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 logarithm/634202: I would like help with this question please (2log base 2 (x-6)) - (log base 2 X)= 3 I am lost.1 solutions Answer 399431 by ankor@dixie-net.com(15661)   on 2012-08-02 17:03:08 (Show Source): You can put this solution on YOUR website!(2log base 2 (x-6)) - (log base 2 X)= 3 We can write it 2log2(x-6) - log2(x) = 3 : we can put the exponent inside log log2((x-6)^2) - log2(x) = 3 : Subtraction of logs is divide, we can write it as a single log = 3 : The exponent equiv of logs = Multiply both sides by x (x-6)^2 = 8x : FOIL (x-6)(x-6) = 8x : A quadratic equation x^2 - 12x - 8x + 36 = 0 x^2 - 20x + 36 = 0 Factors to (x-18)(x-2) = 0 Two solutions x = 2; not a solution x-6 would put a neg inside the log and x = 18 is our solution
 Linear-equations/634163: I need to determine the slope and y intercept of the graph of the linear equation 6x-5y+3=2x-2y-6. In addition to solving can you show me the steps I need to be able to solve like problems? I am not understanding my professor nor is the Math 90 book we are using helping. Thank You1 solutions Answer 399419 by ankor@dixie-net.com(15661)   on 2012-08-02 16:12:45 (Show Source): You can put this solution on YOUR website!determine the slope and y intercept of the graph of the linear equation 6x-5y+3=2x-2y-6 : We want this in the slope/intercept form, y = mx + b : 6x - 5y + 3 = 2x - 2y - 6 subtract 6x from both sides -5y + 3 = 2x - 6x - 2y - 6 -5y + 3 = -4x - 2y - 6 : Add 2y to both sides -5y + 2y + 3 = -4x - 6 -3y + 3 = -4x - 6 : Subtract 3 from both sides -3y = -4x - 6 - 3 -3y = -4x - 9 : y has to be positive, mult both sides by -1 3y = 4x + 9 : y has to have a coefficient of 1, divide both sides by 3 y = x + 3; this is slope intercept form therefore slope (m) = y intercept occurs when x=0, so y intercept = 3 : The graph of this You can see the y axis is intercepted at y=3 and the slope, rises 4 units for each 3 units horizontally
 Mixture_Word_Problems/634167: Tom and Jerry have to sort and organize all the nails on their father's workbench. Tom can sort 220 nails in 2 hours. Jerry can sort 150 nails in 3 hours. How long will it take them to sort 500 nails if they work together (round to the nearest hundredth)?1 solutions Answer 399405 by ankor@dixie-net.com(15661)   on 2012-08-02 15:20:02 (Show Source): You can put this solution on YOUR website!Tom and Jerry have to sort and organize all the nails on their father's workbench. Tom can sort 220 nails in 2 hours. Jerry can sort 150 nails in 3 hours. How long will it take them to sort 500 nails if they work together (round to the nearest hundredth)? : Let t = no. of hrs for 500 nails working together : Find how many nails each can sort in an hour Tom: 220/2 = 110 per hr Jerry: 150/3 = 50 " " : 110t + 50t = 500 160t = 500 t = 500/160 t = 3.125 hrs which is 3 + .125(60) = 3 hrs 7.5 minutes : : We can confirm this 3.125(110) + 3.125(50) = 500
 Word_Problems_With_Coins/634033: VALUE OF COINS. Mary has \$3.00 in nickels, dimes, and quarters. If she has twice as many dimes as quarters and five more nickels than dimes, how many coins of each type does she have? (NOTE: nickel = 5 cents; dime = 10 cents; quarter = 25 cents)1 solutions Answer 399401 by ankor@dixie-net.com(15661)   on 2012-08-02 15:09:18 (Show Source): You can put this solution on YOUR website!Let n = no.of nickels let d = no. of dimes let q = no. of quarters : Write an equation for each statement, we are going to get all the coins in terms of d: : "Mary has \$3.00 in nickels, dimes, and quarters." .05n + .10d + .25q = 3.00 : "If she has twice as many dimes as quarters" d = 2q or divide both sides by 2: q = .5d : " and five more nickels than dimes," n = d + 5 : In the Total Value equation, replace q with .5d and n with (d+5) .05(d+5) + .10d + .25(.5d) = 3.00 .05d + .25 + .10d + .125d = 3.00 Combine like terms .275d = 3.00 - .25 .275d = 2.75 d = d = 10 dimes then n = 10 + 5 n = 15 nickels and q = .5(10) q = 5 quarters : See if that checks out .05(15) + .10(10) + .25(5) = 3.00
