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 Rectangles/312661: What is the area and perimeter of a square with a diagnol of 10 inche?1 solutions Answer 223529 by mananth(12270)   on 2010-06-08 21:58:43 (Show Source): You can put this solution on YOUR website!diagonal of square = 10 in. let the side be x in. The diagonal and the sides of square form a right angle. Apply pythagoras theorem x^2 +x^2 = 10^2 2x^2 =100 x^2=50 x= 7.07 in Area = 50 sq. in perimeter = 4*7.07 =28.28 inches
 Miscellaneous_Word_Problems/312658: the length of a rose garden is 6 feet more than the width. the garden is surrounded by a uniform pathway which is three feet wide. the area of the pathway alone is 216 square feet. what is the perimeter of the rose garden?1 solutions Answer 223527 by mananth(12270)   on 2010-06-08 21:53:07 (Show Source): You can put this solution on YOUR website!let the width of the rose garden be x feet The length will be x+6 feet .. Pathway is 3 feet wide. So width and length will increas by 6 feet .. x+6 will be the width of whole plot x+6+6 will be the length of the whole plot .. Area of whole plot - area of pathway = area of rose garden. (x+6)(x+12)-216 = x(x+6) x^2+18x+144-216=x^2+6x 12x=72 x= 6 the width Length will be x+6 = 12 .. The perimeter of rose garden will be 2*6+2*12 =36 feet
 Polynomials-and-rational-expressions/312666: the product of the page numbers of 2 facing pages of a book is 110. Find the page numbers.1 solutions Answer 223525 by mananth(12270)   on 2010-06-08 21:45:52 (Show Source): You can put this solution on YOUR website!if the pages are facing each other they have to be cosequtive pages. let one page number be x the other will be x+1 .. x(x+1)=110 x^2+x-110=0 x^2+11x-10x-110=0 x(x+11)-10(x+11)=0 (x+11)(x-10)=0 x=10 since page number cannot be negative 10 & 11 are the page numbers
 Polynomials-and-rational-expressions/312663: a rectangular table is 4 feet longer as long as it is wide. If the area is 144 ft to the 2nd power find the length and width.1 solutions Answer 223523 by mananth(12270)   on 2010-06-08 21:42:32 (Show Source): You can put this solution on YOUR website!let the width be x feet length = x+4 feet Area = L*W .. x(x+4)=144 x^2+4x-144=0 .. Find X1, X2 the roots X1= -4 +sqrt(16+576) / 2 = 10.165 X2 =-4 -sqrt(16+576) / 2 = -14.165 .. X= 10.165 feet the width Length = 14.165 feet . CHECK 14.165*10.165== 143.98
 Expressions-with-variables/312659: I am confused on the following problem: During a 3000 mi flight, a plance encountered a strong tail wind that increased its speed by 100 mi/h. This increase in speed shortened the flying time by one hour. Find the speed of the plane relative to the ground.1 solutions Answer 223519 by mananth(12270)   on 2010-06-08 21:32:24 (Show Source): You can put this solution on YOUR website!distance traveled = 3000 miles. let speed of plane in still air be x mph speed with tail wind = x+100 mph .. if it had traveled without any wind it would take 3000 / x hours with tail wind the time = 3000/x+100. .. It took 1 hour less. 3000/x - 3000/ x+100 =1 LCM = x(x+100) 3000(x+100) - 3000x = x(x+100) 3000x +300 000 - 3000x = x^2 +100x x^2+100x-300000=0 x^2 +600x-500x-300000=0 x(x+600)-500(x+600)=0 (x+600)(x-500)=0 x=500 mph in still air speed with tail wind = 600 mph
 Permutations/312560: solve 3/x^2+x-2 + 3/x-1 = 1/x+21 solutions Answer 223515 by mananth(12270)   on 2010-06-08 20:20:15 (Show Source): You can put this solution on YOUR website!3/x^2+x-2 + 3/x-1 = 1/x+2 . 3/(x+2)(x-1) +3/x-1 -1/ x+2=0 . LCM (x+2)(x-1) 3+3(x+2)-1(x-1) / (x+2)(x-1)=0 .. 3+3x+6-x+1 / (x+2)(x-1)=0 2x+10 /(x+2)(x-1)=0 x+5 /(x+2)(x-1)=0 x+5=0 x=-5
 Problems-with-consecutive-odd-even-integers/312627: The larger of two numbers is four times the smaller. If their difference is eighteen, find the numbers.1 solutions Answer 223512 by mananth(12270)   on 2010-06-08 20:10:27 (Show Source): You can put this solution on YOUR website!let one number be x the other number will be 4x .. 4x-x=18 3x=18 x=6 the other number = 4x=24
