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 Money_Word_Problems/758759: A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The trick ski requires 6 labor hours for fabricating and 1 labor hour for finishing. The slalom ski requires 4 labor hours for fabricating and 1 labor hour for finishing. The maximum labor hours available per day for fabricating and finishing are 108 and 24, respectively. If X is the number of trick skis and Y is the number of slalom skis produced per day, write a system of linear inequalities that indicates appropriate restraints on X and Y. Find the set of feasible solutions graphically for the number of each type of ski that can be produced. Please help me with this, I am totally lost. Please expalin the steps so I'll understand how to solve these problems. 1 solutions Answer 461712 by ankor@dixie-net.com(15745)   on 2013-06-17 21:47:48 (Show Source): You can put this solution on YOUR website!company makes two types of water skis, a trick ski and a slalom ski. The trick ski requires 6 labor hours for fabricating and 1 labor hour for finishing. The slalom ski requires 4 labor hours for fabricating and 1 labor hour for finishing. The maximum labor hours available per day for fabricating and finishing are 108 and 24, respectively. If X is the number of trick skis and Y is the number of slalom skis produced per day, write a system of linear inequalities that indicates appropriate restraints on X and Y. Find the set of feasible solutions graphically for the number of each type of ski that can be produced. : Fabricating equation 6x + 4y <= 108 : Finishing equation 1x + 1y <= 24 : since you can make negatives skis x => 0 y => 0 : Find the set of feasible solutions graphically for the number of each type of ski that can be produced. We have to put the equations into the slope/intercept to graph 6x + 4y = 108 4y = -6x + 108 divide by 4 y = -1.5x + 27; Red and x + y = 24 y = -x + 24; Green Graph these two equations The feasibility region is at or below the area bounded by the points x=0, y=24; x=6, y=18; x=18; y=0 : you can prove this to yourself using the fabricating equation 6x + 4y <= 108 x=6 trick skies, y=18 salom skies 6(6) + 4(18) = 36 + 72 = 108 total hrs
 Numeric_Fractions/758705: A wheel makes 12 3/8 revolutions per minute. If it rotates for 68 minutes, how many revolutions does it make?1 solutions Answer 461640 by ankor@dixie-net.com(15745)   on 2013-06-17 11:10:40 (Show Source): You can put this solution on YOUR website!12.375 * 68
 Travel_Word_Problems/758663: Can You Please Help? Here is the question--- A man walked 12km at a certain rate and then 6km farther at a rate of 1 and a half km/hour faster. If he had walked the whole distance at the faster rate, his time would have been 20 minutes less. How long did it really take him to walk the 18km? Thank You for Your Time :D1 solutions Answer 461638 by ankor@dixie-net.com(15745)   on 2013-06-17 11:06:41 (Show Source): You can put this solution on YOUR website!A man walked 12km at a certain rate and then 6km farther at a rate of 1 and a half km/hour faster. If he had walked the whole distance at the faster rate, his time would have been 20 minutes less. How long did it really take him to walk the 18km? : let r = "a certain rate" then (r+1.5) = the faster rate : Change 20 min to hr : Actual time - faster time = 20 min + - = Subtract like terms - = multiply by 3r(r+1.5) 3(r+1.5)(12) - 3r(12) = r(r+1.5) (3r + 4.5)(12) - 36r = r^2 + 1.5r 36r + 54 - 36r = r^2 + 1.5r 0 = r^2 + 1.5r - 54 Use the quadratic formula to find r You can do the math, I got a positive value: r = 6.6366 km/hr : Find the time: t(r) = + t(r) = 1.8 + .74 t(r) = 2.545 hrs : : You can check this by finding the time at the faster rate Should be .333 hrs less