 Average/634012: √72x^2y _______ = it says to rationalize the denominator thanks for your help! :) √24xy 1 solutions Answer 399345 by ankor@dixie-net.com(15661)   on 2012-08-02 08:27:52 (Show Source): You can put this solution on YOUR website! First factor inside both radicals to reveal the perfect squares Extract the square root of those squares, cancel 2 = : Multiply by the denominator over itself (same as multiplying by 1) * = = We have two perfect squares we can extract = cancel 2y : A lot of steps, but did each one make sense to you? If you know these, it will greatly help you to deal with these radicals. C
 Travel_Word_Problems/633896: Stephanie and her friend, Paula, are waiting for a shuttle to take them to their terminal at the airport. The first shuttle that arrives only has room for one more passenger, so Stephanie gets on. The next shuttle arrives 10 minutes later and Paula gets on. If Stephanie's shuttle travels at a speed of 20 mph and Paula's shuttle travels at a speed of 35 mph, how long will it take Paula's shuttle to catch up to Stephanie's shuttle? 1 solutions Answer 399266 by ankor@dixie-net.com(15661)   on 2012-08-01 20:07:17 (Show Source): You can put this solution on YOUR website!The first shuttle that arrives only has room for one more passenger, so Stephanie gets on. The next shuttle arrives 10 minutes later and Paula gets on. If Stephanie's shuttle travels at a speed of 20 mph and Paula's shuttle travel at a speed of 35 mph, how long will it take Paula's shuttle to catch up to Stephanie's shuttle? : When the 2nd shuttle (35mph) catches the 1st (20mph) they will have traveled the same distance : Change 10 min to hrs : Let t = travel time of the 2nd shuttle then (t+) = travel time of the 1st shuttle : Write a distance equation, dist = speed * time 35t = 20(t+) 35t = 20t + 35t - 20t = 15t = multiply both sides by 6 6(15t) = 20 90t = 20 t = t = * 60 = 13 minutes for the 2nd shuttle to catch the 1st.
 Problems-with-consecutive-odd-even-integers/633892: Find three consecutive odd numbers such that the square of the second number is 192 less than the square of the third number. WE ARE STUDYING POLYNOMIALS AND I NEED SOME HELP WITH THE WORD PROBLEMS PLEASE1 solutions Answer 399260 by ankor@dixie-net.com(15661)   on 2012-08-01 19:23:56 (Show Source): You can put this solution on YOUR website!Find three consecutive odd numbers such that the square of the second number is 192 less than the square of the third number. : Let x = the 1st integer, then (x+2) and (x+4) are the next two odd integers : Write an equation for the statement: "the square of the second number is 192 less than the square of the third number." (x+2)^2 = (x+4)^2 - 192 FOIL x^2 + 4x + 4 = x^2 + 8x + 16 - 192 Combine the variables on the left x^2 - x^2 + 4x - 8x = 16 - 192 - 4 : -4x = -180 x = x = +45 is the 1st odd number then 47 and 49 are the 2nd and 3rd odd digits : : Check 47^2 = 49^2 - 192 2209 = 2401 - 192
 Average/633879: my grade is a 78 and the final exam is 15% of our grade and its only 25 question. and what if i scored a 60?1 solutions Answer 399250 by ankor@dixie-net.com(15661)   on 2012-08-01 18:48:27 (Show Source): You can put this solution on YOUR website! my grade is a 78 and the final exam is 15% of our grade and its only 25 question. and what if i scored a 60? : Then your 78 is 85% of your grade, : Av = : Av = : Av = Av = 75.3 would be your average if you got a 60 on your exam : .6 * 25 = 15, you must get 15 right to score 60
