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# Recent problems solved by 'AnlytcPhil'

AnlytcPhil answered: 1275 problems
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 Divisibility_and_Prime_Numbers/15650: what is the number factorization for 36 1 solutions Answer 7937 by AnlytcPhil(1278)   on 2005-10-20 04:01:18 (Show Source): You can put this solution on YOUR website!36 = 6×6 = (2×3)×(2×3) = 2×2×3×3 = 2232 Edwin
 Radicals/15041: evaluate or simplify (27y^9)^-1/3 I am at a lost please help1 solutions Answer 7867 by AnlytcPhil(1278)   on 2005-10-18 21:01:07 (Show Source): You can put this solution on YOUR website!(27y9)-1/3 ` Write 27 as 33 ` (33y9)-1/3 ` Multiply the outer exponent -1/3 by each inner exponent: ` 3-1y-3 ` To get rid of the negative exponents move base and exponent from numerator to denominator and chaneg the sign of the exponent to + ` ` 1 ----- 31y3 ` Erase the 1 exponent ` ` 1 ----- `3y3 ` Edwin AnlytcPhil@aol.com
 absolute-value/16045: solve the problem and describe the steps you used 7 - 4c = 10c 1 solutions Answer 7866 by AnlytcPhil(1278)   on 2005-10-18 20:46:37 (Show Source): You can put this solution on YOUR website! solve the problem and describe the steps you used 7 - 4c = 10c ` ` 7 - 4c = 10c ` There are two terms on the left. They are 7 and -4c. There is one term on the right, 10c. ` We want to get rid of all terms on the left which DON'T contain c, and get rid of all terms on the right that DO contain c. ` The term 7 is on the left and does not contain c. So we get rid of it on the left by adding the opposite of 7, namely -7, to both sides of the equation: ` ` ` ` ` ` ` ` ` `7 - 4c = 10c ` ` ` ` ` ` ` `7 - 4c - 7 = 10c - 7 ` That gives ` ` ` ` `-4c = 10c - 7 ` The term 10c on the right contains c. So we get rid of it on the right by adding the opposite of 10c, namely -10c, to both sides of the equation: ` ` ` ` ` ` ` ` -4c - 10c = 10c - 7 - 10c ` That gives ` ` ` ` -14c = -7 ` Now we divide both sides of the equation by the coefficient of c on the left, which is -14: ` ` ` ` ` ` ` ` ` ` `-14c` ` `-7 ` ` ` ` ` ` ` ` ` ------ = ----- ` ` ` ` ` ` ` ` ` ` -14 ` ` -14 ` Now cancel the -14's on the left, and cancel the negative signs on the right, and get ` ` ` ` ` ` ` ` ` ` ` ` ` ` `7 ` ` ` ` ` ` ` ` ` ` ` `c = ----- ` ` ` ` ` ` ` ` ` ` ` ` ` ` 14 ` Now reduce 7/14 to 1/2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` `c = --- ` ` ` ` ` ` ` ` ` ` ` ` ` ` 2 ` Edwin AnlytcPhil@aol.com
 Functions/16043: how do you identify funktions? can you show me how to do this problem the rule: evaluate the function f(x)=3x-10 for the given value of the variable. x=-2 can you show me how to do it please!!! 1 solutions Answer 7865 by AnlytcPhil(1278)   on 2005-10-18 20:26:27 (Show Source): You can put this solution on YOUR website!can you show me how to do this problem the rule: evaluate the function f(x)=3x-10 for the given value of the variable. x=-2 can you show me how to do it please!!! ` f(x) = 3x - 10 ` Since x = -2, just replace x everywhere by -2 and simplify the right side ` f(-2) = 3(-2) - 10 ` f(-2) = -6 - 10 ` f(-2) = -16 ` That's all there is to it! ` Edwin AnlytcPhil@aol.com
