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 Miscellaneous_Word_Problems/235797: A lot is in the shape of a right triangle. The shorter leg measures 60 meters. The hypotenuse is 20 meters longer than the length of the longer leg. How long is the longer leg help Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. i know that the 5 steps of problem, solving process is to familiarize translate carry out check and state but i am not sure what order i start with to do the formula. the 1 solutions Answer 173791 by ankor@dixie-net.com(15660)   on 2009-11-06 21:16:34 (Show Source): You can put this solution on YOUR website!A lot is in the shape of a right triangle. The shorter leg measures 60 meters. The hypotenuse is 20 meters longer than the length of the longer leg. How long is the longer leg : Let x = the longer leg then (x+20) = the hypotenuse : 60^2 + x^2 = (x+20)^2 : FOIL the right side 3600 + x^2 = x^2 + 40x + 400 : Group the x's on the left, numbers on the right x^2 - x^2 - 40x = 400 - 3600 : -40x = -3200 Multiply both sides by -1 40x = 3200 : divide both sides by 40 x = x = 80 meters is the longer leg ; : Check: hypotenuse = 80 + 20 = 100 60^2 + 80^2 = 100^2
 Travel_Word_Problems/236033: Care one travels from point a to c (244 miles). Car two travels at 60 mph from point a to b(140 miles)and 50 mph from b to c (200 miles). If both cars arrive at point c at the same time, how fast did car one drive?1 solutions Answer 173788 by ankor@dixie-net.com(15660)   on 2009-11-06 20:58:19 (Show Source): You can put this solution on YOUR website!Care one travels from point a to c (244 miles). Car two travels at 60 mph from point a to b(140 miles)and 50 mph from b to c (200 miles). If both cars arrive at point c at the same time, how fast did car one drive? : Find the time required for car two to go a to b to c Time = dist/speed : total time = time at 60mph + time at 50mph t = + t = 2.33 + 4 t = 6.33 hrs : Find the speed of car one to drive 244 mi in 6.33 hrs s = s = 38.5 mph speed of car one
 Polynomials-and-rational-expressions/236011: Use the FOIL method to find the product: (5x^8-3)(x^9-9) Is the answer 5x^17 + 3x +27 1 solutions Answer 173784 by ankor@dixie-net.com(15660)   on 2009-11-06 20:40:06 (Show Source): You can put this solution on YOUR website!Use the FOIL method to find the product: (5x^8 - 3)(x^9 - 9) I think it would be 5x^17 - 45x^8 - 3x^9 + 27
 Finance/235985: in 1995 the life span of males in a certain country was 64.7 years. in 2001 it was 66.7 years. Let E represent the life span in year t represent the number of years since 1995. E(t)=____t+____ E(11)= 1 solutions Answer 173782 by ankor@dixie-net.com(15660)   on 2009-11-06 20:35:12 (Show Source): You can put this solution on YOUR website!in 1995 the life span of males in a certain country was 64.7 years. in 2001 it was 66.7 years. Let E represent the life span in year t represent the number of years since 1995. : Find the slope In 1995; x1=0 and y1=64.7 In 2001; x2=6 and y2=66.7 : Find the slope (m) using the slope equation: m = m = = = therefore: The Linear function E(t) that fits the data is. E(t)= t + 64.7 : E(11)= (11) + 64.7 E(11)= 3.67 + 64.7 E(11)= 68.4 yrs is the life expectancy in 2006
 Miscellaneous_Word_Problems/236021: Sally is building a box with a square base for her ant colony. The bottom of the box and all four sides are con- structed of glass costing \$1/ft2, and the top is to be con- structed of glass costing \$5/ft2. Sally has \$72 to spend on the box. How should she choose the dimensions so that the volume of the box is greatest?1 solutions Answer 173779 by ankor@dixie-net.com(15660)   on 2009-11-06 20:19:07 (Show Source): You can put this solution on YOUR website! The bottom of the box and all four sides are constructed of glass costing \$1/ft2, and the top is to be constructed of glass costing \$5/ft2. Sally has \$72 to spend on the box. How should she choose the dimensions so that the volume of the box is greatest? : Let x = the side of the square base and top Let h = height of the box 5 of the sides cost \$1 a sq/ft Top cost 5x^2 : We need to get h in terms of x : Top + bottom + 4 sides = 72 5x^2 + x^2 + 4(xh) = 72 6x^2 + 4(xh) = 72 4xh = 72 - 6x^2 h = Simplify h = : Find the volume: V = x^2*h replace h V = x^2* Cancel x V = x* V = Write the equation as: -1.5x^3 + 18x = 0 : Graph this Max volume when x=2 : find h, when x=2 h = h = h = h = 6 ; A box: 2 * 2 * 6 = 24 cu (as seen on the graph) ; Check the cost; Top + bottom + 4 sides = \$72 5(4) + 4 + 4(2*6) = 20 + 4 + 48 = \$72
 Expressions-with-variables/236018: how do i write 35 less than half of a number is the same as three times the number. what is the number? 1 solutions Answer 173770 by ankor@dixie-net.com(15660)   on 2009-11-06 19:02:06 (Show Source): You can put this solution on YOUR website!how do i write 35 less than half of a number is the same as three times the number. How about .5x - 35 = 3x?