 Rate-of-work-word-problems/633851: Three boys can build a fence in 6 hours, 7 hours, and 8 hours working individually. How long will it take to build the fence if the boys work together?1 solutions Answer 399223 by ankor@dixie-net.com(15661)   on 2012-08-01 17:09:38 (Show Source): You can put this solution on YOUR website!Three boys can build a fence in 6 hours, 7 hours, and 8 hours working individually. How long will it take to build the fence if the boys work together? : Let t = the time required when the three work together Let the completed job = 1 : Each will do a fraction of fence, the three fractions add up to 1 : + + = 1 Least Common Multiple would be 168, multiply eq by 168, results 28t + 24t + 21t = 168 73t = 168 t = 168/73 t ~ 2.3 hrs : : You can confirm this, calculate 2.3/6 + 2.3/7 + 2.3/8
 Travel_Word_Problems/633670: A proton is traveling at a constant speed of 0.5 c (half the speed of light) along a circular path inside a particle accelerator. The area enclosed inside the accelerator is 1.6 square kilometers. How many times can the proton go around in 80 nanoseconds?1 solutions Answer 399211 by ankor@dixie-net.com(15661)   on 2012-08-01 16:54:16 (Show Source): You can put this solution on YOUR website!A proton is traveling at a constant speed of 0.5 c (half the speed of light) along a circular path inside a particle accelerator. The area enclosed inside the accelerator is 1.6 square kilometers. How many times can the proton go around in 80 nanoseconds? : We know that light only travels about 30 cm in 1 nanosecond At half the speed of light: 15 cm : 80 * 15 = 1200 cm or 12 meters, not even close to making one round : No point in finding the circumference and all that stuff.
 Numbers_Word_Problems/633693: In a certain three digit number, the hundreds digit is the sum of the other two digits. If the units and tens digits of this number are interchanged,the new number is 9 more than the original number. If the hundreds and ten digits of the original number are interchanged, the new number is 360 less than the original number. Find the original number. 1 solutions Answer 399151 by ankor@dixie-net.com(15661)   on 2012-08-01 13:14:22 (Show Source): You can put this solution on YOUR website!The three digits: a, b, c; write an equation for each statement Simplify each equation as much as possible : In a certain three digit number, 100a + 10b + c : the hundreds digit is the sum of the other two digits. a = b + c : If the units and tens digits of this number are interchanged,the new number is 9 more than the original number. 100a + 10c + b = 100a + 10b + c + 9 Subtract 100a from both sides 10c + b = 10b + c + 9 10c - c = 10b - b + 9 9c = 9b + 9 simplify, divide by 9 c = b + 1 : If the hundreds and ten digits of the original number are interchanged, the new number is 360 less than the original number. 100b + 10a + c = 100a + 10b + c - 360 subtract c from both sides 100b + 10a = 100a + 10b - 360 100b - 10b = 100a - 10a - 360 90b = 90a - 360 Simplify, divide by 90 b = a - 4 or a = b + 4 : Using the equation: a = b + c, replace a and c (b+4) = b + (b+1) 4 - 1 = 2b - b 3 = b then a = 3 + 4 a = 7 and c = 3 + 1 c = 4 : 734 is the original number : You can confirm this solution in the last two statements
 Linear_Equations_And_Systems_Word_Problems/633577: I am trying to show linear examples in real life. I am still a bit confused, therefore I am having issues with making up an example. Please help this is for my homework. I know how linear equations are used : Travel Temperature Conversion Exchange Rates Cell Phones I just don't understand how to put it into an example. 1 solutions Answer 399027 by ankor@dixie-net.com(15661)   on 2012-07-31 22:04:30 (Show Source): You can put this solution on YOUR website!Travel: You start for home which is 1000 miles away, your av speed is 60 mph Let t = driving time Let d = distance from home d = -60t + 1000 Example: after 10 hrs (t=10) driving you would be 400 mi (d) from home : Temperature Conversion: convert Fahrenheit to Celsius C = (F-32) When it's 86 degrees f, what is it Celsius C = (86-32) C = *54 C = 30 degrees C : Exchange Rates Convert dollars (d) to baht, the Thai currency. \$1 = 20 baht (b) b = 20d : Cell Phones Cost vs minutes, Monthly fee = \$10 First 100 min are free, .25 for each minute thereafter C = .25(m-100) + 10
