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 Finance/303960: Use te clue to find the secret two-digit number. The sum of the digits is 9. The product of the digits is 18. The number is between 40 and 90. What is the number?1 solutions Answer 217789 by ankor@dixie-net.com(15628)   on 2010-05-12 21:34:41 (Show Source): You can put this solution on YOUR website!The sum of the digits is 9. The product of the digits is 18. The number is between 40 and 90. What is the number? : Let 10x + y = the two digit number : "The sum of the digits is 9." x + y = 9 y = (9-x) : The product of the digits is 18. x * y = 18 Replace y with (9-x) x(9-x) = 18 -x^2 + 9x = 18 -x^2 + 9x - 18 = 0 Multiply by -1 to change the signs x^2 - 9x + 18 = 0 Factors easily to (x-6)(x-3) = 0 x = 6, (no. is greater than 40) then y = 3 : The number is between 40 and 90. What is the number? It's 63
 Exponential-and-logarithmic-functions/303996: Soil from beneath the Kish Church in Azerbaijan was found to have lost 12% of its carbon-14. How old was the soil?1 solutions Answer 217783 by ankor@dixie-net.com(15628)   on 2010-05-12 21:24:07 (Show Source): You can put this solution on YOUR website!If soil was found to have lost 12% of it's carbon-14, then how old was the soil? : They should give you the half-life of Carbon 14. Most sources say it's 5730 yrs : The decay formula: A = Ao*2^(-t/h) where A = resulting amt after t yrs Ao = initial amt (t=0) t = time in yrs h = half-life of substance (5730 yrs in this case) : Let Ao = 1, then remaining amt (A) after t yrs: 1 -.12 = .88 (lost 12%) : 1*2^(-t/5730) = .88 using nat logs ln[2^(-t/5730)] = ln(.88) log equiv of exponents *ln(2) = ln(.88) *.693 = -.128 = = -.1844 t = -5730 * -.1844 t = 1057 yrs old ; : Check solution on a calc: enter 2^(-1057/5730) = .8799 ~.88 or 88% remaining
 Percentage-and-ratio-word-problems/303897: I'm having trouble figuring out the percentage of carbon-14. If soil was found to have lost 12% of it's carbon-14, then how old was the soil?1 solutions Answer 217780 by ankor@dixie-net.com(15628)   on 2010-05-12 21:21:20 (Show Source): You can put this solution on YOUR website!percentage of carbon-14. If soil was found to have lost 12% of it's carbon-14, then how old was the soil? : They should give you the half-life of Carbon 14. Most sources say it's 5730 yrs : The decay formula: A = Ao*2^(-t/h) where A = resulting amt after t yrs Ao = initial amt (t=0) t = time in yrs h = half-life of substance (5730 yrs in this case) : Let Ao = 1, then remaining amt (A) after t yrs: 1 -.12 = .88 (lost 12%) : 1*2^(-t/5730) = .88 using nat logs ln[2^(-t/5730)] = ln(.88) log equiv of exponents *ln(2) = ln(.88) *.693 = -.128 = = -.1844 t = -5730 * -.1844 t = 1057 yrs old ; : Check solution on a calc: enter 2^(-1057/5730) = .8799 ~.88 or 88% remaining
 Rectangles/303652: the width of a rectangle is 5 inches shorter than the length and that the perimeter or the rectangle is 50 inches. set up and equation for the perimeter involving the length. solve this equation algebraically to find the length and width. Thank-you Shirley Sims shirleysims174@aol.com1 solutions Answer 217644 by ankor@dixie-net.com(15628)   on 2010-05-12 14:17:03 (Show Source): You can put this solution on YOUR website!the width of a rectangle is 5 inches shorter than the length and that the W = L - 5 : perimeter or the rectangle is 50 inches. 2L + 2W = 50 : set up an equation for the perimeter involving the length. Replace W with (L-5) 2L + 2(L-5) = 50 solve this equation algebraically to find the length and width. 2L + 2L - 10 = 50 4L = 50 + 10 4L = 60 L = L = 15 in is the lenght then W = L - 5 W = 15 - 5 W = 10 in is the width : : Check solution by finding the perimeter with these values for L & W 2(15) + 2(10) = 50
 Quadratic_Equations/303705: What quadratic equation would have solutions x= 2/3 and x=1/51 solutions Answer 217619 by ankor@dixie-net.com(15628)   on 2010-05-12 12:26:37 (Show Source): You can put this solution on YOUR website!What quadratic equation would have solutions x= 2/3 and x=1/5 x = 2/3; from the factor: (3x - 2) and x = 1/5; from the factor: (5x - 1) : FOIL (3x - 2)(5x-1) = 15x^2 - 3x - 10x + 2 = (15x^2 - 13x + 2) is the equation