 Travel_Word_Problems/758580: The sanderling is a small shorebird about 6.5 in. long, with a thin, dark bill and a wide, white wing stripe. If a sanderling can fly 30 mi with the wind in the same time it can fly 18 mi against the wind when the wind speed is 8 mph, what is the speed of the bird in still air?1 solutions Answer 461580 by ankor@dixie-net.com(15745)   on 2013-06-16 21:46:01 (Show Source): You can put this solution on YOUR website! If a sanderling can fly 30 mi with the wind in the same time it can fly 18 mi against the wind when the wind speed is 8 mph, what is the speed of the bird in still air? : Let s = bird speed in still air then (s+8) = ground speed of the bird with the wind and (s-8) = ground speed against the wind : Write a time equation; time = dist/speed : = cross multiply 30(s-8) = 18(s+8) 30s - 240 = 18s + 144 30s - 18s = 144 + 240 12s = 384 s = 384/12 s = 32 mph is the speed in still air : : Check this by finding the time of each way, should be equal With: 30/40 = .75 hrs Against: 18/24 = .75 hrs
 Linear-systems/758466: kx+y+z=1 x+ky+z=1 x+y+kz=1 find the value of k1 solutions Answer 461579 by ankor@dixie-net.com(15745)   on 2013-06-16 21:32:47 (Show Source): You can put this solution on YOUR website!kx+y+z=1 kx = 1-y-z k = : x+ky+z=1 ky = 1-x-z k = : x+y+kz=1 kz = 1-x-y k =
 Reduction-of-unit-multipliers/758473: a rectangular lot with a dimension of 5m by 8m is to be fenced and tiled. determine the perimeter fence in terms of yard and number of tiles needed if the owner prefers an 8 in by 8 in tile. i really need your help. please1 solutions Answer 461486 by ankor@dixie-net.com(15745)   on 2013-06-16 07:44:15 (Show Source): You can put this solution on YOUR website!a rectangular lot with a dimension of 5m by 8m is to be fenced and tiled. determine the perimeter fence in terms of yard and number of tiles needed if the owner prefers an 8 in by 8 in tile. : Convert to yards: 1.094 * 5 = 5.47 1.094 * 8 = 8.752 then 2(5.47) * 2(8.752) = 28.444 yds is the perimeter, (28 yds 16 inches) : Find the area in square inches 5.47 * 8.752 * 36 * 36 = 62044 sq/inches : Each tile is 8*8 = 64 sq/inches therefore 62044/64 = approx 970 tiles required
 Word_Problems_With_Coins/758336: a student has 55 coins worth a total of \$7.35. each coin is either a nickel or a quarter. of x is the number of nickels, then x can be determined for the equation1 solutions Answer 461472 by ankor@dixie-net.com(15745)   on 2013-06-15 21:53:56 (Show Source): You can put this solution on YOUR website!a student has 55 coins worth a total of \$7.35. each coin is either a nickel or a quarter. If x is the number of nickels, then x can be determined for the equation : Let x = no. of nickels total coins is 55, therefore (55-x) = no. quarters : .05x + .25(55-x) = 7.35 .05x + 13.75 - .25x = 7.35 .05x - .25x = 7.35 - 13.75 -.20x = -6.40 x = -6.4/-.2 x = +32 nickels : : See if this checks out: 55-32 = 23 quarters .05(32) = 1.60 .25(23) = 5.75 ----------------- total\$ = 7.35
 Quadratic-relations-and-conic-sections/758377: A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 196 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center. 1 solutions Answer 461462 by ankor@dixie-net.com(15745)   on 2013-06-15 21:09:54 (Show Source): You can put this solution on YOUR website!A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 196 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center. : Let the left side of the arch be at origin (0,0) then axis of symmetry and max will be at x=98, y=30 and the right side: x=196,y=0 Using the form ax^2 + bx + c = y; c=0 so we can ignore that x=98, y= 30 98^2a + 98b = 30 9604a + 98b = 30 and x=196, y=0 196^2a + 196b = 0 38416a + 196b = 0 : Multiply the 1st equation by 2, subtract from the above equation 38416a + 196b = 0 19208a + 196b = 60 -------------------subtraction eliminate b, find a 19208a = -60 a = -60/19208 a = -.0031237 : Find b using the 1st equation 9604(-.0031237) + 98b = 30 -30 + 98b = 30 98b = 30 + 30 98b = 60 b = 60/98 b = .612 : The equation for the arch: y = -.0031237x^2 + .612x : Graphically : Find the height of the arch at 15 feet from its center. (Green line) You can do this replace x with 83 and find y (height) Do the same with x = 113