 Mixture_Word_Problems/312625: How many milliliters of water must be added to 10 milliliters of a 30%-sulfuric acid solution to make a 15%-sulfuric acid solution?1 solutions Answer 223510 by mananth(12270)   on 2010-06-08 20:08:33 (Show Source): You can put this solution on YOUR website!30% sulphuric acid = 70% water 15% sulphuric acid = 85% water Let quantity of water be x ml concentration equation x+0.7*10 = 0.85(x+10) x+7=0.85x+8.5 0.15x=1.5 x= 1.5/0.15 x=10 ml
 test/312624: How do you convert 6200 cubic inches to cubic feet useing 3 unit multiplyers1 solutions Answer 223507 by mananth(12270)   on 2010-06-08 20:01:21 (Show Source): You can put this solution on YOUR website!one cubic feet = 12 *12*12 cu. inches =1728 cu.inches. .. 6200 cu. in /1728 = 3.587 cu.feet
 Average/312593: Please help me solve this finance: Ben, Jim, Alice, Erin, and Rick are friends. Ben is 20 years old, Jim is 17 years old, Alice is 21 years old, and Erin is 19 years old. The average age of the 5 friends is 20. How old is Rick?1 solutions Answer 223488 by mananth(12270)   on 2010-06-08 18:50:18 (Show Source): You can put this solution on YOUR website!The average age of 5 = 20. The total of their ages =100 .. The total age of Ben, Jim, Alice, Erin,= 20+17+21+19=77 The difference = 33 So Ricks age = 33 years
 Word_Problems_With_Coins/312601: IF YOU HAVE 205 COINS AND YOU HAVE THREE TIMES THE AMOUNT OF DIMES THEN NICKELS HOW MANY OF EACH ARE THERE I KNOW HOW MANY WHATS THE FORMULA USED1 solutions Answer 223486 by mananth(12270)   on 2010-06-08 18:40:17 (Show Source): You can put this solution on YOUR website!let the number of nickels be x the number of dimes will be 3x
 Square-cubic-other-roots/312599: each edge measured 1.5cm. What is the volume of the cube in cubic centimeters?1 solutions Answer 223481 by mananth(12270)   on 2010-06-08 18:32:39 (Show Source): You can put this solution on YOUR website!volume of cube = L*W*H ALL ARE EQUAL IN A CUBE 1.5*1.5*1.5 =3.375 cu.cm
 Percentage-and-ratio-word-problems/312406: A class has 28 students. The ratio of girls to boys is 4:3. How many girls are in the class?1 solutions Answer 223319 by mananth(12270)   on 2010-06-08 09:15:06 (Show Source): You can put this solution on YOUR website!the ratio of girls to boys = 4/3 there are 4+3 = 7 parts total .. 4/7 * 28 are girls 16 are girls & balancce 12 are boys. CHECK 16/12 = 4/3
 Polynomials-and-rational-expressions/312415: Factor by grouping 8x^3-8x^2-x+11 solutions Answer 223317 by mananth(12270)   on 2010-06-08 09:12:37 (Show Source): You can put this solution on YOUR website!8x^3-8x^2-x+1 . 8x^2(x-1)-1(x-1) (8x^2-1)(x-1)
 Polynomials-and-rational-expressions/312414: Solve v^2+4v-32=01 solutions Answer 223315 by mananth(12270)   on 2010-06-08 09:10:20 (Show Source): You can put this solution on YOUR website!v^2+4v-32=0 . v^2+8v-4v-32=0 v(v+8)-4(v+8)=0 (v+8)(v-4)=0 v= -8 or 4
 Polynomials-and-rational-expressions/312417: Factor trinomial c^2-10c+211 solutions Answer 223314 by mananth(12270)   on 2010-06-08 09:08:04 (Show Source): You can put this solution on YOUR website!c^2-10c+21 c^2 -7c-3x+21 c(c-7)-3(c-7) (c-3)(c-7)
 Circles/312419: A circul dinner plate hase a radius of 13 cm. Calculate thearea of th plate?1 solutions Answer 223311 by mananth(12270)   on 2010-06-08 09:05:08 (Show Source): You can put this solution on YOUR website!radius = 13 cm Area = pi*r^2 = pi* 13^2 = 531 sq. cm rounded off
 Unit_Conversion_Word_Problems/312407: A school club is planning a bus trip to the wildlife park. A bus which will hold up to 45 people will cost 600 dollars and admission tickets cost 30 dollars each. If you intend to charge each person 50 dollars, including bus and admission ticket, what is the minimum number of people who must participate to ensure that these costs are covered?1 solutions Answer 223310 by mananth(12270)   on 2010-06-08 09:03:13 (Show Source): You can put this solution on YOUR website!let the number of persons be x cost will be 30x +600 50x will be the amount collected. if the costs have to be met the revenue must be equal to the collection 30x+600=50x 20x =600 x= 30 To break even they have to have a minimum of 30 persons.