 Linear-equations/303515: find the slope of 15x = 5y + 21 solutions Answer 217526 by ankor@dixie-net.com(15628)   on 2010-05-11 21:59:17 (Show Source): You can put this solution on YOUR website!find the slope of 15x = 5y + 2 Subtract 15x from both sides 0 = -15x + 5y + 2 subtract 5y from both sides -5y = -15x + 2 Multiply both sides by -1 5y = 15x - 2 divide both sides by 5 y = 3x - or y = 3x - .4 : This this is the slope intercept form y - mx - b slope (m) = +3
 Linear_Equations_And_Systems_Word_Problems/303374: the hundreds digits is two times the ones digits. the ones digits is two times the tens digit. All the digits are even numbers what is the number? sweetmako@ymail.com1 solutions Answer 217523 by ankor@dixie-net.com(15628)   on 2010-05-11 21:45:29 (Show Source): You can put this solution on YOUR website!Let x = the 100's digit Let y = the 10's digit Let z = the ones digit : 100x + 10y + z = the number : Write an equation for each statement: "the hundreds digits is two times the ones digits." x = 2z : "the ones digits is two times the tens digit." z = 2y : replace z with 2y in the 1st equation x = 2(2y) x = 4y All the digits are even numbers from this we know y has to = 2 then x = 8 : thn z = 2(2) = 4: : The number 824
 Percentage-and-ratio-word-problems/303492: Im thinking of an integer. Half of this integer is more than one third of the next integer. What is this integer?1 solutions Answer 217516 by ankor@dixie-net.com(15628)   on 2010-05-11 21:29:44 (Show Source): You can put this solution on YOUR website!Im thinking of an integer. Half of this integer is more than one third of the next integer. What is this integer? : x = "the integer" : x > (x+1) multiply by 6, results 3x > 2(x+1) 3x > 2x + 2 3x - 2x > 2 x > 2 : See if that is true, assume x=3 (3) > (4) 1.5 > 1.33
 Polynomials-and-rational-expressions/303313: Please Help, I am confused about how to work with third roots. I am supposed to multiply then simplify by factoring. (3rd root)of y^7 * (3rd root) of 16y^8 Use Rational exponents to simplify the third root of x^6 Find the 16th root of (-8)^16 Rewrite the 4th root of 23 with a rational exponent. Simplify the 3rd root of -1/64 Simplify by taking roots of the numerator and denominator (3rd root) of 1000x^14/y^3 Solve The square root of 5x+29 = x+3 I am completely lost when working with roots. Any help would be greatly appreciated!1 solutions Answer 217510 by ankor@dixie-net.com(15628)   on 2010-05-11 21:07:05 (Show Source): You can put this solution on YOUR website!multiply then simplify by factoring. Use this as a cube root symbol : (3rd root)of y^7 * (3rd root) of 16y^8 : We can combine these under single radical : Add exponents when you multiply : Factor to reveal perfect cubes : Extract those perfect cubes : : Use Rational exponents to simplify the third root of x^6 to raise on power to another power, multiply exponents = = : : Find the 16th root of (-8)^16 = = = -8 : : Rewrite the 4th root of 23 with a rational exponent. : : Simplify the 3rd root of -1/64 = = : : Simplify by taking roots of the numerator and denominator (3rd root) of 1000x^14/y^3 Extract cube root 1/y^3 Extract the cube root of 1000 Factor inside the radical Extract : ; Solve The square root of 5x+29 = x+3 square both sides: 5x + 29 = (x+3)^2 FOIL the right side 5x + 29 = x^2 + 6x + 9 combine like terms on the right 0 = x^2 + 6x - 5x + 9 - 29 A quadratic equation x^2 + x - 20 = 0 Factors to (x+5)(x-4) = 0 two solutions x = -5 and x = +4 : Check both solution in original equation x = -5 not a solution x = 4 ; a good solution (x=4)
 Travel_Word_Problems/303296: A family makes a 43.25 km trip in 5.5 hours. On the first part of the trip they crossed a lake in a canoe paddling at 12 km/h. For the rest of the trip, they hiked on a scenic trail. If their average walking speed was 5 km/h, how far did they walk?1 solutions Answer 217448 by ankor@dixie-net.com(15628)   on 2010-05-11 19:00:11 (Show Source): You can put this solution on YOUR website!A family makes a 43.25 km trip in 5.5 hours. On the first part of the trip they crossed a lake in a canoe paddling at 12 km/h. For the rest of the trip, they hiked on a scenic trail. If their average walking speed was 5 km/h, how far did they walk? : let x = distance walked then (43.25-x) = distance paddled : Write a time equation: time = dist/speed : walk time + paddle time = 5.5 hrs + = 5.5 Multiply by 60 to clear the denominators, results 12x + 5(43.25-x) = 60(5.5) : 12x + 216.25 - 5x = 330 : 12x - 5x = 330 - 216.25 : 7x = 113.75 x = x = 16.25 km walked then 43.25 - 16.25 = 27 km paddled : : Check solutions by finding the total time 16.25/5 =3.25 hrs 27/12 = 2.25 hrs ------------------ total hrs:5.5 hrs, confirms our solutions of x = 16.25 km walked