 Numeric_Fractions/16018: PLEASE HELP ME W/ THIS PROBLEM. THANK YOU. REDUCE 45/75 TO LOWEST TERMS.1 solutions Answer 7864 by AnlytcPhil(1278)   on 2005-10-18 20:20:42 (Show Source): You can put this solution on YOUR website!"PLEASE HELP ME W/ THIS PROBLEM. THANK YOU. REDUCE 45/75 TO LOWEST TERMS. ` Think of a whole number smaller than the numerator 45 that will divide evenly into 45. ` I thought of 5. So write ` 45 = 5×9 ` There is no integer smaller than 5 that will divide evenly into 5. So think of a number smaller than 9 that will divide evenly into 9. ` I thought of 3. So write ` 45 = 5×9 = 5×3×3 ` Now there are no whole numbers smaller than 3 that will divide evenly into 3, so we have prime factored 45 as 5×3×3 ` Now lets do the same thing with the denominator 75. ` Think of a whole number smaller than 75 that will divide evenly into 75. ` I thought of 5. So write ` 75 = 5×15 ` There is no integer smaller than 5 that will divide evenly into 5. So think of a number smaller than 15 that will divide evenly into 15. ` I thought of 5. So write ` 75 = 5×5×3 ` Now there are no whole numbers smaller than 3 that will divide evenly into 3, so we have prime factored 75 as 5×5×3 ` So we have ` `45 ` ` 5×3×3 ---- = -------- `75 ` ` 5×5×3 ` Now we cancel the 5's ` ` ` ` ` 1 `45 ` ` 5×3×3 ---- = -------- `75 ` ` 5×5×3 ` ` ` ` 1 ` That leaves ` `45 ` ` 3×3 ---- = ----- `75 ` ` 5×3 ` Now cancel the 3's ` ` ` ` ` 1 `45 ` ` 3×3 ---- = ----- `75 ` ` 5×3 ` ` ` ` ` 1 ` That leaves ` `45 ` ` 3 ---- = --- `75 ` ` 5 ` So that's the answer, 3/5. ` Edwin
 decimal-numbers/15939: What is the answer to the equation: 10 to the zero power. Is it zero or n/a??1 solutions Answer 7853 by AnlytcPhil(1278)   on 2005-10-18 15:15:08 (Show Source): You can put this solution on YOUR website!What is the answer to the equation: 10 to the zero power. Is it zero or n/a?? ' 10 = 1, 20 = 1, 30 = 1, 2.70 = 1, 8.470 = 1, (-7)0 = 1 ` Every number raised to the zero power is 1 with one exception. ` That one exception is that 00 is not defined". ` 10 is not 0, so therefore 100 = 1 ` Edwin
 Linear-systems/15907: how do you solve this problem using substitution? X + Y-Z=3 -3X +Z=-5 X +2Y-Z=31 solutions Answer 7849 by AnlytcPhil(1278)   on 2005-10-18 15:06:41 (Show Source): You can put this solution on YOUR website! ` X +` Y - Z =` 3 -3X ` ` `+ Z = -5 ` X + 2Y - Z =` 3 ` Here are the seven steps. 1. Pick a letter. (If one of the equations has only two letters, choose the ` `letter that is missing) 2. Pick an equation that contains that letter 3. Solve for that letter in that equation. 4. Substitute what you get into any other equations that contains that letter, ` `and simplify. 5. Now you have only two equations in one unknown 6. Solve that system for the two letters they contain 7. Substitute the values of those two letters in the result of step 3. ` 1. Pick a letter. (If one of the equations has only two letters, choose the letter that is missing) ` Since the second equation, -3X +Z=-5, has no Y, we pick Y ` 2. Pick an equation that contains that letter ` I pick the first equation X + Y - Z = 3 ` 3. Solve for that letter in that equation. ` X + Y - Z = 3 ` ` ` ` Y = 3 - X + Z ` 4. Substitute what you get into any other equations that contains ` `that letter, and simplify. ` The third equation, X + 2Y - Z = 3, contains Y, so replace Y by 3-X+Z in it and simplify ` ` ` ` ` ` X + 2Y - Z = 3 X + 2(3 - X + Z) - Z = 3 `X + 6 - 2X + 2Z - Z = 3 ` ` ` ` ` ` ` -X + Z = -3 ` 5. Now you have only two equations in one unknown ` These are ` -3X + Z = -5 and -X + Z = -3 ` 6. Solve that system for the two letters they contain. ` -3X + Z = -5 `-X + Z = -3 ` Solve for Z in the second one just above, ` ` ` ` Z = -3 + X ` Substitute -3+X for Z in the first one just above ` ` ` ` `-3X + Z = -5 -3X + (-3 + X) = -5 ` `-3X - 3 + X = -5 ` ` ` ` ` `-2X = -2 ` ` ` ` ` ` `X = 1 ` Substitute 1 for X in Z = -3 + X ` Z = -3 + (1) = -3 + 1 = -2 ` 7. Substitute the values of those two letters in the result of step 3. ` Substitute 1 for X and -5 for Z in Y = 3 - X + Z ` Y = 3 - X + Z Y = 3 - (1) + (-2) Y = 3 - 1 - 2 Y = 0 ` Edwin
