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 Equations/690712: please help solve this equation?? I do not understand how to do this. (5x+5)(10x-6)=01 solutions Answer 426431 by ankor@dixie-net.com(15652)   on 2012-12-06 21:23:22 (Show Source): You can put this solution on YOUR website!(5x+5)(10x-6)=0 Make each factor equal to 0, and find x 5x + 5 = 0 subtract 5 from both sides 5x = -5 Divide both sides by 5 x = -1, is one solution and 10x - 6 = 0 add 6 to both sides 10x = 6 divide both sides by 10 x = 6/10 x = .6 is the other solution
 Average/690922: The mean of five numbers is 56. Four of the numbers are the same. The average of one of the five numbers and the fifth number is 80. What are the five numbers?1 solutions Answer 426430 by ankor@dixie-net.com(15652)   on 2012-12-06 21:17:08 (Show Source): You can put this solution on YOUR website!The mean of five numbers is 56. Four of the numbers are the same. The average of one of the five numbers and the fifth number is 80. What are the five numbers? : Let a = the 4 numbers that are the same Let b = the fifth number = 56 4a + b = 5(56) 4a + b = 280 : " The average of one of the five numbers and the fifth number is 80." = 80 a + b = 2(80) a + b = 160 : Subtract the above equation from the 1st equation 4a + b = 280 a + b = 160 ---------------subtracting eliminates b, find a 3a = 120 a = 120/3 a = 40 : Find b 40 + b = 160 b = 160 - 40 b = 120 : What are the five numbers? 40,40,40,40,120
 Average/690912: if i need a 92% on my final and my final is worth 40% and by getting a 92% i get an 80% in the final course mark. what is my avg. sitting at right now?1 solutions Answer 426426 by ankor@dixie-net.com(15652)   on 2012-12-06 20:58:34 (Show Source): You can put this solution on YOUR website! if i need a 92% on my final and my final is worth 40% and by getting a 92% i get an 80% in the final course mark. what is my avg. sitting at right now? : Let x = the present average : = 80 6x + 368 = 10(80) 6x = 800 - 368 6x = 432 x = (432/6} x = 72 is your present average
 Travel_Word_Problems/690848: A car travels 60 meters and it takes the car 3 seconds to go that distance. What is the cars speed?1 solutions Answer 426423 by ankor@dixie-net.com(15652)   on 2012-12-06 20:52:31 (Show Source): You can put this solution on YOUR website!A car travels 60 meters and it takes the car 3 seconds to go that distance. What is the cars speed? : = 20 m/sec is the speed To change to km/hr: = 72 km/hr
 Expressions-with-variables/690852: Solve Ax+By=C for y. Your answer should be written in slope-intercept form.1 solutions Answer 426413 by ankor@dixie-net.com(15652)   on 2012-12-06 20:14:17 (Show Source): You can put this solution on YOUR website!Solve Ax+By=C for y. Subtract Ax from both sides By = -Ax + c Divide both sides by B y = x +
 Travel_Word_Problems/690873: The radius of Earth is 6,371 kilometers. A space shuttle orbits 315 kilometers above the surface of Earth. The space shuttle completes 240° of a revolution around Earth in one hour. What is the average speed of the space shuttle?1 solutions Answer 426411 by ankor@dixie-net.com(15652)   on 2012-12-06 20:07:19 (Show Source): You can put this solution on YOUR website!The radius of Earth is 6,371 kilometers. A space shuttle orbits 315 kilometers above the surface of Earth. Find the circumference equal to the shuttle's path C = 2*pi*(6371+315) C = 42,009.4 km : The space shuttle completes 240° of a revolution around Earth in one hour * 42009.4 = 28,006.25 km/hr is the speed of the shuttle