 Rational-functions/312290: please help me simplify the following equation: x^2+4x-5 over x^2+x-2 times 4x+8 over x+31 solutions Answer 223271 by mananth(12270)   on 2010-06-07 20:33:14 (Show Source): You can put this solution on YOUR website!x^2+4x-5 / x^2+x-2 * 4x+8 / x+3 .. (x+5)(x-1)/(x+2)(x-1) * 4(x+2) / (x+3) 4(x+5)/(x+3)
 Travel_Word_Problems/312281: How much work is done when a 40.0kg mass is lifted vertically against gravity to a height of 5.0 meters?1 solutions Answer 223270 by mananth(12270)   on 2010-06-07 20:28:59 (Show Source): You can put this solution on YOUR website!W= F* S F= force g= 9.8 m/sec^2 m= 40 kg .. F= mg = 40*9.8 N =39.2 N .. Distance moved = 5 meters work done = F * displacement work done =39.2 * 5 J =195 J Work done = 195 J
 Travel_Word_Problems/312278: The fastest car at a top speed can cover 5miles in 72 seconds. What is the speed of the car in miles/hours?1 solutions Answer 223269 by mananth(12270)   on 2010-06-07 20:11:14 (Show Source): You can put this solution on YOUR website!it can travel 5 miles in 72 seconds. . 72 seconds = 72 /3600 hours = 0.02 hours . Speed = distance in miles / speed in hours =5/0.02 =250 mph
 Travel_Word_Problems/312273: a train leves at 9 am going 60 mph and another train leaves at 12 noon going 75 mph. how long until the second train catches the first 1 solutions Answer 223267 by mananth(12270)   on 2010-06-07 20:07:33 (Show Source): You can put this solution on YOUR website!train A leaves 9.00am at 60 mph. Train B leaves at 12 noon at 75 mph .. Before train B leaves train A has traveled 60*3 = 180 miles. From this point let train A travel x miles before they meet. .. So train B travels x+180 miles to catch up. .. time taken by train A = x/60 time taken by train B = x+180 / 75 .. x/60 = x+180 / 75 75x = 60(x+180) 75x=60x +10800 15x=10800 x= 720 miles. Train B has to travel 720 miles to catch up. its speed is 75 mph time taken = 720/75 =9.6 hours
 Miscellaneous_Word_Problems/312269: The sum of a number and its reciprocal is 10/3. What is the number?1 solutions Answer 223265 by mananth(12270)   on 2010-06-07 19:54:26 (Show Source): You can put this solution on YOUR website!let the number be x reciprocal = 1/x . x+1/x = 10/3 x^2+1 / x =10/3 3(x^2+1)=10x 3x^2+3 = 10x 3x^2 -10x+3=0 3x^2-9x-x+3=0 3x(x-3)-1(x-3)=0 (3x-1)(x-3)=0 x=3 the number CHECK 3 + 1/3 = 10/3
 Geometry_Word_Problems/312263: two buildings are 60 feet apart acrooss a street. a person on top of the building finds the angle of elevation of the roof of the taller building to be 20 degrees and the angke of depression of its base to be 35 degrees. how tall is the taller building to the nearest foot?1 solutions Answer 223264 by mananth(12270)   on 2010-06-07 19:51:12 (Show Source): You can put this solution on YOUR website!Angle of elevation = 20 angle of depression to the foot = 35 . let h1 be the difference in heights of the building Let h2 be the height of the smaller building h1+h2 = H the height of the taller building. . tan 20 + tan 35 = h1/D+h2/D tan 20 + tan 35= h1+h2 /D d*(tan 20 + tan 35)= H 60*(tan 20 + tan 35)=H 163 feet