 Linear-equations/758341: I have an algebra problem. What it is is a letter from a basic math student and I need to come up with the equation and the answer then be able to explain it to them in a simple way they can understand. Here is the basic math students question.. During his shift at the school carnival he sold 112 drinks. He thought he only needed to keep track of the total amount of drinks sold, but it turns out they want to know how many bottles of water and how many bottles of soda were sold as separate numbers. The question is: If the number of bottles of water sold was 4 less than 3 times the number of bottles of soda, how many of each did he sell ? I have to figure out the answer ( how many water and how many sodas) explain how i set up the equation and solved it. So in case the situation happens again they could answer the question. 1 solutions Answer 461439 by ankor@dixie-net.com(15745)   on 2013-06-15 17:23:21 (Show Source): You can put this solution on YOUR website!During his shift at the school carnival he sold 112 drinks. He thought he only needed to keep track of the total amount of drinks sold, but it turns out they want to know how many bottles of water and how many bottles of soda were sold as separate numbers. The question is: If the number of bottles of water sold was 4 less than 3 times the number of bottles of soda, how many of each did he sell? : Let w = no. of bottles of water sold Let s = no. of bottles of soda : Total sold equation w + s = 112 w = (112-s); use this for substitution : "the number of bottles of water sold was 4 less than 3 times the number of bottles of soda," w = 3s - 4 A big mistake here. Let me correct this Replace w with (112-s) 112-s = 3s - 4 112 + 4 = 3s + s 116 = 4s s = 116/4 s = 29 sodas then w = 112 - 29 w = 83 waters sold : See if that checks out in the statement: "the number of bottles of water sold was 4 less than 3 times the number of bottles of soda, 83 = 3(29) - 4 83 = 87 - 4
 Geometry_Word_Problems/758127: twice the first angle is 20 deg less than the third, 1/2 of the third is 60 deg less than the sum of the 1st and 2nd angles.find the angles1 solutions Answer 461428 by ankor@dixie-net.com(15745)   on 2013-06-15 16:55:42 (Show Source): You can put this solution on YOUR website!Three angles, A,B,C; Just write an equation for what it says. : twice the first angle is 20 deg less than the third, 2A = C-20 or C = 2A+20 : 1/2 of the third is 60 deg less than the sum of the 1st and 2nd angles. .5C = A + B - 60 multiply both sides by 2 C = 2A + 2B - 120 therefore 2A+20 = A + B - 60 2A - A = B - 60 - 20 A = B-80 or B = A+80 : And assuming this is a triangle A + B + C = 180 replace B with (A+80); replace C with (2A+20) A + A+80) + 2a+20 = 180 4A + 100 = 180 4A = 180 - 100 4A = 80 Divide both sides by 4 A = 20 degrees then B = 20 + 80 B = 100 degrees and C = 2(20)+20 C = 60 degrees : 20 + 100 + 60 = 180; confirms our solutions
 Linear_Equations_And_Systems_Word_Problems/758328: A number consists of two digits. The digit in the unit's place is less than the digit in the ten's place by 2. If the number is subtracted from 11times the sum of the digits then the digits are reversed. Find the number.1 solutions Answer 461422 by ankor@dixie-net.com(15745)   on 2013-06-15 16:27:02 (Show Source): You can put this solution on YOUR website!A number consists of two digits. 10a + b : The digit in the unit's place is less than the digit in the ten's place by 2. b = a-2 : If the number is subtracted from 11 times the sum of the digits, then the digits are reversed. 11(a+b) - (10a+b) = 10b + a 11a + 11b - 10a - b = 10b + a combine the like terms on the left 11a - 10a - a + 11b - b - 10b = 0 and you get 0! So that's not very helpful, just choose a number 97 is good one 11(9+7) - 97 = 79 or how about 64 11(6+4) - 64 = 46 or 75 11(7+5) - 75 = 57 Take your pick
 Polynomials-and-rational-expressions/758165: find the value of 1/(root3-root2-1) correct upto 3 decimals if root2=1.414 and root6=2.45.1 solutions Answer 461323 by ankor@dixie-net.com(15745)   on 2013-06-14 22:03:42 (Show Source): You can put this solution on YOUR website!find the value of correct up to 3 decimals if and We know the square root of 3 = square root of 6/ sqrt of 2 therefore = = = -1.468