 Linear-systems/235355: The sum of the digits of a 2-digit number is 8. When 36 is added to the number, the digits are reversed. What would be the number?1 solutions Answer 173769 by ankor@dixie-net.com(15660)   on 2009-11-06 18:58:40 (Show Source): You can put this solution on YOUR website!Let x = the 10's digit Let y = the units : 10x + y = the two digit number : The sum of the digits of a 2-digit number is 8. x + y = 8 y = (8-x) : When 36 is added to the number, the digits are reversed. 10x + y + 36 = 10y + x 10x - x = 10y - y - 36 9x = 9y - 36 Simplify, divide by 9: x = y - 4 : What would be the number? replace y with (8-x) x = (8-x) - 4 x + x = 8 -4 2x = 4 x = 2 then y = 8 - x y = 8 - 2 y = 6 : 26 is the number : : Check solution 26 + 36 = 62
 Numbers_Word_Problems/235995: the Quotent of the number and 3 is the same as the difference of the number and 2. Find the the number1 solutions Answer 173768 by ankor@dixie-net.com(15660)   on 2009-11-06 18:49:51 (Show Source): You can put this solution on YOUR website!the Quotient of the number and 3 is the same as the difference of the number and 2. Find the the number ; = x - 2 : x = 3(x - 2) : x = 3x - 6 ; 6 = 3x - x : 6 = 2x : x = 3 : : Check = 3 - 2
 Miscellaneous_Word_Problems/235882: The Body Mass Index,I,can be used to determine an individual's risk for heart disease. An index below 25 indicates a low risk. The body mass index is given by the formula I=700W ------ H^2 where W=weight in pounds, and H=height in inches. Jerome is 70 inches tall. What weight will keep his body mass index between 20 and 28? Jerome's body mass index will fall between 20 and 28 for the set of all weights such that ? I can't seem to figure out how to do this problem without a weight given....1 solutions Answer 173761 by ankor@dixie-net.com(15660)   on 2009-11-06 18:22:44 (Show Source): You can put this solution on YOUR website!The Body Mass Index,I,can be used to determine an individual's risk for heart disease. An index below 25 indicates a low risk. The body mass index is given by the formula: I = where: W=weight in pounds, and H=height in inches. ; Jerome is 70 inches tall. What weight will keep his body mass index between 20 and 28? : Use an index of 24, for a height of 70, find w 24 = : 24 = : 24 * 4900 = 700W : 117600 = 700W W = W = 168 lb should have an index of 24 ; : Check on calc: enter (700*168)/70^2 = 24
 Trigonometry-basics/235403: A carpenter charges a set fee for each job in addition to his hourly charge. If a carpenter bills his customer \$125 for a job which takes him 3 hours and bills a second customer \$200 for a 6 hour job, how much would he charge for a job that takes 8 hours?1 solutions Answer 173759 by ankor@dixie-net.com(15660)   on 2009-11-06 18:08:28 (Show Source): You can put this solution on YOUR website!A carpenter charges a set fee for each job in addition to his hourly charge. If a carpenter bills his customer \$125 for a job which takes him 3 hours and bills a second customer \$200 for a 6 hour job, : Let f = fixed fee Let h = hourly rate : Two equations: 3h + f = 125; "\$125 for a job which takes him 3 hours" 6h + f = 200; "\$200 for a 6 hr job" : Subtract the 1st equation from the 2nd equation 6h + f = 200 3h + f = 125 --------------- eliminates f, find h 3h = 75 h = \$25 an hr ; Find f in the 1st equation 3(25) + f = 125 f = 125 - 75 f = \$50 set fee : : Check solution in the 2nd equation 6(25) + 50 = 200 150 + 50 = 200 : how much would he charge for a job that takes 8 hours? 8(25) + 50 = \$250