 Human-and-algebraic-language/15929: An empty swimming pool can be filled in 5hrs. When full, the pool can be drained in 17hrs. How long will it take to fill the empty pool if the drain is left open? 1 solutions Answer 7847 by AnlytcPhil(1278)   on 2005-10-18 14:21:52 (Show Source): You can put this solution on YOUR website!An empty swimming pool can be filled in 5hrs. When full, the pool can be drained in 17hrs. How long will it take to fill the empty pool if the drain is left open? ` Suppose it will take x hours. ` >>...An empty swimming pool can be filled in 5hrs...<< ` Translation: ` In 5 hours, 1 poolful of water goes in. In 1 hour, 1/5 of a poolful of water goes in. In x hours, x/5 of a poolful of water goes in. ` >>...the pool can be drained in 17hrs...<< ` Translation: ` In 17 hours, 1 poolful of water goes out. In 1 hour, 1/17 of a poolful of water goes out. In x hours, x/17 of a poolful of water goes out. ` In x hours: ` water coming in in x hours - water going out in x hours = 1 poolful x/5 of a poolful - x/17 or a poolful = 1 poolful ` x/5 - x/17 = 1 ` Can you solve that? If not post again. Answer 85/12 hours or 7 1/12 hours or 7 hours 5 minutes. ` Edwin
 logarithm/15933: Sonya has x amount of money. Bob has three times as much as Sonya has, less \$14.62. Write an expression, using x, that tells how much money Bob has.1 solutions Answer 7845 by AnlytcPhil(1278)   on 2005-10-18 14:01:51 (Show Source): You can put this solution on YOUR website!Sonya has x amount of money. Bob has three times as much as Sonya has, less \$14.62. Write an expression, using x, that tells how much money Bob has. ``` Sonya has x amount of money. >>...Bob has three times as much as Sonya has, less \$14.62...<< Translation: Bob's money = 3 times Sonya's money, minus \$14.62 Replace the word's "Sonya's money" by x Bob's money = 3 times x, minus \$14.62 Replace the words "3 times x" by "3x" Bob's money = 3x, minus \$14.62 Replace the word "minus" by a minus sign Bob's money = 3x - \$14.62 Erase the \$ sign, since it is understood Bob's money = 3x - 14.62 Edwin ```
 Human-and-algebraic-language/15931: Some bank robbers leave town, speeding at 80mph. 15min later, the polive give chase, traveling at 90mph. How long (hrs) will it take the police to overtke the robbers? Can you explain how you get the answer?1 solutions Answer 7844 by AnlytcPhil(1278)   on 2005-10-18 13:52:22 (Show Source): You can put this solution on YOUR website!Some bank robbers leave town, speeding at 80mph. 15min later, the polive give chase, traveling at 90mph. How long (hrs) will it take the police to overtke the robbers? Can you explain how you get the answer? ' 15 minutes after robbers leave town they have traveled 1/4 hour at 80 mph, and thus have traveled 20 miles, (using D = RT = (80 mi/hr)(1/4 hr) = 20 miles.) ' So the robbers have a 20 mile lead on the cops when the cops set out. ' Since the cops are going 90 mph and the robbers are going 80 mph, the cops are gaining on the robbers by 10 mph. Therefore the cops will gain the whole 20 mile lead the robbers have on them in 2 hours, (using T = D/R = 20/10 = 2). ' Edwin AnlytcPhil@aol.com
 Age_Word_Problems/15213: The sum of Carol's and Sandy's ages is 47. In 10 years Carol will be 10 years older than Sandy was 7 years ago. Find their present ages.1 solutions Answer 7556 by AnlytcPhil(1278)   on 2005-10-13 19:00:38 (Show Source): You can put this solution on YOUR website! The sum of Carol's and Sandy's ages is 47. In 10 years Carol will be 10 years older than Sandy was 7 years ago. Find their present ages. ` The sum of Carol's and Sandy's ages (C+S) is 47. In 10 years Carol (C+10) will be 10 years older than(10 more than) Sandy was 7 years ago (S-7). ` (C+S) = 47 (C+10) = 10 more than (S-7), which means "(S-7) plus 10" ` or ` C + S = 47 C + 10 = (S - 7) + 10 ` Can you solve this system, after simplifying the second one? ` Answer: Carol is 20 and Sandy is 27 ` Edwin