 logarithm/758160: What does x equal when 7e^5x+3 = 4900.1 solutions Answer 461317 by ankor@dixie-net.com(15745)   on 2013-06-14 21:42:03 (Show Source): You can put this solution on YOUR website!What does x equal when assume it's divide both sides by 7 find the nat log of both sides, ln of e is 1 therefore 5x + 3 = 6.55108 5x = 6.55108 - 3 5x = 3.55108 x = x ~ .710216 : : Check this for yourself on your calc enter: 7*e^(5(.710216)+3)
 Age_Word_Problems/758092: the sum of the ages of the parents and the three children is decades over a century. The father is twice as old as the eldest child. When the eldest child was born, the sum of the parents age is 54. When the youngest child was born, the sum of the parents age was 70. In 38 years, the sum of the parents ages will be equal to the sum of the childrens ages. How old is the second child? 1 solutions Answer 461316 by ankor@dixie-net.com(15745)   on 2013-06-14 21:29:18 (Show Source): You can put this solution on YOUR website!the sum of the ages of the parents and the three children is decades over a century. : f, m, a, b, c; (a is the oldest child) The father is twice as old as the eldest child. f = 2a : When the eldest child was born, the sum of the parents age is 54. (f-a) + (m-a) = 54, f + m - 2a = 54 we know that f = 2a 2a + m - 2a = 54 m = 54 is mom's age : When the youngest child was born, the sum of the parents age was 70. (f-c) + (m-c) = 70, f + m - 2c = 70 : Use elimination with these two equations f + m - 2c = 70 f + m - 2a = 54 ---------------subtraction eliminates f and m +2a - 2c = 16 simplify a - c = 8 or c = a - 8 : In 38 years, the sum of the parents ages will be equal to the sum of the children's ages. (f+38) + (m+38) = (a+38) + (b+38) + (c+38) combine the values f + m + 76 = a + b + c + 114 subtract 76 from both sides f + m = a + b + c + 38 Replace f with 2a 2a + m = a + b + c + 38 subtract a from both sides and we have a + m = b + c + 38 replace c with (a-8) a + m = b + a - 8 + 38 subtract a from both sides m = b + 30 We know that mom is 54 54 = b + 30 b = 54 - 30 b = 24 is the 2nd child's age : : : Check this mess out by assuming the total of their present ages is an even 10 (a decade) over 100 and a=30 f = 60 (2a) m = 54 a = 30 b = 24 (m-30) c = 22 (a-8) ------- tot: 190
 Travel_Word_Problems/758091: A car traveling at 70 kilometers per hour is passed by a second car going in the same direction at a constant speed. After 30 seconds, the two cars are 500 meters apart. Find the speed of the second car.1 solutions Answer 461266 by ankor@dixie-net.com(15745)   on 2013-06-14 15:35:06 (Show Source): You can put this solution on YOUR website!A car traveling at 70 kilometers per hour is passed by a second car going in the same direction at a constant speed. After 30 seconds, the two cars are 500 meters apart. Find the speed of the second car. : let s = speed of the passing car : We're working km/hr: change 500 m to km change 30 sec to hrs : Write a distance equation; dist = speed * time : Passing car dist - 70 km/hr car dist = 500 meters s - (70) = multiply eq by 120 to cancel the denominators, results: 1s - 1(70) = 120* s - 70 = 60 s = 60 + 70 s = 130 km/hr speed of the passing car ; : Confirm this by finding the distance each car traveled *130 = 1.08 km * 70 = .58 km ------------------------- difference in dist: .5 km which is 500 m
 Travel_Word_Problems/758088: The cruising speed of an airlines is 150 miles per hour (relative to the ground). you wish to hire the plane for 3 hour sightseeing trip. You instruct the pilot to fly north as far as he can and still return to the airport at the end of the allotted time. how far north should the pilot fly if the wind is blowing far from the north at 30 miles per hour.1 solutions Answer 461265 by ankor@dixie-net.com(15745)   on 2013-06-14 14:01:53 (Show Source): You can put this solution on YOUR website!The cruising speed of an airlines is 150 miles per hour (relative to the ground). you wish to hire the plane for 3 hour sightseeing trip. You instruct the pilot to fly north as far as he can and still return to the airport at the end of the allotted time. how far north should the pilot fly if the wind is blowing from the north at 30 miles per hour. : Let d = one way distance to point of return we know 150 - 30 = 120 mph, ground speed going north and 150 + 30 = 180 mph, ground speed going south : Write a time equation; time = dist/speed : time north + time back = 3 hrs + = 3 multiply by 360 to cancel the denominators, results: 3d + 3d = 360(3) 5d = 1080 d = 1080/5 d = 216 miles to return point ; : Check this by finding the actual times: 216/120 = 1.8 hrs 216/180 = 1.2 hrs ------------------ total time: 3 hrs