 Percentage-and-ratio-word-problems/303126: To make a shade of orange paint that you like, you must mix 2/3 of a bottle of red paint with each 4/5 of a bottle of yellow paint that you use. You need 88 bottles of this orange paint. How many bottles of red paint will you need and how many bottles of yellow paint will you need? (All bottles are the same size.)1 solutions Answer 217436 by ankor@dixie-net.com(15628)   on 2010-05-11 17:02:18 (Show Source): You can put this solution on YOUR website!o make a shade of orange paint that you like, you must mix 2/3 of a bottle of red paint with each 4/5 of a bottle of yellow paint that you use. You need 88 bottles of this orange paint. How many bottles of red paint will you need and how many bottles of yellow paint will you need? (All bottles are the same size.) : Ratio of red:yellow to make orange = * = = : r:y = 5:6 then we know: r + y = 11 therefore *88 = 40 bottles of red and *88 = 48 bottles of yellow :
 Linear-systems/303263: Please help me to solve this equation: x+y+z=2 -x+2y+3z=2 2x-3y-z=1 x-y-z=01 solutions Answer 217382 by ankor@dixie-net.com(15628)   on 2010-05-11 16:06:48 (Show Source): You can put this solution on YOUR website!solve this equation: x + y + z = 2 -x+2y +3z = 2 2x-3y -z = 1 x - y -z = 0 : Using the 1st and 4th equation x + y + z = 2 x - y - z = 0 ---------------------Addition eliminates y and z, find x 2x = 2 x = 1 : Use the 2nd and 3rd equation, replace x with 1 -1+2y +3z = 2 2 -3y -z = 1 : +2y +3z = 2 + 1 3y - z = 1 - 2 : +2y +3z = 3 3y - z = -1 : Multiply the above equation by 3, and add to 2y + 3z = 3 9y - 3z = -3 2y + 3z = 3 ----------------- addition eliminates z, find y 11y = 0 y = 0 : Find z using: x + y + z = 2 1 + 0 + z = 2 z = 2 -1 z = 1 : Summarize x=1, y=0, z=1 : Check solution in the 2nd equation: -x+2y +3z = 2 -1 + 2(0) + 3(1) = -1 + 3 = 2
 Miscellaneous_Word_Problems/303234: Walking beside you, your friend takes 50 strides per minute while you take 48 strides per minute. If you start in step, when will you be in step again?1 solutions Answer 217351 by ankor@dixie-net.com(15628)   on 2010-05-11 15:13:59 (Show Source): You can put this solution on YOUR website!Walking beside you, your friend takes 50 strides per minute while you take 48 strides per minute. If you start in step, when will you be in step again? : Let m = no. of minutes to be in step 50(m-1) = 48m 50m - 50 = 48m 50m - 48m = 50 2m = 50 m = 25 minutes : therefore in 25 min you will be in step because: your friend has completed 25*50 = 1250 steps while you have completed 25*48 = 1200 steps
 Pythagorean-theorem/303246: your boat is traveling due north at 20 miles per hour. a friend's boat left at the same time and is traveling due west at 15 miles per hour. after an hour you get a call from your friend who tells you that he has just stopped because of engine trouble. how far must you travel to reach your friend?1 solutions Answer 217338 by ankor@dixie-net.com(15628)   on 2010-05-11 14:29:27 (Show Source): You can put this solution on YOUR website!boat is traveling due north at 20 miles per hour. a friend's boat left at the same time and is traveling due west at 15 miles per hour. after an hour you get a call from your friend who tells you that he has just stopped because of engine trouble. how far must you travel : this a right triangle problem, the distance between the boat is the hypotenuse c^2 = a^2 + b^2 where a = 20 b = 15 c = distance between the boats : c^2 = 20^2 + 15^2 c^2 = 400 + 225 c^2 = 625 c = c = 25 miles to travel to the friend
 Complex_Numbers/303258: Simplify if possible. 4a+10/a-1 Devide 3a+7/a-11 solutions Answer 217334 by ankor@dixie-net.com(15628)   on 2010-05-11 14:12:40 (Show Source): You can put this solution on YOUR website!Simplify if possible. ------------------ : Invert the dividing fraction and multiply * Cancel (a-1)'s =
