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# Recent problems solved by 'mananth'

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 Angles/346961: The supplement of an angle is 36 degrees less than twice the supplement of the complement of the angle. Find the measure of the supplement. Can you also explain it too? Thank you so much1 solutions Answer 248109 by mananth(12270)   on 2010-09-22 21:24:13 (Show Source): You can put this solution on YOUR website!let the angle be x degrees the supplement of this angle will be 180-x .. The complement of the angle will be 90-x supplement of this complement angle will be 180 - (90-x) Twice this = 2[180-(90-x)] Less 36 =2[180-(90-x)]-36 .. 180-x = 2[180-(90-x)]-36 ... 180-x= 2[180-90+x]-36 180-x=2[90+x]-36 180-x=180+2x-36 3x=180-180+36 3x=36 x= 12 supplement of 12 = 180-12 = 168
 Travel_Word_Problems/346953: A bullet is fired horizontally at a target, and the sound of its impact is heard 1.5 seconds later. If the speed of the bullet is 3300 ft/sec and the speed of sound is 1100 ft/sec how far away is the target?1 solutions Answer 248100 by mananth(12270)   on 2010-09-22 21:15:05 (Show Source): You can put this solution on YOUR website!let target distance be x bullet speed = 3300ft/sec sound speed = 1100 ft/sec sound heard after 1.5 seconds = 3/2 .. x/3300 + x/ 1100 = 3/2 LCD = 3300 x+3x /3300 = 3/2 4x/3300 = 3/2 4x= 3*3300/2 4x=9900/2 4x= 4950 x= 4950/4 x=1237.5 feet
 Expressions-with-variables/346948: find the values of the variables (3x-40) (2x-10)1 solutions Answer 248087 by mananth(12270)   on 2010-09-22 21:05:54 (Show Source): You can put this solution on YOUR website!(3x-40) (2x-10) If (3x-40) (2x-10)=0 Then 3x=40 x=40/3 OR 2x-10=0 2x=10 x=5
 Graphs/346945: what is the x and y intercept of -3x+8y=481 solutions Answer 248083 by mananth(12270)   on 2010-09-22 20:59:07 (Show Source): You can put this solution on YOUR website!-3x+8y=48 .. for x intercept y=0 -3x+0=48 x=48/-3 x=-16.. For y intercept x=0 0+8y=48 8y=48 y=6
 Triangles/346942: 1.) The perimeter of a triangle is 76 centimeters. The second side is twice as long as the first side. The third side is four centimeters shorter than the second side. How long is each side?1 solutions Answer 248080 by mananth(12270)   on 2010-09-22 20:56:03 (Show Source): You can put this solution on YOUR website!let first side be x second side= = 2x third side= 2x-4 ... x+2x+2x-4=76 5x-4=76 5x=76+4 5x=80 x=16 cm first side second side = 2*16= 32 cm third side = 2x-4 = 2*16 -4 =28 cm
 Equations/346938: A pasta machine cost \$33.oo and the ingredients to make one batch of pasta costs .33. One batch of pasta bought in a store costs .99. How many batches of pasta will you have to make for the cost of the machine and ingredients to equal the cost of buying the same amount of pasta at the store.1 solutions Answer 248073 by mananth(12270)   on 2010-09-22 20:46:35 (Show Source): You can put this solution on YOUR website!Let the number of batches be x cost of x batches = 0.33x cost of machine = 33 cost of x batches in store = 0.99x 0.33x+33=0.99x 0.99x-0.33x=33 0.66x=33 x=33/0.66 x= 50 batches of pasta.