 test/633586: Simplify (X^2+5x-14)/(x^2-4)1 solutions Answer 399021 by ankor@dixie-net.com(15661)   on 2012-07-31 21:44:46 (Show Source): You can put this solution on YOUR website!Simplify Factoring greatly simplifies this : cancel the x-2's, leaving us with:
 Radicals/633544: simplifying radical expressions assuming that the variable is a non negative How do you solve the square root of 24x raised to the fifth power √24x^5?1 solutions Answer 399016 by ankor@dixie-net.com(15661)   on 2012-07-31 21:32:47 (Show Source): You can put this solution on YOUR website!; we can't solve this, only simplify factor inside the radical to reveal perfect squares Extract the square roots of those perfect squares 2*x*x =
 Problems-with-consecutive-odd-even-integers/633493: Our integer is 6 less than another integer. The product of the lesser integer and -7 is 42 more than the greater integer. What are the integers?1 solutions Answer 398994 by ankor@dixie-net.com(15661)   on 2012-07-31 19:15:08 (Show Source): You can put this solution on YOUR website!Let x = our integer then (x+6) = another integer : Write an equation for the statement: : " The product of the lesser integer and -7 is 42 more than the greater integer" -7x = (x+6) + 42 -7x - x = 48 -8x = 48 x = x = -6 is the lesser integer then -6 + 6 = 0 is greater integer : Check solution in the given statement: -7(-6) = 0 + 42
 Geometry_Word_Problems/633505: A baseball hit from home plate is described by the equation h = -16t2 + 100t + 5, where the height is h and the time is t. The bleachers are 20 feet from the ground. When will the baseball land in the bleachers? Round your answer to the nearest tenth of a second. 1 solutions Answer 398952 by ankor@dixie-net.com(15661)   on 2012-07-31 15:09:53 (Show Source): You can put this solution on YOUR website!A baseball hit from home plate is described by the equation h = -16t^2 + 100t + 5, where the height is h and the time is t. The bleachers are 20 feet from the ground. When will the baseball land in the bleachers? Round your answer to the nearest tenth of a second. : The equation for this scenario; h = 20, therefore -16t^2 + 100t + 5 = 20 -16t^2 + 100t + 5 - 20 = 0 -16t^2 + 100t - 15 = 0 Use the quadratic formula In this equation x=t; a=-16; b=100; c=-15 : You should be able to do the math now, only one solution will make sense
 Trigonometry-basics/633404: a river has parallel banks which run directly east-west.Kylie takes a bearing to a tree on the opposite side. The bearing is 47degrees true. She then walks 10m due east, and take sa second bearing to the tree. This is 305 degrees true.Find: a. her distance from the second measuring point to the tree. b. the width of the river, to the nearest metre1 solutions Answer 398947 by ankor@dixie-net.com(15661)   on 2012-07-31 14:38:02 (Show Source): You can put this solution on YOUR website!a river has parallel banks which run directly east-west. Kylie takes a bearing to a tree on the opposite side. The bearing is 47 degrees true. he then walks 10m due east, and takes a second bearing to the tree. This is 305 degrees true. : Drawing a diagram of this will help a lot ; Find the interior angles of the triangle formed by the 1st meas point (A), the 2nd meas point (B), and the tree (C) A = 90 - 47 = 43 degrees B = 305 - 270 = 35 degrees C = 180 - 43 - 35 = 102 degrees : Find: a. distance from the second measuring point to the tree. let a = this distance, use the law of sines = = a = 6.97 meters from the tree to the 2nd meas point : b. the width of the river, to the nearest meter A right angle triangle formed by a perpendicular of the near side river bank and the tree, this is the dist across the river (d). find the interior angle at the tree 180 - 90 - 35 = 55 degrees Use the cosine of 55 here cos(55) = .57*6.97 = d d ~ 4 meters across the river