 Miscellaneous_Word_Problems/303077: Quinn can refinish hardwood floors four times as fast as Jack. They have to refinish 100 ft^2 of flooring. Working together, Quinn and Jack can finish the job in 3 hours. How long would it take each of them working alone?1 solutions Answer 217332 by ankor@dixie-net.com(15628)   on 2010-05-11 14:05:14 (Show Source): You can put this solution on YOUR website!Quinn can refinish hardwood floors four times as fast as Jack. They have to refinish 100 ft^2 of flooring. Working together, Quinn and Jack can finish the job in 3 hours. How long would it take each of them working alone? : Let t = time required by Q to complete job alone then 4t = time required by J : Let the completed job (refinishing 100sq/ft) = 1 : + = 1 multiply each term by 4t, results 4(3) + 3 = 4t 12 + 3 = 4t 15 = 4t t = t = 3.75 hrs, Q alone then 4(3.75) = 15 hrs, J alone : : Check this: 3/3.75 + 3/15 = .8 + .2 = 1
 Polynomials-and-rational-expressions/303005: Hi My name is Nick and I was having probloms with the question as follows: Find The Product of the Square of the Binomial. (10r-1) Squared. 1 solutions Answer 217307 by ankor@dixie-net.com(15628)   on 2010-05-11 12:17:42 (Show Source): You can put this solution on YOUR website!Find The Product of the Square of the Binomial. (10r - 1)^2 : FOIL (10r - 1)(10r - 1) = 100r^2 - 10r - 10r + 1 = 100r^2 - 20r + 1; is the product
 Age_Word_Problems/303143: Jack is twice as old as Jill but in five years time he will only be one and half times as old. How old is Jack and Jill now?1 solutions Answer 217245 by ankor@dixie-net.com(15628)   on 2010-05-11 08:44:38 (Show Source): You can put this solution on YOUR website!Jack is twice as old as Jill Ja = 2Ji : but in five years time he will only be one and half times as old. Ja + 5 = 1.5(Ji+5) Ja + 5 = 1.5Ji + 7.5 Ja = 1.5Ji + 7.5 - 5 Ja = 1.5Ji + 2.5 Replace Ja with 2Ji 2Ji = 1.5Ji + 2.5 2Ji - 1.5Ji = 2.5 .5Ji = 2.5 Mult both sides by 2 Ji = 5 : I'll let you find Ja's age
 Square-cubic-other-roots/303139: the square root of 200x^3y/ the square root of 2xy^51 solutions Answer 217244 by ankor@dixie-net.com(15628)   on 2010-05-11 08:38:14 (Show Source): You can put this solution on YOUR website!the square root of 200x^3y/ the square root of 2xy^5 Cancel 2 into 200 combine like terms, in a manner to avoid neg exponents =
 Divisibility_and_Prime_Numbers/303133: The tens digit of a two-digit number is 3 and the units digit is H. if the two-digit number is divisible by H, which of the following cannot be the value of H ? A 2 b 3 c 4 d 5 e 6 1 solutions Answer 217242 by ankor@dixie-net.com(15628)   on 2010-05-11 08:02:58 (Show Source): You can put this solution on YOUR website!The tens digit of a two-digit number is 3 and the units digit is H. if the two-digit number is divisible by H, which of the following cannot be the value of H ? 4, 34 is not divisible by 4
 Radicals/302920: How do you perform the necessary steps to isolate the radical on the right-hand side of the equation? 3x - 6 = 2x + 2y + 1 - 9 2y + 1 is under a radical Thank you! 1 solutions Answer 217205 by ankor@dixie-net.com(15628)   on 2010-05-10 21:57:19 (Show Source): You can put this solution on YOUR website!Assume the problem is subtract 2x and add 9 to both sides and you hve : :
 Linear-equations/302916: Here is more of the same, an accuplacer practice. 3/10x plus 9/14x^2 ie 3 over 10x plus 9 over 14x squared = ? The correct answer is 3(7x+15) over 70x squared. How to get there, I don't know. With apologies beforehand to London Maths Tutor and others, I should point out that I'm kind of dense. So if anybody tackling this one could include and explain steps in the process even if they seem blindingly obvious, that would be super! Thanks much, Mike1 solutions Answer 217202 by ankor@dixie-net.com(15628)   on 2010-05-10 21:49:01 (Show Source): You can put this solution on YOUR website!3/10x plus 9/14x^2 Assume the problem is: + looking at the denominator you can see the common denominator will be 70x^2 : Divide the denominator into the common denominator and multiply the numerator by that value. = Factor out 3 in the numerator : Did that make sense, Mike?