 Linear-equations/14032: How do I write an equation that corresponds to the given inequality? example: y<4 Thank You 1 solutions Answer 7048 by AnlytcPhil(1278)   on 2005-10-05 17:43:21 (Show Source): You can put this solution on YOUR website!How do I write an equation that corresponds to the given inequality? example: ` y < 4 ` Thank You ` The left side is y, the right side in 4 ` Since the left side is LESS THAN the right side, you must add a positive number to the left side to make it equal to the right side. ` This positive number is often called a "slack variable", because it takes up the slack between the smaller left side and the larger right side. ` Let this positive number be represented by " s ". Then ` y + s = 4 ` Edwin
 Quadratic_Equations/14028: Find all solutions of the equations. 1. x6 - 64 = 0 2. 9x4 - 24x3 + 16x2 = 0 1 solutions Answer 7046 by AnlytcPhil(1278)   on 2005-10-05 17:35:29 (Show Source): You can put this solution on YOUR website! Find all solutions of the equations. 1. ` x6 - 64 = 0 ` First factor as the difference of squares. ` (x3)2 - 82 = 0 ` (x3 - 8)(x3 + 8) = 0 ` Next factor these two parenthetical expressiona as the difference and sum respectively of two cubes ` (x3 - 23)(x3 + 23) = 0 ` (x - 2)(x2 + 2x + 4)(x + 2)(x2 - 2x + 4) = 0 ` Set each of the four factors = 0 ` x - 2 = 0, solving gives x = 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` _ x2 + 2x + 4 = 0, solving by the quadratic formula gives x = -1±Ö3 ` x + 2 = 0, solving gives x = -2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `_ x2 - 2x + 4 = 0, solving by the quadratic formula gives x = 1±Ö3 ` ----------------------------------------------- ` 2. ` 9x4 - 24x3 + 16x2 = 0 ` Factor out x2 ` x2(9x2 - 24x + 16) = 0 ` Factor the expression in parentheses ` x2(3x - 4)(3x - 4) = 0 ` x2(3x -4)2 = 0 ` Set each factor equal to 0 ` x2 = 0 gives x = 0 ` (3x - 4)2 = 0, gives x = 4/3 ` Edwin
 percentage/14029: When constructing a circle ("pie") graph, how do you find the number of degrees the central angle should be which represents a certain percent of the total?1 solutions Answer 7042 by AnlytcPhil(1278)   on 2005-10-05 17:09:53 (Show Source): You can put this solution on YOUR website!When constructing a circle ("pie") graph, how do you find the number of degrees the central angle should be which represents a certain percent of the total? ` Answer: ` 1. Change the percent to a decimal, by moving the decimal point two places left and removing the "%" sign ` 2. Multiply this decimal by 360°. ` Edwin
 Polynomials-and-rational-expressions/12375: A, B, and C can finish a job in 6 days. If B and C work together, the job will take 9 days; if A and C work together, the job will take 8 days. How many days will it take each man to do the job alone? A. A in 9 days, B in 1 day, and C in 8 days B. A in 25 days, B in 12 2/3 day, and C in 28 days C. A in 20 1/2 days, B in 16 day, and C in 25 days D. A in 18 days, B in 24 day, and C in 14 2/5 days I don't have a clue where to begin with this problem. I would appreciate any help--thanks1 solutions Answer 6337 by AnlytcPhil(1278)   on 2005-09-24 12:12:44 (Show Source): You can put this solution on YOUR website!