 Quadratic_Equations/633475: In two hpurs, a motorboat can travel 8 miles down a river and return 4 miles back. If the river flows at a rate of 2 mph, what is the rate of the boat in still water?1 solutions Answer 398936 by ankor@dixie-net.com(15661)   on 2012-07-31 13:22:30 (Show Source): You can put this solution on YOUR website!In two hours, a motorboat can travel 8 miles down a river and return 4 miles back. If the river flows at a rate of 2 mph, what is the rate of the boat in still water? : Let s = boat speed in still water then (s+2) = effective speed down river and (s-2) = effective speed up river : Write a time equation: time = dist/speed ; Down riv time + up riv time = 2 hrs + = 2 Multiply by (s-2)(s+2) to get rid of the denominators, results: 8(s-2) + 4(s+2) = 2(s-2)(s+2) : 8s - 16 + 4s + 8 = 2(s^2 - 4) 12s - 8 = 2s^2 - 8 add 8 to both sides 12s = 2s^2 0 = 2s^2 - 12s 0 = 2s(s - 6) The reasonable solution s = 6 mph is the speed in still water : : See if that checks out find the time each way 8/(6+2) = 1 hr 4/(6-2) = 1 hr ------------- total time 2 hrs
 �t�e�s�t/633288: 3x - y + 4z = 12 x + y - 3z = -4 4x + y - z = 7 x = y = z = 1 solutions Answer 398931 by ankor@dixie-net.com(15661)   on 2012-07-31 12:58:44 (Show Source): You can put this solution on YOUR website!3x - y + 4z = 12 x + y - 3z = -4 4x + y - z = 7 -------------------add the three equations, eliminates z 8x + y = 15 : Using the 2nd and 3rd equations, multiply the 3rd by -3, add to the 2nd x + y - 3z = -4 -12x - 3y + 3z = -21 -------------------- adding eliminates z -11x - 2y = -25 16x + 2y = 30; multiplied 8x+y=15 by 2 ---------------adding eliminates y, find x 5x = 5 x = 1 : Find y 8x + y = 15 8(1) + y = 15 y = 15 -8 y = 7 : Find z 3x - y + 4z = 12 3(1) - 7 + 4z = 12 -4 + 4z = 12 4z = 12 + 4 z = 16/4 z = 4 : Summarize x = 1 y = 7 z = 4 : : Check this in the 2nd equation x + y - 3z = -4 1 + 7 - 3(4) = -4 8 - 12 = -4 : You can check this in the other two equations
 Miscellaneous_Word_Problems/633468: a farmer had a total of 700 goats and sheep. if he sold 3/4 of his goats and 400 sheep , he would have an equal number of goats and sheep left. how many more sheep than gots did he have in the beginning?1 solutions Answer 398923 by ankor@dixie-net.com(15661)   on 2012-07-31 12:35:33 (Show Source): You can put this solution on YOUR website!Write an equation for each statement : a farmer had a total of 700 goats and sheep. g + s = 700 g = (700-s); use this form for substitution : if he sold 3/4 of his goats and 400 sheep, he would have an equal number of goats and sheep left. g = s - 400 multiply both sides by 4 g = 4(s - 400) g = 4s - 1600 replace g with (700-s) 700 - s = 4s - 1600 700 + 1600 = 4s + s 2300 = 5s s = s = 460 sheep in the beginning and 700 - 460 = 240 goats in the beginning : how many more sheep than goats did he have in the beginning? 460 - 240 = 220 more sheep
 Travel_Word_Problems/633400: It took Malcolm 6 minutes to walk 500m from the bus stop to the opera house. How fast was he travelling? Sorry I am just not good at Maths!1 solutions Answer 398920 by ankor@dixie-net.com(15661)   on 2012-07-31 12:23:44 (Show Source): You can put this solution on YOUR website!Speed = dist/time : S = s = 83 meters/minute is his speed