 Travel_Word_Problems/690729: You run at a rate of 4 miles per hour and your friend runs at a rate of 3.5 miles per hour. Your friend starts running 10 minutes before you, and you run for a half hour on the same path. Will you catch up to your friend? Use a graph to support your answer.1 solutions Answer 426406 by ankor@dixie-net.com(15652)   on 2012-12-06 19:59:52 (Show Source): You can put this solution on YOUR website!You run at a rate of 4 miles per hour and your friend runs at a rate of 3.5 miles per hour. Your friend starts running 10 minutes before you, and you run for a half hour on the same path. Will you catch up to your friend? Use a graph to support your answer. : The question is, Does your friend run further in 40 min than you run in 30 min. : Friend: * 3.5 = 2 mi You: * 4 = 2 mi You won't catch up in a half hour : Graph it in ft/min; You in red, friend in green : 4 mph: = 352 ft/min; y = 352x 3.5 mph: = 308 ft/min; y = 308(x+10) : You can see that at 30 min green is still ahead of red Take about 70 min for you to catch your friend
 Travel_Word_Problems/690468: A train running at 60 kmph takes 30 seconds to pass a platform. It takes 18 seconds to pass a person walking at 7 kmph in the same direction in which the train is running. What is the length of the railway platform and also the length of the train.1 solutions Answer 426368 by ankor@dixie-net.com(15652)   on 2012-12-06 17:00:28 (Show Source): You can put this solution on YOUR website!A train running at 60 kmph takes 30 seconds to pass a platform. It takes 18 seconds to pass a person walking at 7 kmph in the same direction in which the train is running. What is the length of the railway platform and also the length of the train. : The effective speed between the train and the walker: 60-7 = 53 km/hr How long a train takes 18 sec to pass a point at 53 km/hr? (In meters) d = * 53 * 1000 d = 265 meters is the length of the train : Find the speed of the train in meter/sec = 16.67 m/sec : Find the length of the platform (p) in meters Write a time equation, dist/speed = time = 30 p + 265 = 16.67(30) p + 265 = 500 p = 500 - 265 p = 235 meters is the length of the platform
 Average/690228: Three sisters met for dinner at a restaurant. Their bill was \$30. They divided the amount equally, and each paid \$10. The cashier discovered that an error had been made in tabulating their bill. It should have been \$25 instead of #30. The cashier informed the waiter of this error and gave in \$5 to return to the sisters. On the way back to the table, the waiter decided to keep \$2 and return \$1 to each sister. If each sister received \$1 back, then each paid \$10 - \$1, or \$9 for dinner, which is a total of \$27! The waiter kept \$2 which yields a total of \$29! Where is the missing dollar?1 solutions Answer 426218 by ankor@dixie-net.com(15652)   on 2012-12-05 19:21:28 (Show Source): You can put this solution on YOUR website! Three sisters met for dinner at a restaurant. Their bill was \$30. They divided the amount equally, and each paid \$10. The cashier discovered that an error had been made in tabulating their bill. It should have been \$25 instead of #30. The cashier informed the waiter of this error and gave in \$5 to return to the sisters. On the way back to the table, the waiter decided to keep \$2 and return \$1 to each sister. If each sister received \$1 back, then each paid \$10 - \$1, or \$9 for dinner, which is a total of \$27! The waiter kept \$2 which yields a total of \$29! Where is the missing dollar? : If the total bill was \$25, then each should have paid 25/3 = \$8.33, so each should have gotten 10-8.33 = \$1.67 back, they each got only \$1, short changed 67 cents, that's 3*.67 ~ \$2 the waiter kept
 Travel_Word_Problems/689652: Patricia flew a small airplane for 3 hours with the wind and traveled 585km. The return trip against the wind took 5 hours. Find the rate at which she flew in still air. What I have tried and failed: 3(r+w)=585 --> 3r+3w=585 5(r-w)=585 --> 5r-5w=585 15r+15w=2925 15r=8775 15r-15w=1755 r=585 3(585)+3w=585 1755+3w=585 -1755 -1755 <--- I figured this was wrong because it was negative.. 1 solutions Answer 426209 by ankor@dixie-net.com(15652)   on 2012-12-05 19:05:07 (Show Source): You can put this solution on YOUR website!a small airplane for 3 hours with the wind and traveled 585km. The return trip against the wind took 5 hours. Find the rate in still air : Let's do it this way : Write a distance equation for each way 3(r+w) = 585 5(r-w) = 585 : Simplify, divide the 1st equation by 3, divide the 2nd equation by 5, results: r + w = 195 r - w = 117 -------------addition eliminates w, find r 2r = 312 r = 312/2 r = 156 km/h in still air : : You can confirm this, find w and check in the original equations