 Equations/346934: You earn \$9 per hour. On major holidays, such as Thanksgiving, you earn twice as much per hour. You earned a total of \$405 for the week including thanksgiving. Write and solve an equation to find how many hours you worked on thanksgiving if you worked 35 hours during the rest of the week.1 solutions Answer 248067 by mananth(12270)   on 2010-09-22 20:38:28 (Show Source): You can put this solution on YOUR website!thanks giving day x hours .. other days 35-x hours .. earning = 9*(35-x) on normal day Thanksgiving day - 18x .. 18x+9(35-x)=405 18x+315-9x = 405 9x=405-315 9x=90 x=10 hours on Thanksgiving day
 test/346925: at 9:00 on Saturday two bicyclist heading in opposite directions pass each other on a bicycle path. the bicyclist heading north is riding 6km/hr faster than the bicyclist heading south. at 10:15,they are 42.5km apart. find the two bicyclists rates.1 solutions Answer 248064 by mananth(12270)   on 2010-09-22 20:29:55 (Show Source): You can put this solution on YOUR website!at 9:00 two bicyclist heading in opposite directions the bicyclist heading south x km/h bicyclist heading north x+6 km/hr. at 10:15,= 1 1/4 hour = 5/4 hours they are 42.5km apart. ..... 5/4 *x +5/4 *(x+6) = 42.5 5x/4+(5x+30) /4 =42.5 (5x+5x+30)=4*42.5 10x+30=170 10x=170-30 10x=140 x=14 km/h south 14 +6 = 20km/h north bound
 Surface-area/346549: Finding the area of a rectangle when the length is v+3 and the width is 5, the answer is 5v + 15. I understand how I arrived at 15 but I don't understand the 5v part. Thank you1 solutions Answer 247755 by mananth(12270)   on 2010-09-22 02:22:26 (Show Source): You can put this solution on YOUR website!length = v+3 width =5 Area A = L*W A= 5*(v+3) A= 5*v+5*3 A=5v+15
 Finance/346550: An investment of \$37,000 was deposited in the bank. Interest was computed on a semi-annual basis and was kept there for 10 years. If the maturity value of this investment is \$74,000, at what interest rate was it invested?1 solutions Answer 247754 by mananth(12270)   on 2010-09-22 02:04:47 (Show Source): You can put this solution on YOUR website!Investment = 37000 FV= 74,000 years = 10 compunded semi annual =2 number of periods = 2*10 = 20 r= r=0.0352 =7.052% /year
 Travel_Word_Problems/346537: the bus travel at 30mph left city at 10:30 am the car follow at 50mph leave at 12 noon at what time the car catch up with the bus?1 solutions Answer 247752 by mananth(12270)   on 2010-09-22 00:17:52 (Show Source): You can put this solution on YOUR website!Bus 10.30 30mph car 12.00 50mph ... the bus has already traveled 30*1.5 = 45 miles when car starts. the car catches up 50-30 = 20 mph It has to catch up 45 miles 45/20 = 2.25 hours add 2.25 hours to 12.00 .25*60=15 minutes ... it catches up at 2.15 p.m
 Graphs/346520: graph this system: 2x + y > 2 x - y < 11 solutions Answer 247750 by mananth(12270)   on 2010-09-21 23:38:35 (Show Source): You can put this solution on YOUR website!2x + y > 2 y>-2x+2......................1 x - y < 1 add y x-y+y>y+1 x>y+1 add -1 (x-1>y) y Assume an equal to sign instead of < or >. For both the equations find values of y for 3 or more values of x. The red line indicates graph 1 In this equation y > something so all values above the line are solutions. and green line for equation 2. y< something so all points below the graph are solutions
