^2 Moving the Right hand side expression to Left hand side we get x^2 + 2x+ 1 - (x^2 -2x+1 + x^2)= 0 grouping the like terms, (x^2 - x^2 -x^2) + (2x + 2x ) + (1 -1)=0 -x^2 + 4x =0 -x(x-4)=0 which gives x=0 and x=4 as two possible solutions. But we cannot have a triangle with side of length 0. So discarding x=0 we get the other solution as x=4 Hence, the sides of the triangle are The longest side=4 The shorter side=4-1=3 hypotenuse=4+1=5
 Numbers_Word_Problems/140068: Choose three consecutive odd integers such that three times the second decreased by 4 is equal to twice the third increased by 15. Answers (choose one): (a) 11, 13, 15 (b) 13, 15, 17 (c) 23, 25, 27 (d) 25, 27, 29. I don't get how to do this at all. What is "consecutive" anyways? Thanks.1 solutions Answer 102077 by mathslover(135)   on 2008-05-05 01:14:38 (Show Source): You can put this solution on YOUR website!What is "consecutive" anyways? By consecutive we mean appearing one after the other. So for example 1,3,5 are consecutive odd integers.Again 7,9,11 are similarly 3 consecutive odd integers. Now to the solution of the actual problem. Let the three integers be x,x+2,(x+2)+2 Notice in the example above how they differ by 2. i.e. x,x+2 and x+ 4 are the 3 consecutive odd integers. Given = = = Group the like terms = x=21 therefore the other 2 numbers are 23 and 25 Numbers are 21,23,25 Verify
 Percentage-and-ratio-word-problems/140063: On Monday, Popeye ate a third of a new case of spinach. On Tuesday, he ate 75% of what remained in the case after Mondays meal. On Wednesday, he finished the case. Tuesday's meal consisted of 12 cans of spinach. How much spinach did he eat on Monday? Show how you know? Ohhh, I am so frustrated with this problem. Is this something I have to work backwards on? Please helo me. Thankyou dani..1 solutions Answer 102076 by mathslover(135)   on 2008-05-05 00:54:54 (Show Source): You can put this solution on YOUR website!Let the total spinach cans in the case be x On Monday he ate of the spinach cans. So amount left after Monday = = =2x/3 On Tuesday he ate 75% of the remaining i.e. Given that on Tuesday he at 12 cans. Therefore, = = simplifying 75/100 as 3/4 = The amount he ate on Monday = x/3 = 24/3 = 8 cans
 Probability-and-statistics/140064: There are two spinners. The first spinner is a circle that is cut in fours. the numbers read 10, 12, 14, 18. The other spinner is also cut in fours and the numbers are 1, 2, 3, 4 Ok.. The two spinners shown are spun and the difference between the results is found. Find the probability that the difference is a multiple of 3. Thankyou.. Danielle, AKA Dani1 solutions Answer 102075 by mathslover(135)   on 2008-05-05 00:39:55 (Show Source): You can put this solution on YOUR website!The total different outcomes of the two spinners are 4* 4= 16 The outcomes are (10,1),(10,2),(10,3),(10,4),(12,1),(12,2),(12,3),(12,4),(14,1), (14,2),(14,2),(14,3),(18,1),(18,2),(18,3),(18,4) Out of these pairs, the ones for which the difference is multiple of 3 are: (10,1), difference 9 (10,4) difference 6 (12,3) difference 9 (14,2) difference 12 (18,3) difference 15 So the required probability = favorable outcomes/ total outcome = 5/16
 Inequalities/98512: Hello out there,I really need some help with some problems,the first one is Solve the inequality:[2x]<8.The next one is,Solve the inequality:[p+2]<6.The third is,Solve the inequality:Solve the inequality:[z+3]>2.And the last one is,Which of the points satisfy y-3<2x? (0,0)or(1,5)or(-2,0).Thanks for anyone that can help.1 solutions Answer 71675 by mathslover(135)   on 2007-09-16 14:14:16 (Show Source): You can put this solution on YOUR website!Before giving out the solution to the problem here is something you should know [x] means the greatest integer