 Miscellaneous_Word_Problems/758061: The ratio of the weight of an object on Mars to the weight of an object on Earth is 0.4 to 1. A- How much will a 7 ton rocket weigh on Mars? B- How much will a 132 lb astronaut weigh on Mars? A: A 7 ton rocket will weigh ____ ton on Mars. (round to the nearest tenth) 1 solutions Answer 461209 by ankor@dixie-net.com(15745)   on 2013-06-13 21:57:47 (Show Source): You can put this solution on YOUR website!The ratio of the weight of an object on Mars to the weight of an object on Earth is 0.4 to 1. A- How much will a 7 ton rocket weigh on Mars? = Cross multiply r = .4(7) r = 2.8 tons on Mars : B- How much will a 132 lb astronaut weigh on Mars? = a = 132 * .4 a = 52.8 lb
 Polynomials-and-rational-expressions/758012: How do I work this problem? Please help. ( u-v/8v) + (6u - 3v/ 8v) 1 solutions Answer 461204 by ankor@dixie-net.com(15745)   on 2013-06-13 20:50:52 (Show Source): You can put this solution on YOUR website!How do I work this problem? Please help. I assume it is: + Each fraction has the same denominator so we can write it combine like terms
 Rate-of-work-word-problems/758019: Tina can completely weed her vegetable garden in 1hr and 30 min. Her friend marisa can do the same in 2 hrs. if they worked together, how long would it take? I'm not sure what steps to go about using to complete this. I thought it might be done by using a system of equations but I think I would need more information in order to solve that.1 solutions Answer 461187 by ankor@dixie-net.com(15745)   on 2013-06-13 20:00:47 (Show Source): You can put this solution on YOUR website!Tina can completely weed her vegetable garden in 1hr and 30 min. Her friend marisa can do the same in 2 hrs. if they worked together, how long would it take? : Let t = the time required when working together (in hrs) Let the completed job = 1 : Each will do a fraction of the job, the two fractions add up to 1 : + = 1 multiply by 6 to get rid of the denominators, results 4t + 3t = 6 7t = 6 t = 6/7 hrs, or converted to minutes: 6/7 * 60 = 51.4 minutes : :
 Bodies-in-space/757981: Suppose three spherical balls of wax with radius r are packed in a cylinder also with radius r and the balls are melted down. To what depth will the cylinder be filled. The answer needs to be in terms of r. I am totally stumped. Thank you1 solutions Answer 461184 by ankor@dixie-net.com(15745)   on 2013-06-13 19:41:45 (Show Source): You can put this solution on YOUR website!Suppose three spherical balls of wax with radius r are packed in a cylinder also with radius r and the balls are melted down. To what depth will the cylinder be filled. The answer needs to be in terms of r. : Find the vol of the three balls in terms of r V(r) = 3 * * Cancel the 3 V(r) = cu/units is the volume of the wax : let d = the depth of the wax in the cylinder when melted = divide both sides by d = 4r units is the depth
 test/758039: Show me how to solve e/2+7=4e1 solutions Answer 461183 by ankor@dixie-net.com(15745)   on 2013-06-13 19:31:42 (Show Source): You can put this solution on YOUR website!solve + 7 = 4e multiply both sides by 2 e + 14 = 8e 14 = 8e - e 14 = 7e e = 14/7 e = 2