 Rational-functions/689599: Please help me figure out how to find the x intercepts of this equation: y= x^4 -x^3 -6x^21 solutions Answer 426202 by ankor@dixie-net.com(15652)   on 2012-12-05 18:35:27 (Show Source): You can put this solution on YOUR website!find the x intercepts of this equation: x intercept occurs when y = 0 x^4 - x^3 - 6x^2 = 0 Factor out x^2 x^2(x^2 - x - 6) = 0 Factor again x^2(x-3)(x+2) = 0 Three solutions x^2 = 0 x = 0 and x = 3 and x = -2
 Surface-area/689772: A rancher wants to enclose a rectangular field with 220 ft of fencing. One side is a river and will not require a fence. What is the maximum area that can be enclosed? Please and Thanks a lot!1 solutions Answer 426154 by ankor@dixie-net.com(15652)   on 2012-12-05 16:05:10 (Show Source): You can put this solution on YOUR website!A rancher wants to enclose a rectangular field with 220 ft of fencing. One side is a river and will not require a fence. What is the maximum area that can be enclosed? : The field requires only 3 sides of fence, therefore L + 2W = 220 L = (220-2W); we can use this for substitution in the Area equation : Area A = L*W replace L with (220-2W) A = W(220-2W) A = -2W^2 + 220W A quadratic equation, max A occurs at the axis of symmetry, x = -b/(2a) In this equation W = W = 55 ft is the width for max area : Find the max area A = -2(55^2) + 220(55) A = -2(3025) + 12100 A = 6050 sq/ft is the max area : : Confirm this with the dimensions calculated; 110 * 55 = 6050
 Money_Word_Problems/689766: "My salary next year will be 7% more than this year and I will take home \$695.50 each week. How much am I taking home a week right now?" What I tried: 7%(x) = 695.50 .07(x) = 6.9550 7x = 695.50 x = 99.36 Some extra steps, I suppose...I was writing out my thoughts as I went along. Thank you in advance!1 solutions Answer 426048 by ankor@dixie-net.com(15652)   on 2012-12-04 22:06:36 (Show Source): You can put this solution on YOUR website!My salary next year will be 7% more than this year and I will take home \$695.50 each week. How much am I taking home a week right now?" : I would do it this way : x = amt your are taking home now 1.07x = 695.50 x = 695.5/1.07 x = \$650
 �t�e�s�t/689727: start at 12 o'clock: what will minute hand catch the hour hand (this was a problem given to me 60 yrs ago--am I right in remembering the answer to be 16 4/11?). THANKS1 solutions Answer 426046 by ankor@dixie-net.com(15652)   on 2012-12-04 22:00:32 (Show Source): You can put this solution on YOUR website! start at 12 o'clock: when will the minute hand catch the hour hand? (this was a problem given to me 60 yrs ago--am I right in remembering the answer to be 16 4/11?) : I don't think so, won't the minute hand catch up with the hour hand after one hr? The hour hand will be slightly passed 1 when the minute hand catches it. : Using degrees, one hr = 30 degrees, 1 min = 6 degrees : let m = minutes after the hr when this happens : Hour hand degrees = min hand degrees 30 + *30 = 6m 30 + = 6m mult by 2 60 + m = 12m 60 = 12m - m 60 = 11m m = 60/11 m = 5 minutes when it catches the hour hand
 Graphs/689663: how do i do answer the question "write an equation of a line that passes through the point (1,6) and has a slope of -3 1 solutions Answer 426035 by ankor@dixie-net.com(15652)   on 2012-12-04 21:21:44 (Show Source): You can put this solution on YOUR website! how do i do answer the question "write an equation of a line that passes through the point (1,6) and has a slope of -3 : Use the point slope formula: y - y1 = m(x - x1) in the problem x1=1, y1=6, m=-3 so you have y - 6 = -3(x - 1) y - 6 = -3x + 3 y = -3x + 3 + 6 y = -3x + 9, is the equation for the line ; : You can prove to yourself that this is the equation, replace x with 1 and find y