 Sequences-and-series/302992: The mean of five numbers is 6. If one of the five numbers is removed, the mean becomes 7. What is the value of the number that was removed?1 solutions Answer 217192 by ankor@dixie-net.com(15628)   on 2010-05-10 21:30:41 (Show Source): You can put this solution on YOUR website!The mean of five numbers is 6. If one of the five numbers is removed, the mean becomes 7. What is the value of the number that was removed? : Let x = value of the 1st 4 numbers Let y = value of the number to be removed : = 6 x + y = 5(6) x + y = 30 then "one of the five numbers is removed, the mean becomes 7. = 7 x = 4(7) x = 28 : Substitute 28 for x in the equation: x + y = 30 28 + y = 30 y = 20 - 28 y = 2, is the value of the number removed
 Rectangles/302721: A hawk can fly 300 miles in 8 hours with the wind. Flying against the wind, the hawk covers only one-third of the distance in 7 hours. What is the rate of the wind?1 solutions Answer 217189 by ankor@dixie-net.com(15628)   on 2010-05-10 21:17:56 (Show Source): You can put this solution on YOUR website!A hawk can fly 300 miles in 8 hours with the wind. Flying against the wind, the hawk covers only one-third of the distance in 7 hours. What is the rate of the wind? ; let w = the rate of the wind let s = the flying rate of the hawk then (s+w) = effective speed with the wind (s-w) = effective speed against the wind : Two distance equations: 8(s+w) = 300 7(s-w) = 100 : 8s + 8w = 300 7s - 7w = 100 : Multiply the 1st equation by 7 & the 2nd equation by 8, subtract 56s + 56w = 2100 56s - 56w = 800 -------------------subtraction eliminates s, find w 112w = 1300 w = w = 11.6 mph is the rate of the wind : : Find the speed of the hawk to check our solution for the wind 8s + 8(11.6) = 300 8s = 92.8 = 300 8s = 300 - 92.8 s = s = 25.9 mph : Check it in the 2nd equation 7s - 7w = 100 7(25.9) - 7(11.6) = 181.3 - 81.2 = 100.1 ~ 100; confirms our solution for wind = 11.6 mph
 Expressions-with-variables/302548: It takes a small jet plane 4 hours less time than it takes a propeller driven plane to travel from Glen Rock to Oakville. The jet plane averages 637 km/h while the propeller plane averages 273 km/h. How far is it from Glen Rock to Oakville?1 solutions Answer 217161 by ankor@dixie-net.com(15628)   on 2010-05-10 19:20:13 (Show Source): You can put this solution on YOUR website!It takes a small jet plane 4 hours less time than it takes a propeller driven plane to travel from Glen Rock to Oakville. The jet plane averages 637 km/h while the propeller plane averages 273 km/h. How far is it from Glen Rock to Oakville? : Let d = distance between these two towns : Write a time equation, Time = dist/speed : Prop time = Jet time + 4 hrs = + 4 Multiply by 173901(273*637) to clear the denominators, results: 637d = 273d + 4(173901) : 637d - 273d = 695604 : 364d = 695604 d = d = 1911 km between these two downs ; : Check solution by finding the times of each 1911/273 = 7 hrs 1911/637 = 3 hrs ------------------- difference 4 hrs
 Polynomials-and-rational-expressions/302714: x^5-11^4+30x^3 x^5-11x+30....I don't know if I'm on the right track, but any help is appreciated so much I believe this needs to be factored completly. Thank you!!!1 solutions Answer 217155 by ankor@dixie-net.com(15628)   on 2010-05-10 19:02:05 (Show Source): You can put this solution on YOUR website!x^5 - 11^4 + 30x^3 Factor out x^3 x^3(x^2 - 11x + 30) Factor further x^3(x-5)(x-6)