 Numbers_Word_Problems/235800: The problem is one number is 2 more then 5 times another number their sum is 24. what are the number. I need the steps on how to solve the problem 1 solutions Answer 173744 by ankor@dixie-net.com(15660)   on 2009-11-06 16:44:18 (Show Source): You can put this solution on YOUR website!Let x= " a number" Let y = "another number" : Write an equation for what it says (the word "is" usually means =: : "one number is 2 more then 5 times another number" their sum is 24." x = 5y + 2 : "their sum is 24" x + y = 24 x = (24-y); this form for substitution : what are the numbers? : Substitute (24-y) for x in the 1st equation 24 - y = 5y + 2 : 24 - 2 = 5y + y : 22 = 6y y = = y = 3 : Find x x = 5y + 2 x = 5() + 2 x = + 2 x = 18 + 2 x = 20 : : Check by finding the sum: 20 + 3 = 24
 Systems-of-equations/235957: Day 1 drive 40 miles per hour and arrive one minute late. Day 2 drive 45 miles per hour and arrive one minute early. How far do you drive to work? I know the answer is 12 miles, but how do you set up the problem?1 solutions Answer 173737 by ankor@dixie-net.com(15660)   on 2009-11-06 15:42:41 (Show Source): You can put this solution on YOUR website!Here is yet another way, perhaps simpler. Day 1 drive 40 miles per hour and arrive one minute late. Day 2 drive 45 miles per hour and arrive one minute early. How far do you drive to work : Let t = time to drive to work at 45 mph then (t+) = time to work at 40 mph (takes 2 min longer) which is (t+) ; The distance both days is the same, write a dist equation d = speed * time : day 1 dist = day 2 dist 40(t+) = 45t : 40t + = 45t = 45t - 40t 5t = t = * t = hr : Find the dist 45 * = 12 mi
 Travel_Word_Problems/235389: I had a flat tire after biking 3/4 of the way home. I walked the rest of the way home. if my walking time was twice my biking time, how many times faster is my biking speed than my walking speed ? a) 6 b) 5 c) 4 d) 3 e) 21 solutions Answer 173727 by ankor@dixie-net.com(15660)   on 2009-11-06 15:06:50 (Show Source): You can put this solution on YOUR website!had a flat tire after biking 3/4 of the way home. I walked the rest of the way home. if my walking time was twice my biking time, how many times faster is my biking speed than my walking speed? : Let w = walking speed Let b = biking speed Let d = distance to his home : Write a time equation, Time = dist/speed : Walking time = twice biking time () = 2() : () = () divide both sides by d () = () cross multiply 1.5w = .25b multiply both sides 4 6w = 1b or b = 6w : Biking speed is 6 times walking speed ; : Is this really true? check equation if walking speed is 3 mph & biking speed is 18 mph and dist = 12 mi, then: 1/4 = 3 mi; and 3/4 = 9 mi : walk time = twice ride time = 2() 1 = 1
 Complex_Numbers/235440: I am having problem with this problem complex simplifying fraction. 2x-4/xy^2/3x-6y/x^3y 1 solutions Answer 173705 by ankor@dixie-net.com(15660)   on 2009-11-06 13:25:28 (Show Source): You can put this solution on YOUR website!Assume the problem is: ------------ : Invert the dividing fraction and multiply * ; Factor and cancel the xy's * = ;
 Linear_Equations_And_Systems_Word_Problems/235911: Velocity of a bullet. A gun is fired straight upward. The bullet leaves the gun at 100 feet per second (time t 0). After 2 seconds the velocity of the bullet is 36 feet per second. There is a linear equation that gives the velocity v in terms of the time t. Find the equation and find the velocity after 3 seconds.1 solutions Answer 173702 by ankor@dixie-net.com(15660)   on 2009-11-06 13:02:16 (Show Source): You can put this solution on YOUR website!Velocity of a bullet. A gun is fired straight upward. The bullet leaves the gun at 100 feet per second (time t 0). After 2 seconds the velocity of the bullet is 36 feet per second. There is a linear equation that gives the velocity v in terms of the time t. Find the equation and find the velocity after 3 seconds. ; Assign the given values as follows x1=0 y1=100 x2=2 y2=36 ; find the slope: m = = -32 ft/sec : y - y1 = m(x-x1) y - 100 = -32(x - 0) y = -32x + 100; V(t) = -32t + 100; the equation : after 3 sec, (t=3) V = -32(3) + 100 V = -96 + 100 V = 4 ft/sec