``` A, B, and C can finish a job in 6 days. If B and C work together, the job will take 9 days; if A and C work together, the job will take 8 days. How many days will it take each man to do the job alone? A. A in 9 days, B in 1 day, and C in 8 days B. A in 25 days, B in 12 2/3 day, and C in 28 days C. A in 20 1/2 days, B in 16 day, and C in 25 days D. A in 18 days, B in 24 day, and C in 14 2/5 days I don't have a clue where to begin with this problem. I would appreciate any help--thanks Let x = the number of days it would take A to do 1 job alone. Let y = the number of days it would take B to do 1 job alone. Let z = the number of days it would take C to do 1 job alone. Make this chart: Number of jobs | Rate(jobs/days) | Time(days) A alone | | B alone | | C alone | | A,B,& C | | B & C only | | A & C only | | In each case 1 job was done, so fill in 1 for each of the numbers of jobs Number of jobs | Rate(jobs/days) | Time(days) A alone 1 | | B alone 1 | | C alone 1 | | A,B,& C 1 | | B & C only 1 | | A & C only 1 | | Now fill in the times (numbers of days. Number of jobs | Rate(jobs/day) | Time(days) A alone 1 | 1/x | x B alone 1 | 1/y | y C alone 1 | 1/z | z A,B,& C 1 | 1/6 | 6 B & C only 1 | 1/9 | 9 A & C only 1 | 1/8 | 8 Now fill in the rates using rate = (jobs done)/(time) The rate for A,B,& C equals the sum of their individual rates, which must equal 1/6, so 1/x + 1/y + 1/z = 1/6 The rate for A & C equals the sum of their individual rates, which must equal 1/8, so 1/x + 1/z = 1/8 The rate for B & C equals the sum of their individual rates, which must equal 1/9, so 1/y + 1/z = 1/9 So we have this system of equations: 1/x + 1/y + 1/z = 1/6 1/x + 1/z = 1/8 1/y + 1/z = 1/9 Don't clear of fractions, but solve for 1/x, 1/y, and 1/z. Can you do this system? If not, post again and ask how to solve it. You'll get 1/x = 1/18, 1/y = 1/24, and 1/z = 5/72, which means x = 18 days, y = 24 days, z = 72/5 or 14 2/5 days, and the correct choice is D. Edwin ```
 Systems-of-equations/12428: please help me solve this problem. Solve the system using any algebraic method x + y + 2z =5 x + 2y + z = 8 2x + 3y - z = 1 Thanks for helping me solve this problem. KAt 1 solutions Answer 6329 by AnlytcPhil(1278)   on 2005-09-24 10:39:19 (Show Source): You can put this solution on YOUR website! `x +` y + 2z = 5 `x + 2y +` z = 8 2x + 3y -` z = 1 ` One way is to eliminate the three lower left terms, the ones I have colored red: ` `x +` y + 2z = 5 `x + 2y +` z = 8 2x + 3y -` z = 1 ` Instead of solving yours, I'll solve one just like it, OK? Then you can use it as a model to solve yours. ` `x - 3y + 4z =` 45 3x + 2y - 5z = -21 4x + 5y - 3z = -32 ` `x - 3y + 4z = `45 3x + 2y - 5z = -21 4x + 5y - 3z = -32 ` To get rid of the 3x, multiply the top equation by -3 and add it to 1 times the middle equation, but restore the top equation: ` -3[ x - 3y + 4z =` 45] `1[3x + 2y - 5z = -21] ` `4x + 5y - 3z = -32 ` `x - 3y +` 4z = ` 45 ` ` 11y - 17z = -156 4x + 5y -` 3z =` -32 ` To get rid of the 4x, multiply the top equation by -4 and add it to 1 times the bottom equation, but again restore the top equation: ` -4[ x - 3y +` 4z = ` 45] ` ` ` `11y - 17z = -156 `1[4x + 5y - `3z = `-32] ` x - 3y + `4z = ` 45 ` `11y - 17z = -156 ` `17y - 19z = -212 ` To get rid of the last one, 17y, multiply the middle equation by -17 and add it to 11 times the bottom equation, but restore the middle equation: ` ` ` x - 3y + 4z = ` 45 -17[ ` 11y - 17z = -156 `11[ ` 17y - 19z = -212 ` x - 3y + `4z = ` 45 `` 11y - 17z = -156 ` ` ` ` `80z = 320 ` Now that those three bottom left terms have been eliminated, solve the bottom equation: ` ` ` ` ` `80z = 320 ` ` ` ` ` `z = 4 ` Substitute z=4 into the middle equation and solve for y ` `11y - 17(4) = -156 ` ` 11y - 68 = -156 ` ` ` ` `11y = -88 ` ` ` ` ` `y = -8 ` Fimally substitute z=4 and y=-8 into the top equation and solve for x: ` x - 3(-8) + 4(4) = 45 ` ` `x + 24 + 16 = 45 ` ` ` ` ` x + 40 = 45 ` ` ` ` ` ` ` `x = 5 ` So the solution is (x, y, z) = (5, -8, 4) ` Now use this as a model to solve yours by. The solution is ` (x, y, z) = (-7, 6, 3) Edwin