 Age_Word_Problems/689712: The age of a man is the same as his wife's age with the digits reversed. The sum of their ages is 99 and the man is 9 years older than his wife. How old is the man? 1 solutions Answer 426033 by ankor@dixie-net.com(15652)   on 2012-12-04 21:08:58 (Show Source): You can put this solution on YOUR website! The age of a man is the same as his wife's age with the digits reversed. 10x + y = man's age 10y + x = wife's age : The sum of their ages is 99 10x+y + 10y+x = 99 Combine like terms 11x + 11y = 99 Simplify, divide by 11 x + y = 9 : the man is 9 years older than his wife. (10x+y) - (10y+x) = 9 10x - x + y - 10y = 9 9x - 9y = 9 simplify, divide by 9 x - y = 1 : Using elimination from the two equations x + y = 9 x - y = 1 ---------------adding eliminates y, find x 2x = 10 x = 5 then 5 + y = 9 y = 9 - 5 y = 4 therefore 54 is the man's age 45 is the wife's age
 Money_Word_Problems/689369: I am trying to solve the problem of how much money will I need to invest in order to have \$30,000 in 12 years at a rate of 5 percent. Please help me solve The present value formula is P = A(1+r)-n where P is the present value A is the dollar amount in n years at interest rate r compounded annually using rules of exponent1 solutions Answer 426032 by ankor@dixie-net.com(15652)   on 2012-12-04 20:54:50 (Show Source): You can put this solution on YOUR website!invest in order to have \$30,000 in 12 years at a rate of 5 percent. : The formula we want: P*(1+.05)^12 = 30000 p*1.05^12 = 30000 find 1.05^12 on a calc p * 1.795856 = 30000 p = p = \$16,705.12 : :
 Age_Word_Problems/689632: In 4 years i will be 3 times the age i was 16 years ago1 solutions Answer 426010 by ankor@dixie-net.com(15652)   on 2012-12-04 20:01:40 (Show Source): You can put this solution on YOUR website!In 4 years i will be 3 times the age i was 16 years ago a + 4 = 3(a-16) a + 4 = 3a - 48 4 + 48 = 3a - a 52 = 2a a = 52/2 a = 26 is your present age :
 Rational-functions/689597: Please help me figure out how to find the x intercepts of this equation: y= -3x^3 + 18x - 27x1 solutions Answer 426009 by ankor@dixie-net.com(15652)   on 2012-12-04 19:51:13 (Show Source): You can put this solution on YOUR website!I think the problem is: y= -3x^3 + 18x^2 - 27x x intercept occur when y = 0 -3x^3 + 18x^2 - 27x = 0 Factor out -3x -3x(x^2 - 6x + 9) = 0 a perfect square is revealed, factor it to -3x(x-3)(x-3) = 0 the x intercepts: -3x = 0 x = 0 and x = 3
 Inequalities/689580: How do you solve (7/9)v + 5/12 - (3/18)v ≥ (3/4)v + 1/3? Please show the step-by-step solution because this is a homework problem. I tried the problem, but I know I am wrong. I just can't find the mistake! 1 solutions Answer 426004 by ankor@dixie-net.com(15652)   on 2012-12-04 19:20:43 (Show Source): You can put this solution on YOUR website!How do you solve (7/9)v + 5/12 - (3/18)v ≥ (3/4)v + 1/3? : v + - v >= v + We can get rid of all these denominators by multiplying by 36, resulting in 4(7v) + 3(5) - 2(3v) >= 9(3v) + 12 do the math 28v + 15 - 6v >= 27v + 12 Combine like terms 28v - 6v - 27v >= 12 - 15 -5v >= -3 v has to be positive, mult by -1, this reverses the inequality sign: 5v <= 3 v <=
 test/689585: A sailor on a submarine uses a periscope to view the surface of the ocean. The periscopes height H9in feet) above the surface and the distance d(in miles) that the sailor can see are related by the formula h=d^2/1.4. Suppose the periscope is at a height of 3 feet. To the nearest mile, how far can the sailor see? Please show me how to do this. I don't understand it. Thank you.1 solutions Answer 426003 by ankor@dixie-net.com(15652)   on 2012-12-04 19:02:09 (Show Source): You can put this solution on YOUR website! A sailor on a submarine uses a periscope to view the surface of the ocean. The periscopes height H (in feet) above the surface and the distance d(in miles) that the sailor can see are related by the formula h=d^2/1.4. : Suppose the periscope is at a height of 3 feet. To the nearest mile, how far can the sailor see? : Replace h with 3 and find d, write the equation: = 3 multiply both sides by 1.4 = 1.4(3) = 4.2 d = d = 2.05 miles