 Polynomials-and-rational-expressions/235917: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coeffcient of x^3. The coeffcient of x is three times the coeffcient of x^2. The remaining coeffcient is 2 more than the coeffcient of x^3. The sum of the coeffcients is -4. Find the polynomial.1 solutions Answer 173699 by ankor@dixie-net.com(15660)   on 2009-11-06 12:48:06 (Show Source): You can put this solution on YOUR website! polynomial in x has degree 3. (ax^3 + bx^2 + cx + d) Let coefficient of x^3 = a ; The coefficient of x^2 is 3 less than the coeffcient of x^3. b = (a-3) : The coefficient of x is three times the coefficient of x^2. c = 3b we want everything in terms of a, replace b with (a-3) c = 3(a-3) c = (3a - 9) : The remaining coefficient is 2 more than the coefficient of x^3. d = (a+2) : The sum of the coefficients is -4. Find the polynomial. a + b + c + d = -4 replace b, c, d a + (a-3) + (3a-9) + (a+2) = -4 a + a + 3a + a - 3 - 9 + 2 = -4 6a - 10 = -4 6a = -4 + 10 6a = +6 a = 1 then b = 1 - 3 b = -2 and c = 3(-2) c = -6 and d = 1 + 2 d = 3 : x^3 - 2x^2 - 6x + 3 is the polynomial ; ; Check solution 1 - 2 - 6 + 3 = -4
 Mixture_Word_Problems/235884: Two ships leave port at the same time. One sails south at 15 mi/h and the other sails east at 20 mi/h. Find a function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure.1 solutions Answer 173692 by ankor@dixie-net.com(15660)   on 2009-11-06 12:21:00 (Show Source): You can put this solution on YOUR website!Two ships leave port at the same time. One sails south at 15 mi/h and the other sails east at 20 mi/h. Find a function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure. : This is right triangle, legs formed by the path of the two ships distance between the ships is the hypotnenus a^2 + b^2 = c^2 ; a = 15t b = 20t c = d : d(t) = : d(t) = : d(t) = d(t) = 25t
 Money_Word_Problems/235395: Mary, Megan, and Molly sold magazine subscriptions to raise money for playground equipment/ Megan sold 9 more subscriptions than Mary. Molly sold 3 less than twice as many subscribtions as mary. If together they sold a total of 66 magazine subscriptions, how many subscriptions did each girl sell?1 solutions Answer 173691 by ankor@dixie-net.com(15660)   on 2009-11-06 12:08:13 (Show Source): You can put this solution on YOUR website!Mary, Megan, and Molly sold magazine subscriptions to raise money for playground equipment/ : Write an equation for each statement: : Megan sold 9 more subscriptions than Mary. Me = Ma + 9 : Molly sold 3 less than twice as many subscriptions as Mary. Mo = 2Ma - 3 : If together they sold a total of 66 magazine subscriptions, Ma + Me + Mo = 66 : how many subscriptions did each girl sell? : In the above equation: Replace Me with (Ma+9); and replace Mo with (2Ma-3) Ma + (Ma+9) + (2Ma-3) = 66 Ma + Ma + 2Ma + 9 - 3 = 66 4Ma + 6 = 66 4Ma = 66 - 6 4Ma = 60 Ma = 60/4 Ma = 15 Sold by Mary : I'll let you find Mo and Me
 Expressions-with-variables/235418: What example from my line of work ( catering ) or daily life can be expressed as an inequality with one variable? How do I set up the inequality and solve it.1 solutions Answer 173631 by ankor@dixie-net.com(15660)   on 2009-11-06 09:00:33 (Show Source): You can put this solution on YOUR website!What example from my line of work ( catering ) or daily life can be expressed as an inequality with one variable? How do I set up the inequality and solve it. : I would imagine that you have fixed cost and cost per meal : Let's say your fixed cost = \$500 Let the cost for making each meal = \$3 Let the sale price of each meal = \$5 : To make a profit the sales have to exceed cost : How many meals do you have to sell to make a profit? : Let x = no. of meals made and sold : Sale\$ greater than cost\$ 5x > 3x + 500 solve 5x - 3x > 500 2x > 50 x > x > 250 ; You have to sell more than 250 meals to make a profit ;