 Geometry_Word_Problems/346515: Find the area of a rectangle that has a base of (4a) cm and a height of (2a b) cm.1 solutions Answer 247749 by mananth(12270)   on 2010-09-21 23:21:35 (Show Source): You can put this solution on YOUR website!Area of triangle = 1/2 * base * height A= 1/2 *4a * 2ab A= 2a*2ab A=4a^2b sq.cm
 Angles/346493: the measure of an angle is 20 degrees less than three times its supplement. find the measure of each angle1 solutions Answer 247731 by mananth(12270)   on 2010-09-21 21:56:33 (Show Source): You can put this solution on YOUR website!let angle be x supplement = 180-x x = 3(180-x)-20 x=540-3x-20 3x+x=540-20 4x=520 x=130 supplement = 50 deg
 Complex_Numbers/346490: 1/a+1/b=c solve for a1 solutions Answer 247730 by mananth(12270)   on 2010-09-21 21:52:10 (Show Source): You can put this solution on YOUR website!1/a+1/b=c 1/a= c - 1/b 1/a= (bc-1)/b take reciprocal a=b/(bc-1)
 Functions/346473: 7/x^2-x-6+5/x-31 solutions Answer 247729 by mananth(12270)   on 2010-09-21 21:49:37 (Show Source): You can put this solution on YOUR website! LCD = (x-3)(x+2)
 test/346481: Easy as it might seem, I have forgotten how to take a simple number and turn it into a decimal. so if I want to turn 392 to the third decimal place what is the easiest way to do this? Thanks :o)1 solutions Answer 247728 by mananth(12270)   on 2010-09-21 21:39:42 (Show Source): You can put this solution on YOUR website!divide by 1000 392/1000 = 0.392 ... 25/100 = 0.25 .. 2/10 = 0.2
 real-numbers/346478: -7-3[2+(5-8)]1 solutions Answer 247727 by mananth(12270)   on 2010-09-21 21:37:44 (Show Source): You can put this solution on YOUR website!_7-3[2+(5-8)] -7-3[2+(-3)] -7-3[2-3] -7-3[-1] -7+3 -4
 Miscellaneous_Word_Problems/346443: a gardener is reseeding a city park that has a shape of a right triangle with a base of 150 ft, height of 200 ft, and 250 ft long a) one bag of grass seed covers 3750 sq ft and cost 27.50 how many bags are needed and what is the total cost? b) wire fencing cost \$23.19 for each 50 ft rl how much does it cost to buy fencing to enclose the area? c) fence posts cost \$3.19 ea & needs to be placed every 5 ft how many posts are needed and what is the cost all together?1 solutions Answer 247722 by mananth(12270)   on 2010-09-21 21:08:42 (Show Source): You can put this solution on YOUR website!a gardener is reseeding a city park that has a shape of a right triangle with a base of 150 ft, height of 200 ft, and 250 ft long a) one bag of grass seed covers 3750 sq ft and cost 27.50 how many bags are needed and what is the total cost? .. Area of triangle = 1/2 *base * height A= 1/2 * 150*200 A= 15000 sq. ft 1 bag 3750 sq.ft 15000 = ? 15000/3750 = 4 bags 1 bag = \$27.50 4 bags = 4*27.50= \$110 .... b) wire fencing cost \$23.19 for each 50 ft rl how much does it cost to buy fencing to enclose the area? Perimeter P = sum of all sides = 150+200+250=600 feet 50 ft = 23.19 600 ft = 600*23.19 wire fensing cost =\$13914 ... c) fence posts cost \$3.19 ea & needs to be placed every 5 ft how many posts are needed and what is the cost all together? Perimeter = 600 feet posts are kept 5ft apart 600/5= 120 posts 1 post = 3.19 120 posts = 119*3.19= \$379.61 Add up all the three