 Quadratic_Equations/12429: Question: x²+y²=13 2x+y=1 I then tried to solve by substitution: y=1-2x x²+(1-2x)²=13 I then got a bit muddled up and wasn't sure how to expand (1-2x)² But the answer i got would not factorise into two brackets so i decided to use the quadratic formula: -b+/- sqrt ...... but this did not get the correct answer of: x=-1.2, y=3.4 x=2, y=-3 Please help me because i don't have a clue what to do next!1 solutions Answer 6328 by AnlytcPhil(1278)   on 2005-09-24 09:39:55 (Show Source): You can put this solution on YOUR website!x²+y²=13 2x+y=1 I then tried to solve by substitution: y=1-2x x²+(1-2x)²=13 I then got a bit muddled up and wasn't sure how to expand (1-2x)² ----------- Then you went astray. To expand (1-2x)², write it as (1-2x) multiplied by itself: ` (1-2x)² = (1-2x)(1-2x) ` Now use "FOIL" on that. You'll eventually end up with a quadratic equation which can be solved by factoring. You'll get two answers for x, and then you'll substitute each of these into y=1-2x to get the corresponding values for y. ` If you still have trouble post again. I'll give you the answers: ` There are two solutions ` (2, -3) and (-6/5, 17/5) ` Edwin
 Unit_Conversion_Word_Problems/9397: If traveling on a bicycle at 20mph for 12 miles what is the total time spent traveling, and what is the proper formula used to compute this?1 solutions Answer 5116 by AnlytcPhil(1278)   on 2005-09-02 16:01:38 (Show Source): You can put this solution on YOUR website!```If traveling on a bicycle at 20mph for 12 miles what is the total time spent traveling, and what is the proper formula used to compute this? The proper formula is TIME = DISTANCE/RATE or T = D/R Substitute 12 miles for the distance D and 20mph for the rate R. You should get T = 3/5 of an hour, or 36 minutes. Edwin ```
 Inequalities/9306: THE PRODUCT OF A NUMBER AND SIX IS TEN LESS THAN SIXTY1 solutions Answer 5017 by AnlytcPhil(1278)   on 2005-09-01 18:55:32 (Show Source): You can put this solution on YOUR website!``` THE PRODUCT OF A NUMBER AND SIX IS TEN LESS THAN SIXTY (THE PRODUCT OF A NUMBER AND SIX) IS (TEN LESS THAN SIXTY) (THE PRODUCT OF N AND SIX) IS (TEN LESS THAN SIXTY) (THE PRODUCT OF N AND 6 ) = (10 LESS THAN 60 ) ( N TIMES 6 ) = (10 LESS THAN 60 ) ( 6N ) = ( 60 MINUS 10 ) ( 6N ) = ( 60 - 10 ) ( 6N ) = ( 50 ) 6N = 50 6N = 50 6N/6 = 50/6 N = 25/3 Edwin ```
 Equations/8359: Please help me solve this equation: m + 18 = -91 solutions Answer 4620 by AnlytcPhil(1278)   on 2005-08-25 16:36:26 (Show Source): You can put this solution on YOUR website!```>>Please help me solve this equation: m + 18 = -9<< m + 18 = -9 An equation is like a balance scale. If you perform a mathematical operation to one side of the equation, then you must perform the same mathematical operation to the other side. The left side is m + 18 We wish there were only the letter m on the left side and nothing else. We wish the + 18 weren't there. So we need to get rid of the + 18. The only thing that we can use to get rid of the + 18 is - 18 so we insert - 18 after the + 18 and that makes the left side become m + 18 - 18 However since we put - 18 at the end of the left side, we have no choice but to also put - 18 at the end of the right side too! That will make the right side becoms -9 - 18 So here are the steps so far: m + 18 = -9 m + 18 - 18 = -9 - 18 Now the + 18 - 18 on the left is just 0, so we can just erase the + 18 - 18 on the left and get m = -9 - 18 Now the right side is -9 - 18 and that is -27, so the last step is m = -27 So altogether here are the steps as you should show them on your paper: m + 18 = -9 m + 18 - 18 = -9 - 18 m = -27 That is the solution. Now we check it: m + 18 = -9 Replace m by -27 -27 + 18 = -9 -9 = -9 Since both sides of the equation are the same we know the answer is correct. Edwin ```