 Linear-systems/689340: Please help me solve this question: If a car traveled 5kilometer an hour faster it would take one hour less to travel 210 km. what is the speed of the car and what time does it take? Thank you,1 solutions Answer 426002 by ankor@dixie-net.com(15652)   on 2012-12-04 18:52:51 (Show Source): You can put this solution on YOUR website!If a car traveled 5kilometer an hour faster it would take one hour less to travel 210 km. what is the speed of the car and what time does it take? : Let s = actual speed of the car then (s+5) = the faster speed : Write a time equation; time = dist/speed : Actual time - faster time = 1 hr - = 1 Get rid of the denominators, multiply by s(s+5), results 210(s+5) - 210s = s(s+5) 210s + 1050 - 210s = s^2 + 5s Arrange as a quadratic equation 0 = s^2 + 5s - 1050 Factors to (s+35)(s-30) = 0 The positive solution s = 30 km/h is the actual speed Find the time = 7 hrs actual time : : Confirm this by finding the time at the faster speed 210/35 = 6 hrs, 1 hr less
 Volume/689146: What is the difference in volume between a golf ball with a diameter of 4 cm and a tennis ball with a diameter of 7 cm. I worked the problems and found that the volume of the golf ball is 33.6 cm3 The volume of the tennis ball is 179.6 cm3. The answre key from my teacher says that the answer is 17.8 cm3 but I do not see how she got it. Thank you1 solutions Answer 425921 by ankor@dixie-net.com(15652)   on 2012-12-04 12:17:59 (Show Source): You can put this solution on YOUR website!You are right, the teacher's answer is wrong
 Miscellaneous_Word_Problems/689225: Person A can paint the neighbor's house 5 times as fast as Person B. The year A and B worked together, it took them 7 days. How long would it take each to paint the house?1 solutions Answer 425899 by ankor@dixie-net.com(15652)   on 2012-12-04 10:36:12 (Show Source): You can put this solution on YOUR website! Person A can paint the neighbor's house 5 times as fast as Person B. The year A and B worked together, it took them 7 days. How long would it take each to paint the house? : Let t = time required by A to paint the house " Person A can paint the neighbor's house 5 times as fast as Person B." therefore: 5t = time required by B : Let the completed job = 1 (a painted house) : Each will do a fraction of the job, the two fractions add up to 1 : + = 1 multiply by 5t to get rid of the denominators, resulting in: 5(7) + 7 = 5t 35 + 7 = 5t 42 = 5t t = 42/5 t = 8.4 days required by A then 5(8.4) = 42 days required by B : : : Check this using a calc + = .83 + .17 = 1
 Equations/689286: The length of the base of a triangle three times the height. The area of the triangle is 54 squared. Find the base and height of the triangle. (by factoring) Im confused on the formula I should be using. Do I need a formula?1 solutions Answer 425893 by ankor@dixie-net.com(15652)   on 2012-12-04 09:59:46 (Show Source): You can put this solution on YOUR website!The formula for the area of a triangle would be useful here A = bh : The length of the base of a triangle three times the height. the equation for this statement: b = 3h : The area of the triangle is 54 squared. Assume you mean 54 sq/units here *b*h = 54 multiply both sides by 2, get rid of the fraction b*h = 108 Replace b with 3h 3h*h = 108 3h^2 = 108 Divide both sides by 3 h^2 = 36 find the square root of both sides h = h = 6 units is the height then b = 3h 3(6) = 18 units is base : ; Check this *18*6 = 54 Find the base and height of the triangle. Base = 18, height = 6; (not sure about the factoring requirement)