 Travel_Word_Problems/346433: mike and adam left a bus terminal at the same time and traveled in opposite directions. Mike's bus was in heavy traffic and had to travel 20mi/hr slower than adams's bus. After 3 hours their buses were 270 miles apart. How fast was each bus going1 solutions Answer 247717 by mananth(12270)   on 2010-09-21 20:53:46 (Show Source): You can put this solution on YOUR website!let adam's bus speed be x mph mike's bus speed = x-20 mph .. They are going in opposite directions . the effective speed = x+x-20 2x-20 mph. Time = distance /speed distance = 270 miles 3= 270/2x-2 3(2x-2)=270 6x-6=270 6x=276 x=276/6 x=46 mph adam's bus speed mike's bus speed = 46-20 =26 mph
 Linear-systems/346438: the sum of john and harry's ages is 19 years. if the difference of their ages is 5 years,what are their ages?1 solutions Answer 247711 by mananth(12270)   on 2010-09-21 20:48:19 (Show Source): You can put this solution on YOUR website!x+y=19 x-y=5 add the two equations 2x=19+5 2x=24 /2 x=12 y=7
 Rectangles/346436: How do I solve for x when the area of the rectangle is 30 and the length is 3x+1 and the width is x?1 solutions Answer 247706 by mananth(12270)   on 2010-09-21 20:46:10 (Show Source): You can put this solution on YOUR website!Area of rectangle = L*W 30=(3x+1)*x 30=3x^2+x 3x^2+x-30=0 3x^2+10x-9x-90=0 3x(x+10)-9(x+10)=0 (x+10)(3x-9)=0 3(x+10)(x-3)=0 x=3
 Matrices-and-determiminant/346098: I need to find the intersecting points of two equations: y=.15x and y=.2(x-20)and graph them. I have included my problem and what is expected. I'm lost. Ok this is what I got : You would set the two equations equal to each other and solve for x .15x=.2(x-20) using the Elimination Method Reorder the terms: 0.15x = 0.2(-20 + x) 0.15x = (-20 * 0.2 + x * 0.2) 0.15x = (-4 + 0.2x) Solving 0.15x = -4 + 0.2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2x' to each side of the equation. 0.15x + -0.2x = -4 + 0.2x + -0.2x Combine like terms: 0.15x + -0.2x = -0.05x -0.05x = -4 + 0.2x + -0.2x Combine like terms: 0.2x + -0.2x = 0.0 -0.05x = -4 + 0.0 -0.05x = -4 Divide each side by '-0.05'. x = 80 Simplifying x = 80 Now that X = 80, I plugged it into the equation y=0.15x and got this: y=0.15x y=0.15(80) y= 12 Now this is the question to my problem and I do not know how to get the answer. I have to graph this and show the intersection. a teacher is looking for the best option in purchasing school supplies for a classroom. Where Company A is offering a discount for every dollar amount spent on school supplies and where Company B is offering a higher discount than Company A, but the discount for Company B is only offered for every dollar amount spent above \$20.00. I will determine and explain which company will offer a better price based upon the dollar amount the teacher spends on school supplies. Option 1- Company A will offer her a 15% discount on the total amount spent in the store. Option 2- Company B will offer her a 20% discount on the remaining amount after the first \$20 is spent. Depict the situation graphically, using appropriate graphing software such as Excel or an online graphing utility. Include the following in your graph: • A depiction of each cost option on the same graph • Clear labels of the cost to the hypothetical customer for both options on the graph • The intersection of the cost options (if one exists) I'm so lost. I do not know how to graph this. Please help if you can. 1 solutions Answer 247486 by mananth(12270)   on 2010-09-21 10:49:56 (Show Source): You can put this solution on YOUR website!y=0.15x (10,1.5)(20,3)(30,4.5) y=0.2x-4 (20,0)(30,2)(40,4) Your intersection values of (80,12) is correct. for each equation take 3 values of x and calculate y plot the two graphs you will get 2 graphs as above ...