 Linear_Equations_And_Systems_Word_Problems/633158: joe bought a bag of oranges on Monday, and ate a third of them. On Tuesday he ate half of the remaining oranges. On Wednesday he looked in the bag to find he only had two oranges left. How many oranges were originally in the bag? 1 solutions Answer 398824 by ankor@dixie-net.com(15661)   on 2012-07-30 21:34:13 (Show Source): You can put this solution on YOUR website!Joe bought a bag of oranges on Monday, and ate a third of them. On Tuesday he ate half of the remaining oranges. On Wednesday he looked in the bag to find he only had two oranges left. How many oranges were originally in the bag? : Let x = original number of oranges : x, remain on Monday *x = x remain on Tuesday x = 2 remain on Wednesday multiply both sides by 3 1x = 6 orange originally
 Mixture_Word_Problems/633258: A goldsmith has two gold alloys. The first alloy is 30% gold; the second alloy is 80% gold. How many grams of each should be mixed to produce 40 grams of an alloy that is 70% gold? Amount of 30% gold in grams? Amount of 80% gold in grams??1 solutions Answer 398819 by ankor@dixie-net.com(15661)   on 2012-07-30 21:21:18 (Show Source): You can put this solution on YOUR website!A goldsmith has two gold alloys. The first alloy is 30% gold; the second alloy is 80% gold. How many grams of each should be mixed to produce 40 grams of an alloy that is 70% gold? : Let x = amt of 80% alloy required the resulting total is to be 40 grams, therefore: (40-x) = amt of 30% gold : .80x + .30(40-x) = .70(40) .80x + 12 - .30x = 28 .80x - .30x = 28 - 12 .50x = 16 x = 16/.5 x = 32 grams of the 80% alloy then 40 - 32 = 8 grams of 30% alloy
 Linear_Equations_And_Systems_Word_Problems/633280: solve nonlinear system of equations for real solutions y=x^2-3 8x-y=181 solutions Answer 398801 by ankor@dixie-net.com(15661)   on 2012-07-30 19:14:21 (Show Source): You can put this solution on YOUR website!solve nonlinear system of equations for real solutions y = x^2 - 3 8x - y = 18 rearrange for elimination x^2 - y = 3 8x - y = 18 --------------Subtraction eliminates y, find x x^2 - 8x = -15 A quadratic equation x^2 - 8x + 15 = 0 Factors to (x-3)(x-5) = 0 two solution x = 3, x = 5 : Find y using x=3 in the 2nd equation 8(3) - y = 18 24 - y = 18 y = 6 and Find y using x=5 in the 2nd equation 8(5) - y = 18 40 - y = 18 y = 22 : Solutions: 3,6 and 5,22 : You should check both solutions in the 2nd equation
 Quadratic_Equations/633297: write a quadratic equation in standard form having the given solutions 4i,-4i1 solutions Answer 398784 by ankor@dixie-net.com(15661)   on 2012-07-30 18:08:25 (Show Source): You can put this solution on YOUR website!write a quadratic equation in standard form having the given solutions 4i,-4i x = +/-4i x^2 = 16(i^2) x^2 = 16(-1) x^2 = -16 x^2 + 16 = 0 y = x^2 + 16; is the standard form
 Exponential-and-logarithmic-functions/633093: Near Three Rivers, NM, there is an archaeological site containing petroglyphs. In 1998, archaeologists found that the amount of carbon-14 in the petroglyphs was 88.5%. Determine the approximate age of the petroglyphs. Show the carbon-14 dating model for the age of the petroglyphs and define variables. Explain how you found your answer. There are directions for how to type math characters in the Resource Center that will show you show to enter exponents and fractions. 1 solutions Answer 398782 by ankor@dixie-net.com(15661)   on 2012-07-30 17:56:55 (Show Source): You can put this solution on YOUR website!In 1998, archaeologists found that the amount of carbon-14 in the petroglyphs was 88.5%. Determine the approximate age of the petroglyphs. Show the carbon-14 dating model for the age of the petroglyphs : Radio active decay formula A = Ao(2^(-t/h), where: A = remaining amt after t years Ao = initial amt t=0 t = time in yrs h = half-life of substance t = time of decay : A = .885 Ao = 1 h = 5730, the half life of carbon-14 : 1*2^(-t/5730) = .885 using nat logs *ln(2) = ln(.885) = = -.17625 t = -5730 * -.17625 t = 1010 years is the age of the petro-whatevers