 test/757661: A and B are two cars . they start to move with constant speed from the same spot at the same time . car A moves toward the east with speed 8 km/h . car B moves toward north with speed Vb . after 2 hours the distance between the two cars is 200 km . find Vb ?!1 solutions Answer 461051 by ankor@dixie-net.com(15745)   on 2013-06-12 20:50:01 (Show Source): You can put this solution on YOUR website!A and B are two cars . they start to move with constant speed from the same spot at the same time . car A moves toward the east with speed 8 km/h . car B moves toward north with speed Vb . after 2 hours the distance between the two cars is 200 km . find Vb ?! : Dist = speed * time 2(8) = 16 km traveled by Car A 2Vb km traveled by car B : The is a pythag type problem; a^2 + b^2 = c^2, where: a = 16 b = 2Vb c = 200 therefore: 16^2 + (2Vb)^2 = 200^2 256 + 4Vb^2 = 40000 4Vb^2 = 40000 - 256 4Vb^2 = 39744 Vb^2 = 39744/4 Vb^2 = 9936 Vb = Vb = 99.68 km/hr ; : I'll let you check this: Car B travels 2*99.68 = 199.36 km Use your calc enter:
 Travel_Word_Problems/757518: A 500 yard long train, travelling at 90 mph, enters a three mile long tunnel. How many seconds will elapse between the movement the front of the train enters the tunnel and the moment the end of the train clears the tunnel?1 solutions Answer 461033 by ankor@dixie-net.com(15745)   on 2013-06-12 20:02:25 (Show Source): You can put this solution on YOUR website!A 500 yard long train, travelling at 90 mph, enters a three mile long tunnel. How many seconds will elapse between the movement the front of the train enters the tunnel and the moment the end of the train clears the tunnel? : Convert 500 yds to miles: = .284 mi : * 3600 = 131.36 seconds
 Travel_Word_Problems/757322: Ron and pat leaves for the beach at the same point. Ron leaves first pat leaves 45 mins later traveling 10 mph faster then Ron. pat passes ron 4 hours later. find the rate of each driver.1 solutions Answer 461027 by ankor@dixie-net.com(15745)   on 2013-06-12 19:51:49 (Show Source): You can put this solution on YOUR website!Ron and pat leaves for the beach at the same point. Ron leaves first, Pat leaves 45 mins later traveling 10 mph faster than Ron. Pat passes Ron 4 hours later. find the rate of each driver. : Since we a dealing in hrs here, convert 45 min to .75 hrs : From the information given, we know P's travel time = 4 hrs R's travel time = 4.75 hrs : let s = R's rate then (s+10) = P's rate : When P catches R, they will have traveled the same distance. Write a distance equation; Dist = time * speed : R's dist = P's dist 4.75s = 4(s+10) 4.75s = 4s + 40 4.75s - 4s = 40 .75s = 40 s = 40/.75 s = 53 mph is R's rate then 53 + 10 = 63 mph is P's rate : : You can check this out for yourself, determine the distance each traveled, should be the same. (dist = rate * time)
 Travel_Word_Problems/757565: A started walking in north at 7 am with the speed of 5 km/hr. after one hour B started towards east on a cycle with the speed of 16 km/hr. at what time the distance between them will be 52 km?1 solutions Answer 460978 by ankor@dixie-net.com(15745)   on 2013-06-12 17:11:17 (Show Source): You can put this solution on YOUR website!A started walking in north at 7 am with the speed of 5 km/hr. after one hour B started towards east on a cycle with the speed of 16 km/hr. at what time the distance between them will be 52 km? : Let t = travel time of the bike then (t+1) = walking time : dist = speed * time : This is a pythag problem: a^2 + b^2 = c^2, where a = 16t, bike dist b = 5(t+1), walking dist c = 52, dist apart in t hrs from 8 AM : (16t)^2 + (5(t+1)^2 = 52^2 256t^2 + (5t+5)^2 = 2704 256t^2 + 25t^2 + 50t + 25 = 2704 281t^2 + 50t + 25 - 2704 = 0 281t^2 + 50t - 2679 = 0 solve this equation using the quadratic formula Positive solution t = 3 hrs At 11 AM they will be 52 km apart
 Permutations/757600: Two persons are to run a race, but one can run 11 meters per second, whereas the other can run 7 meters per second. If the slower runner has a 42-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?1 solutions Answer 460947 by ankor@dixie-net.com(15745)   on 2013-06-12 14:25:38 (Show Source): You can put this solution on YOUR website!Two persons are to run a race, but one can run 11 meters per second, whereas the other can run 7 meters per second. If the slower runner has a 42-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time? : We can us relative speed here which is 11 - 7 = 4 m/sec How long would it take to cover 42 meters at this speed : = 10.5 sec : : You can confirm this for yourself, find the distance traveded 10.5 * 11 = 115.5 m 10.5 * 7 = 73.5 m -------------------- the difference: 42 m