 Percentage-and-ratio-word-problems/346091: if you borrowed money at 15% simple interet after paying it off in one year your finally payoff was \$1199.45 what was the original amount borrowed?1 solutions Answer 247479 by mananth(12270)   on 2010-09-21 10:26:03 (Show Source): You can put this solution on YOUR website!Principal = p rate = 15% = 0.15 I = 1199.55 .... 1199.45 = p*0.15*1 1199.45/0.15 = p p= 7,996.33
 Travel_Word_Problems/346073: The winning sailboat completed a 24-mile race at an average speed of 9 miles/hour. The second-place boat finished with an average speed of 8 miles/hour. How many minutes longer than the winner did the second-place boat take to finish the race ? A 20 min B 33 min C 60 min D 120 min 1 solutions Answer 247450 by mananth(12270)   on 2010-09-21 09:33:58 (Show Source): You can put this solution on YOUR website!time taken by winner = 24/9 hours =2.66 hours time taken by second boat = 24/8 hours =3 hours 3-2.66= 0.0.34 hour ... 0.34 * 60 = 20.4 minutes Option A
 Mixture_Word_Problems/346068: a merchant has coffee worth \$20 a pound that she wishes to mix with 90 pounds of coffee worth \$60 a pound to get a mixture that can be sold for \$30 a pound. How many pounds of the \$20 coffee should be used?1 solutions Answer 247447 by mananth(12270)   on 2010-09-21 09:27:32 (Show Source): You can put this solution on YOUR website!coffee \$20 a pound x lbs 90 pounds of coffee worth \$60 a pound mixture x+90 lbs \$30 a pound. ... 20x+90*60=30(x+90) 20x+5400=30x+2700 30x-20x=5400-2700 10x=2700 /10 x= 2700/10 x= 270 lbs of \$20
 Inequalities/346067: A gas station owner makes a profit of 40 cents per gallon of gas he sells. How many gallons must he sell in order to make a profit of \$30,000? 1 solutions Answer 247440 by mananth(12270)   on 2010-09-21 09:17:39 (Show Source): You can put this solution on YOUR website!let the number of gallons he sells be x he makes a profit of 40 cents per gallon = \$ 0.4 0.4* x = total profit = 30000 x=30000/0.4 x=75000 gallons
 Linear_Equations_And_Systems_Word_Problems/346052: A cyclist leaves his training base for a morning workout, riding at the rate of 20 mph. One hour later, his support staff leaves the base in a car going 36 mph in the same direction. How long will it take the support staff to catch up with the cyclist once the car leaves the base? 1 solutions Answer 247438 by mananth(12270)   on 2010-09-21 09:12:58 (Show Source): You can put this solution on YOUR website!cyclist speed = 20 mph so in 1 hour he is ahead by 20 miles. .. car speed = 36 mph .. the car atches up 36-20 =16 mph they have to catch up 20 miles 20/16 = time to catch up 1.25 hours
 Inequalities/346055: Solve the compound inequality of - 9 < b/8 < 0 and write the solution set in interval notation. 1 solutions Answer 247436 by mananth(12270)   on 2010-09-21 09:09:09 (Show Source): You can put this solution on YOUR website! multiply by 8 .. .. (-72,0)
 Inequalities/346063: A long distance telephone service charges 10 cents for the first minute and 5 cents for each minute thereafter. Write an equation representing the cost C for any call, using x for its length. Using that equation, how many minutes can you talk on the phone if you don’t want the cost to exceed \$5.00? 1 solutions Answer 247431 by mananth(12270)   on 2010-09-21 09:02:27 (Show Source): You can put this solution on YOUR website!x mins duration 5 cents/minute 5x per cal + 10 cents ... C= 5x+10 .... 5x+10<500 cents add -10 5x<500-10 5x<490 /5 5x/5 = 490/5 x<98 minutes
 Miscellaneous_Word_Problems/346018: Water weighs about 62.5 lbs. per cubic foot, and there is about 7.5 gallon in a cubic foot. If a 10-gallon can weighs 16 lbs. when empty, how many cans of water can be hauled in one-ton truck? thank you!1 solutions Answer 247410 by mananth(12270)   on 2010-09-21 05:28:40 (Show Source): You can put this solution on YOUR website!7.5 gallons weigh 62.5 lbs 10 gallons will weigh 62.5 *10/7.5 =83.3 lbs. weight of 10 gallon water + weight of 10 gallon empty can = =83.3 +16 = 99.3 pounds .. 1 ton = 2200 lbs number of cans will be 1 ton/99.3 2000/99.3 = 20.14 OR 20 cans.