 Complex_Numbers/8200: Could someone please help me out with this one? I am suppose to evaluate this expression if a= -2, b = 5, c = -4, and d = 6 b^2 - 2bc+c^2 = Here is what I have tried but it really looks wrong to me. 5^ - 2(5)(-4)+ -4^2 = and now I can't even figure out the answer to this. So I know there has to be a better way and I am hoping someone can show me. Thanks 1 solutions Answer 4517 by AnlytcPhil(1278)   on 2005-08-24 14:56:15 (Show Source): You can put this solution on YOUR website!Could someone please help me out with this one? I am suppose to evaluate this expression if a= -2, b = 5, c = -4, and d = 6 ` b^2 - 2bc+c^2 = ` Here is what I have tried but it really looks wrong to me. 5^ - 2(5)(-4)+ -4^2 = and now I can't even figure out the answer to this. So I know there has to be a better way and I am hoping someone can show me. Thanks ` b2 - 2bc + c2 ` Put (5) in place of b ` (5)2 - 2(5)c + c2 ` Put (-4) in place of c ` (5)2 - 2(5)(-4) + (-4)2 ` Replace (5)2 by 25 ` 25 - 2(5)(-4) + (-4)2 ` Replace - 2(5)(-4) by + 40 ` 25 + 40 + (-4)2 ` Replace + (-4)2 by + 16 ` 25 + 40 + 16 ` Replace 25 + 40 by 65 ` 65 + 16 ` Replace 65 + 16 by 81 ` 81 ` Edwin
 Trigonometry-basics/8198: if given a right triangle with the bottom line length being 8, and the hypotenuse bieng 15 how can i find the top angle (angle x) x* l\ l-\ l--\ l---\ l----\ l-----\)))))15 hope the drawing helps :) l------\ l-------\ l_-------\ l_l____\ ))))))81 solutions Answer 4516 by AnlytcPhil(1278)   on 2005-08-24 14:41:38 (Show Source): You can put this solution on YOUR website!if given a right triangle with the bottom line length being 8, and the hypotenuse being 15 how can i find the top angle (angle x). ` The bottom side 8 is the side OPPOSITE the top angle (angle x) ` The HYPOTENUSE = 15 ` sin(x) = (OPPOSITE SIDE)/(HYPOTENUSE) ` sin(x) = 8/15 ` Now making sure calculator is in DEGREE mode, enter ` sin-1(8/15) ` read 32.23095264 ` So the top angle, x = 32.23°, rounded to the nearest hundredths of a degree. ` Edwin
 Graphs/8199: help me solve for y (x-1)^2 + y^2 = 11 solutions Answer 4515 by AnlytcPhil(1278)   on 2005-08-24 14:22:39 (Show Source): You can put this solution on YOUR website!help me solve for y ` ` ` ` ` (x-1)2 + y2 = 1 ` Subtract (x-1)2 from both sides ` ` ` ` ` `y2 = 1 - (x-1)2 Write 1 as 12 ` ` ` ` ` `y2 = 12 - (x-1)2 ` The right side will factor as the difference of two squares: ` ` ` ` ` `y2 = [1 - (x-1)][1 + (x-1)] ` Remove inner parentheses ` ` ` ` ` `y2 = [1 - x + 1)(1 + x - 1] ` Combine like terms ` ` ` ` ` `y2 = [2 - x][x] ` Rewrite with short factor first ` ` ` ` ` `y2 = x(2-x) ` Take square roots of both sides, remembering ± on the right ` ` ` ` ` ` ` ` ______ ` ` ` ` ` y = ±Öx(2-x) ` Edwin
 Linear-equations/7935: Here is my equation : A(M+N)=BN-4m This is what I have so far: -BN+AN=-AM-4M Is this right? If so what's next?1 solutions Answer 4342 by AnlytcPhil(1278)   on 2005-08-21 21:33:40 (Show Source): You can put this solution on YOUR website!>>Here is my equation : A(M+N)=BN-4M This is what I have so far: -BN+AN=-AM-4M Is this right? If so what's next?