 Linear_Equations_And_Systems_Word_Problems/757539: A couple of girls go for a horse race clockwise around the outside of a rectangular field. The rectangular field has 'a' as the shortest side and 'b' as the long side of a rectangle. Mary runs all around the field for a total of 20km. Annabelle only gets half way along the first side marked with 'b' before cutting straight across the field, before heading back to the start. She in total rides for 16 km. What are the dimensions of the field?1 solutions Answer 460889 by ankor@dixie-net.com(15745)   on 2013-06-12 08:24:59 (Show Source): You can put this solution on YOUR website!A horse race clockwise around the outside of a rectangular field. The rectangular field has 'a' as the shortest side and 'b' as the long side of a rectangle. Mary runs all around the field for a total of 20km. Annabelle only gets half way along the first side marked with 'b' before cutting straight across the field, before heading back to the start. She in total rides for 16 km. What are the dimensions of the field? : Mary's perimeter 2a + 2b = 20 Simplify, divide by 2 a + b = 10 : Anna's perimeter 2a + 2(.5b) = 16 simplify, divide by 2 a + .5b = 8 : Using eliminatation a + b = 10 a +.5b = 8 ------------ subtracting eliminates a, find b 0 + .5b = 2 b = 4; (multiplied by 2) then a + 4 = 10 a = 6; (subtracted 4 from both sides) : 4 by 6 is the dimensions
 Exponents/757358: what is x to the seventh power divided by x to the negative second power? The book says the answer is x to the ninth power but how?1 solutions Answer 460811 by ankor@dixie-net.com(15745)   on 2013-06-11 21:22:23 (Show Source): You can put this solution on YOUR website!what is x to the seventh power divided by x to the negative second power? The book says the answer is x to the ninth power but how? : remember you can get rid of the negative exponent by writing the reciprocal, therefore * or just add exponents when you multiply
 Systems-of-equations/757264: Which of these images represents the following system of equations being solved graphically? -2x + 2y = 8 -4x - 6y = -4 1 solutions Answer 460763 by ankor@dixie-net.com(15745)   on 2013-06-11 16:29:50 (Show Source): You can put this solution on YOUR website!Which of these images represents the following system of equations being solved graphically? : Put both equations into the slope/intercept form -2x + 2y = 8 2y = 2x + 8 Divide by 2 y = x + 4, the first equation and -4x - 6y = -4 -6y = 4x - 4 divide -6 y = -x + reduce fractions y = -x + : Plot these two equations solution: -2, 2
 Money_Word_Problems/757291: I am offered a job that pays \$12/hr for 40 hrs a week. I want to rent an apartment with two other friends that requires a year-long lease. Bills and expenses will cost me \$300 per month. I am also making monthly payments on a car in the amount of \$1, 521. If I accept the job, what is the maximum rent I can pay for the apartment?1 solutions Answer 460760 by ankor@dixie-net.com(15745)   on 2013-06-11 15:24:16 (Show Source): You can put this solution on YOUR website!I am offered a job that pays \$12/hr for 40 hrs a week. I want to rent an apartment with two other friends that requires a year-long lease. Bills and expenses will cost me \$300 per month. I am also making monthly payments on a car in the amount of \$1, 521. If I accept the job, what is the maximum rent I can pay for the apartment? : (40*4*12) - 300 - 1521 = \$99 for rent
 Human-and-algebraic-language/757309: translate into language of algebra twelve less than a number x is less than or equal to twenty-eight1 solutions Answer 460752 by ankor@dixie-net.com(15745)   on 2013-06-11 14:48:13 (Show Source): You can put this solution on YOUR website! translate into language of algebra twelve less than a number x is less than or equal to twenty-eight : just write what it says, the word "is" usually means equal "=" x - 12 <= 28