 Volume/312252: Circumference and area of a circle with radius of 2.3 feet. Round to the nearest tenth1 solutions Answer 223263 by mananth(12270)   on 2010-06-07 19:37:37 (Show Source): You can put this solution on YOUR website!circumference = 2*pi*r =2.3.142*2.3 =14.5 cm .. Area of circle = pi*r^2 =pi*(2.3)^2 = 16.6 sq. cm
 expressions/312259: -(5a-3x)- (3x-5a)1 solutions Answer 223258 by mananth(12270)   on 2010-06-07 19:28:19 (Show Source): You can put this solution on YOUR website!-(5a-3x)- (3x-5a) -5a+3x-3x+5a =0
 Polynomials-and-rational-expressions/312255: how do you simplify the rational expression, 3/2-x + 4/x^2-4?1 solutions Answer 223255 by mananth(12270)   on 2010-06-07 19:27:02 (Show Source): You can put this solution on YOUR website!3/2-x + 4/x^2-4? -3/ x-2 +4 (x+2)(x-2) LCM =(x-2)(x+2) -3(x+2) +4(x-2) /(x-2)(x+2) -3x-6+4x-8 / (x-2)(x+2) (x-12)/ (x-2)(x+2)
 Triangles/312226: find area of equilateral triangle of side 4a using heron’s formula. using this formula find area of an equilateral triangle whose perimeter is 540cm.1 solutions Answer 223251 by mananth(12270)   on 2010-06-07 19:21:28 (Show Source): You can put this solution on YOUR website!heron's formula area of triangle = sqrt(s(s-a)(s-b)(s-c)) s= half perimeter = 4a+4a+4a /2 = 6a Area = sqrt(6a(2a)(2a)(2a)) area = sqrt48a^4. . perimeter = 540 side = 180 s=270 area =sqrt(270(90)(90)(90)) =14029.26 sq cm
 Money_Word_Problems/312241: how many years will it take for an amount of money to double when it is compounded annually by a 4.3% interest rate?1 solutions Answer 223241 by mananth(12270)   on 2010-06-07 19:02:43 (Show Source): You can put this solution on YOUR website!let us assume the invested amount = 100 The money at the end of 1 year = 200 rate of interest = 4.3 % compounded annually. . Formula A= p(1+r/t)^nt 200=100(1+.043)^n 2=1.043^n log2/log1.043= n number of years = 16.46 for the money to double
 Travel_Word_Problems/311941: Horizons have a manufacturing plant located 300 mi from company headquarters. Their corporate pilot must fly from headquarters to the plant and back in 4 hrs. If there is a 20-mph headwind going and a 20-mph headwind tailwind returning, how fast must the plane be able to travel in still air?1 solutions Answer 223071 by mananth(12270)   on 2010-06-07 04:25:28 (Show Source): You can put this solution on YOUR website!300/x+20 + 300 / x-20 = 4 LCM (x+20)(x-20) .. 300(x-20)+300(x+20)= 4x^2-1600 300x-6000 +300x+6000= 4x^2-1600 4x^2-600x-1600=0 x^2-150x-400=0 Find X1 , X2 the roots of the equation X1= 150+sqrt((-150)^2+1600) / 2 x= 152.6 mph
 Travel_Word_Problems/311966: An airplane travels 6030km against the wind in 30 hours and 6750 with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind? 1 solutions Answer 223069 by mananth(12270)   on 2010-06-07 04:03:56 (Show Source): You can put this solution on YOUR website!let the speed of plane in still air be xmph speed of wind = y .. against wind speed will be x-y. Time traveled = 30 hour distance = 6030 miles so 30(x-y) = 6030 .. with wind speed will be x+y time taken = 30 hours distance = 6750 miles 30(x+y)=6750 .. 30x-30y=6030 30x+30y=6750 ADD .. 60x = 12780 x= 12780/60 x= 213 mph the speed of plane in still air plug the value of x in any equation x+y= 225 213+y=225 y=12 mph the speed of wind