value less than or equal to x so for e.g [1.2] = 1 [-5.6] = -6 [4]=4 now to the questions 1. [2x] < 8 2[x] < 8 (Note [2x] is not = 2[x] but [2x] <= 2[x] so without loss of inequality we can write [2x] as 2[x]) in the above inequality [x]< 4 for all x < 4, [x] <4 hence solution set for the above is x< 4 2. [ p + 2] <6 for all p+2 < 6 , [p+2] will be less than 6 p < 4 3 [z +3 ] >2 since [z+3] is an integer value [z+3] should be >=3 ( integer greater than 2) which gives z>=0 4.y-3<2x? (0,0)or(1,5)or(-2,0). substitue x=0, y=0 0-3< 2*0 -3 <0 hence it satisfies the equation Substituting x=1 , y=5 5-3 < 2*1 2< 2 It does not satisfy the equation Substituting x= -2 , y=0 0 - 3 < 2* -2 -3 < -4 it does not satisfy the equation The only point satisfying the equation is (0,0)
 Equations/98458: Using the digits 1-9 in order, insert operation signs and grouping symbols to get the value of 100. you can only use a number once.Help Me. Please...1 solutions Answer 71632 by mathslover(135)   on 2007-09-15 23:05:34 (Show Source): You can put this solution on YOUR website! (1 * 2 * ( 3 + 4 ) * 5 ) + 6 + 7 + 8 + 9 =100 verification: (2 * 7 * 5 ) + 6+7+8 +9 70 + 30 =100
 Mixture_Word_Problems/98457: This question is from textbook Algebra and Trigonometry Please help me with this mixture word problem. A jewel has five rings, each weighing 18 g, made of an alloy of 10% silver and 90% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 75%. How much silver should he add? I'm having a lot of difficulty with setting up and equation for this particular problem. I would be very thankful if you would help me out. Thank you1 solutions Answer 71631 by mathslover(135)   on 2007-09-15 22:53:33 (Show Source): You can put this solution on YOUR website!total weight of the rings = 18 * 5 = 90g total amount of silver = 10/100 *90 = 9g Total amount of gold in all the 5 rings = 90 -9 =81g Let the amount of silver added be x grams total weight of the mixture now = 90 + x percentage of gold = 81/(90+x) *100 since the percentage of gold now is to be 75 81/(90+x) *100 = 75 81 * 100 = 75 (90+x) 27 * (3 * 25) * 4= 75(90+x) canceling out 75 on both sided 27* 4 = 90 +x x = 108 -90 =18g
 Polynomials-and-rational-expressions/98446: factor monomials from polynomials 3(x+2)(x-4)+6(x+2)(x+1)1 solutions Answer 71630 by mathslover(135)   on 2007-09-15 22:19:36 (Show Source): You can put this solution on YOUR website!3(x+2)(x-4)+6(x+2)(x+1) =3(x+2)[((x-4 + 2(x+1)] =3(x+2)( x-4 + 2x +2) =3(x+2)(3x -2)
 Graphs/98454: find the slope of the line passing through (3,4) and (3,-4)1 solutions Answer 71627 by mathslover(135)   on 2007-09-15 21:51:33 (Show Source): You can put this solution on YOUR website!Slope = = = infinity which means that the line is perpendicular to the x-axis equation of the line is x=3
 expressions/98456: Insert parentheses to make each pair of expressions equal. 3*8+6squared-8/2=261 solutions Answer 71625 by mathslover(135)   on 2007-09-15 21:46:42 (Show Source): You can put this solution on YOUR website!3*8+6squared-8/2=26 which is true ..does it make sense now ((3*8) + (6^2 - 8 ))/2 =26
 Graphs/98455: what are the solutions for x-y=41 solutions Answer 71623 by mathslover(135)   on 2007-09-15 21:42:33 (Show Source): You can put this solution on YOUR website!Since there are 2 variables in the equation x-y=4 , you need at least 2 equations to find the values of x and y
 Length-and-distance/98450: the distance between the points (4,-3)and (x,3) is 10. find X i am coming up with +12 the answer should be -4, Thanks1 solutions Answer 71619 by mathslover(135)   on 2007-09-15 21:29:28 (Show Source): You can put this solution on YOUR website!Use the distance formula D = 10 = square on both sides x-4 = +-8 x=12 and x=-4 So your answer of 12 is also correct