 Problems-with-consecutive-odd-even-integers/235424: there is a direct variation between number of oranges squeezed and the weight of the orange juice produced. to get 3 pounds of orange juice, you must squeeze about 15 oranges. if a tree has 300 oranges, how many pounds of orange juice will it produce?(simply work the problem through; you do not need a 5 step solution.)1 solutions Answer 173626 by ankor@dixie-net.com(15660)   on 2009-11-06 08:46:33 (Show Source): You can put this solution on YOUR website!there is a direct variation between number of oranges squeezed and the weight of the orange juice produced. to get 3 pounds of orange juice, you must squeeze about 15 oranges. : From this last statement we can say, there are 5 oranges per lb : if a tree has 300 oranges, how many pounds of orange juice will it produce? = 60 lb of juice
 Quadratic_Equations/235839: Another story problem I am having trouble with A photo is 3 inches longer than it is wide. a 2-inch border is placed around the photo making the total area of the photo and border 108in^2. What are the dimensions of the photo1 solutions Answer 173618 by ankor@dixie-net.com(15660)   on 2009-11-06 08:11:07 (Show Source): You can put this solution on YOUR website!A photo is 3 inches longer than it is wide. a 2-inch border is placed around the photo making the total area of the photo and border 108in^2. What are the dimensions of the photo : Let x = the width of the photo It says it is 3" longer than it is wide, therefore (x+3) = the length of the photo : a two inch border will add 4 inches to the photo dimensions, therefore (x+4) = width including the border and (x+3) + 4 which is (x+7) = length including the border : Given that the area of the whole thing as 108 sq/in, therefore (x+4) * (x+7) = 192 FOIL x^2 + 7x + 4x + 28 = 192 : x^2 + 11x + 28 - 192 = 0 : x^2 + 11x - 164 = 0; our old friend, the quadratic equation! : Use the quadratic formula: in this problem: a=1; b=11; c=-164 : : : Positive solution x = x = 8.437" is the width of the photo then 8.437 + 3 = 11.437" is the length ; : Check solution by finding the overall area (8.437+4) * (11.437+4)) = 191.99 ~ 192
 Polynomials-and-rational-expressions/235351: The surface of a balloon varies directly as the square of its radius. The area is when the radius is 5 cm. What is the area when the radius is 10 cm?1 solutions Answer 173580 by ankor@dixie-net.com(15660)   on 2009-11-05 21:59:25 (Show Source): You can put this solution on YOUR website!The surface of a balloon varies directly as the square of its radius. The area is 314 sq/cm when the radius is 5 cm. What is the area when the radius is 10 cm? : If it varies directly as the square, when the radius is doubled the surface area is times 4 4 * 314 = 1256 sq/cm ; : You can check this using the surface area formula S.A = 4*pi*10^2 = 1256.6
 Numbers_Word_Problems/235404: here is the problem : One number is 2 greater than another number.If the sum of their squares is 5 times the square of the smaller number,what are the numbers?1 solutions Answer 173578 by ankor@dixie-net.com(15660)   on 2009-11-05 21:49:06 (Show Source): You can put this solution on YOUR website!Let x = "one number" Let y = "another number" : Write an equation for each statement: : "One number is 2 greater than another number." x = y + 2 : "the sum of their squares is 5 times the square of the smaller number," x^2 + y^2 = 5y^2 x^2 = 5y^2 - y^2 x^2 = 4y^2 : What are the numbers? From the 1st statement we know x = (y+2) replace x with (y+2) (y+2)^2 = 4y^2 FOIL y^2 + 4x + 4 = 4y^2 Arrange as a quadratic on the right 0 = 4y^2 - y^2 - 4x - 4 0 = 3y^2 - 4y - 4 Factor this to (3y + 2)(y - 2) = 0 Two solutions 3y = -2 y = and y = 2 : Find x when y = -2/3 x = + 2 x = : Find x when y = 2 x = 2 + 2 x = 4 : x = 4, y = 2 and x = 4/3, y = -2/3 : You should check both solutions in: x^2 + y^2 = 5y^2