 Average/689273: If I have a 64 average what grade do I need to get a 701 solutions Answer 425889 by ankor@dixie-net.com(15652)   on 2012-12-04 09:08:44 (Show Source): You can put this solution on YOUR website! If I have a 64 average what grade do I need to get a 70 The average of two grades will be half way between the two grades, you need a 76
 Angles/689260: three numbers are in the ratio of 2:3:4,if the sum is 207 what is the largest? 1 solutions Answer 425886 by ankor@dixie-net.com(15652)   on 2012-12-04 08:20:47 (Show Source): You can put this solution on YOUR website! three numbers are in the ratio of 2:3:4,if the sum is 207 what is the largest? : Let x = "the multiplier" then 4x = the largest : 2x + 3x + 4x = 207 9x = 207 x = 207/9 x = 23 therefore 4(23) = 92 is the largest
 logarithm/688555: I'm having a problem figuring out a problem, I've tried it from a million ways and I know it is super easy. Given the points (5,2) which is on the graph of f(x), find b using the function . (hint, first plug the point in the equation, then solve for b)1 solutions Answer 425843 by ankor@dixie-net.com(15652)   on 2012-12-03 21:42:25 (Show Source): You can put this solution on YOUR website!Given the points (5,2) which is on the graph of f(x), find b using the function : We know: x = 5; f(x) = 2 : = 2 Write the exponent equiv = 5 b = + only :
 Rate-of-work-word-problems/689110: It takes 4 minutes longer to drain a Jacuzzi than it does to fill it. If the drain is left open, it takes 15 minutes to fill it. How many minutes does it take to fill the Jacuzzi when the drain is closed?1 solutions Answer 425834 by ankor@dixie-net.com(15652)   on 2012-12-03 20:53:17 (Show Source): You can put this solution on YOUR website!It takes 4 minutes longer to drain a Jacuzzi than it does to fill it. If the drain is left open, it takes 15 minutes to fill it. How many minutes does it take to fill the Jacuzzi when the drain is closed? : Let x = time required to fill it (drain closed) then (x+4) = time required to drain it : Let the completed job = 1, (a filled jacuzzi) + is fill, - is drain : - = 1 multiply by x(x+4) to clear the denominators, resulting in: 15(x+4) - 15x = x(x+4) 15x + 60 - 15x = x^2 + 4x A quadratic equation 0 = x^2 + 4x - 60 Factors to (x+10)(x-6) = 0 the positive solution is all we want here x = 6 minutes to fill it with the drain closed : See if that checks out (10 min to drain it) - = - = = 1
 logarithm/688793: In(x-1)+In6= In(3x)1 solutions Answer 425827 by ankor@dixie-net.com(15652)   on 2012-12-03 20:34:34 (Show Source): You can put this solution on YOUR website!In(x-1)+ In(6) = In(3x) adding logs mean multiply so we can write this as ln[6(x-1)] = ln(3x) therefore 6(x-1) = 3x 6x - 6 = 3x 6x - 3x = +6 3x = 6 x = 2 : : replace x with 2, in the original problem: ln(2-1) + ln(6) = ln(2*3) of course the ln of 1 is 0, so it checks out
 Equations/689019: PLEASE HELP .. I'm trying to help my son w/his hw.. I need answers/solutions to refresh my memory !! 1. x+y=4, 2x+y=5 2. x-y=5, 2x+3y=0 3. x-y=-2, x+y=4 4. y=x+3 (5,0) 5. y=2x+3 (-4,1)1 solutions Answer 425822 by ankor@dixie-net.com(15652)   on 2012-12-03 20:28:16 (Show Source): You can put this solution on YOUR website!1. x + y = 4 2x + y = 5 ------------subtraction eliminates y, find x -x = -1 x = 1 find y 1 + y = 4 y = 4 - 1 y = 3 Check solution of x=1; y=3, in the 2nd equation 2(1) + 3 = 5 : 2. x - y = 5 2x + 3y = 0 Use substitution with the first equation here x - y = 5 x = y+5 replace x with y+5 in the 2nd equation 2(y+5) + 3y = 0 2y + 10 + 3y = 0 2y + 3y = -10 5y = -10 y = -10/5 y = -2 find x using x = y + 5 x = -2 + 5 x = 3 check solution of x=3; y=-2 in the 2nd equation 2(3) + 3(-2) = 0 6 - 6 = 0 : 3. x - y = -2 x + y = 4 ----------------addition eliminates y, find x 2x = 2 x = 1 I'll let you find y, check your solutions in both equations : I'm not sure what (5,0) or (-4,1) mean here, they can't be an x/y pair 4. y = x + 3 (5,0) 5. y = 2x + 3 (-4,1)