 test/633261: If the total cost of x apple is b cents, what is a general formula for the cost, in cents of y apple 1 solutions Answer 398773 by ankor@dixie-net.com(15661)   on 2012-07-30 16:46:19 (Show Source): You can put this solution on YOUR website!If the total cost of x apples is b cents, what is a general formula for the cost, in cents of y apples : each apple will cost cents therefore y* = cents for y apples
 �t�e�s�t/633083: Specify any values that must be excluded from the solution set, and then solve the equation. n-3/6n-6 = 1/9 - n-3/4n-4 Thanks!HELP!1 solutions Answer 398771 by ankor@dixie-net.com(15661)   on 2012-07-30 16:42:08 (Show Source): You can put this solution on YOUR website! = - We can do some factoring here = - Right here we can answer the question about excluded values You can see that n cannot = 1, as it would put zeros in the denominators : The common denominator would be 36(n-1), multiply equation by this 36(n-1)* = 36(n-1)* - 36(n-1)* Cancel the denominators and you have 6(n-3) = 4(n-1) - 9(n-3) 6n - 18 = 4n - 4 - 9n + 27 6n - 18 = -5n + 23 Combine n's on the left, numbers on the right 6n + 5n = 23 + 18 11n = 41 n = n ~ 3.73, kind of a nasty solution but it seems to check out. C
 Systems-of-equations/633177: Solve using a system of two equations and two unknowns. A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side.1 solutions Answer 398760 by ankor@dixie-net.com(15661)   on 2012-07-30 15:58:43 (Show Source): You can put this solution on YOUR website!Solve using a system of two equations and two unknowns. A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side. : Call the two sides L & W : the perimeter 2L + 2W = 28 Simplify, divide by 2 L + W = 14 L = (14-W); use this form for substitution : The hypotenuse, (diagonal) L^2 + W^2 = 10^2 L^2 + W^2 = 100 : Replace L with (14-W) (14-W)^2 + W^2 = 100 ; FOIL (14-W)*(14-W) 196 - 28W + W^2 + W^2 = 100 2W^2 - 28W + 196 - 100 = 0 : A quadratic equation 2W^2 - 28W + 96 = 0 : Simplify, divide by 2 W^2 - 14W + 48 = 0 : Factors to (W-6)(W-8) = 0 : Two solutions W = 6 and W = 8 Make W = 6 cm as the width, then L = 8 cm as the length : : Check our solution on a calc, find the hypotenuse: Results: 10
 Exponential-and-logarithmic-functions/633098: An investment of \$25,400 is placed into an account that earns 6.5% interest compounded quarterly. In how many years will the investment be worth twice the original amount? 2) Solve: log3(x+8) + log3x=2 The 3 are are at the bottom right corner. 3) log5x-log5(5-2)=log5(4) The 5 is in the bottom right corner also 4) 2^3x+1=13.41 solutions Answer 398750 by ankor@dixie-net.com(15661)   on 2012-07-30 15:26:02 (Show Source): You can put this solution on YOUR website!An investment of \$25,400 is placed into an account that earns 6.5% interest compounded quarterly. In how many years will the investment be worth twice the original amount? : How long to double, the amt doesn't matter let t = no. of yrs to double (1+)^(4t) = 2 = 2 4t = 4t = 43 t = 43/4 t = 10.75 yrs to double in value : : 2) Solve: log3(x+8) + log3(x) = 2 addition of logs is multiply log3(x(x+8)) = 2 exponent of equiv of logs x(x+8) = 3^2 x^2 + 8x = 9 a quadratic equation x^2 + 8x - 9 = 0 Factors to (x+9)(x-1) = 0 only the positive solution can be used here x = 1 : : 3) log5(x) - log5(5-2)= log5(4) log5(x) - log5(3)= log5(4) subtraction of log means divide log5 = log5(4) eliminate log5 from both sides = 4 x = 3(4) x = 12 : : 4) 2^3x+1=13.4 Assume this is = 13.4 3x + 1 = 3x + 1 = 3.744 3x = 3.744 - 1 3x = 2.744 x = x = .9147 Check this on your calc: enter 2^(3(.9147)+1), results: ~13.4
 logarithm/633103: log base x(5)=3 1 solutions Answer 398722 by ankor@dixie-net.com(15661)   on 2012-07-30 14:25:34 (Show Source): You can put this solution on YOUR website!log base x(5)=3 The exponent equiv of logs x^3 = 5 x = ; cube root of 5 x ~ 1.71