<< ` We have to know whether you are solving for A, M, or N. You forgot to tell us which of the three letters you are supposed to solve for. It looks as though you are solving for N since you got all the terms with N on the left side, so I'll assume you are solving for N ` A(M+N) = BN-4M ` `AM+AN = BN-4M ` -BN+AN = -AM-4M (this is what you have so far) ` Next step is to factor out N on the left side: ` N(-B+A) = -AM-4M ` Now we divide both sides by the parenthetical expression (-B+A) ` N(-B+A) ` `-AM-4M -------- = ------- `(-B+A)` ` `(-B+A) ` Now we can cancel the (-B+A)'s on the left ` N(-B+A) ` `-AM-4M -------- = ------- `(-B+A) ` ` (-B+A) ` ` ` -AM-4M N = ------- ` ` `(-B+A) ` This will do for an answer. However we like to see if we can make the answer look simpler. Factor -M out of the numerator ` ` ` -M(A+4) N = ------- ` ` `(-B+A) ` We can dispense with the parentheses in the denominator: ` ` ` -M(A+4) N = ------- ` ` ` -B+A ` Next factor -1 out of the denominator ` To understand how to do this, place 1's in front of the letters in the denominator ` ` ` `-M(A+4) N = --------- ` ` `-1B+1A ` Now it's easy to see how to factor -1 out of the denominator: ` ` ` -M(A+4) N = ------- ` ` -1(B-A) ` We can now cancel the negative signs ` ` ` `M(A+4) N = ------- ` ` `1(B-A) ` We don't need the 1 or the parentheses around the B-A ` ` ` `M(A+4) N = ------- ` ` ` B-A ` This could be the simplest form, or you could remove the parentheses in the numerator and have ` ` ` `MA+4M N = ------- ` ` ` B-A ` One of these last two forms should be identical to the answer given in your book. ` Edwin
 Square-cubic-other-roots/6305: simplify: sqrt 81c^5d^41 solutions Answer 4087 by AnlytcPhil(1278)   on 2005-08-16 13:46:15 (Show Source): You can put this solution on YOUR website!simplify: `______ Ö81c5d4 ` Prime factor 81 = 9·9 = 3·3·3·3 Prime factor c5 = c·c·c·c·c Prime factor d4 = d·d·d·d `______ Ö81c5d4 = `_________________________ Ö3·3·3·3·c·c·c·c·c·d·d·d·d = `_____________________________________ Ö(3·3)·(3·3)·(c·c)·(c·c)·c·(d·d)·(d·d) = `_______________________________ Ö(32)·(32)·(c2)·(c2)·c·(d2)·(d2) = `__ `__` __`__ `_` __` __ Ö32·Ö32·Öc2·Öc2·Öc·Öd2·Öd2 = ` ` ` ` ` ` ` ` `_ `3 · 3 · c · c ·Öc· d · d = ` ` ``_ 9·c2·Öc·d2 ` ` ` _ 9c2d2Öc ` Edwin
 real-numbers/7352: Tom's father is three times as old as Tom. Four years ago Tom's father was four times as old as Tom. How old is Tom?1 solutions Answer 4086 by AnlytcPhil(1278)   on 2005-08-16 13:12:55 (Show Source): You can put this solution on YOUR website!Tom's father is three times as old as Tom. Four years ago Tom's father was four times as old as Tom. How old is Tom? ``` Let: Tom's age now = T >>...Tom's father is three times as old as Tom...<< TRANSLATION: Tom's father's age now = 3T Then Tom's age four years ago = T-4 and Tom's father's age four years ago = 3T-4 >>... Four years ago Tom's father was four times as old as Tom...<< TRANSLATION: Tom's father's age four years ago = 4 times Tom's age 4 years ago 3T-4 = 4(T-4) 3T-4 = 4T-16 3T-4T = 4-16 -T = -12 T = 12 Check: Tom is 12 years old. His father is 3 times as old as Tom, or 36. Four years ago, Tom was 8 and his father was 32. So indeed Tom's father was four times as old as Tom was then. Edwin ```
 Travel_Word_Problems/7353: Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together1 solutions Answer 4085 by AnlytcPhil(1278)   on 2005-08-16 12:54:54 (Show Source): You can put this solution on YOUR website!Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together. ``` What we need is this equation: Jim's rate + Sue's rate + Tony's rate = their combined rate >>...How quickly can all three fill the pool together...<< Let the time be x minutes. THEREFORE their combined rate = 1 pool per x minutes or their combined rate = 1/x pool per minute >>...Jim can fill a pool...in 30 minutes...<< TRANSLATION: Jim's rate is 1 pool per 30 minutes or Jim's rate = 1/30 pool per minute >>...Sue can do the same job in 45 minutes...<< TRANSLATION: Sue's rate is 1 pool per 45 minutes or Sue's rate = 1/45 pool per minute >>...Tony can do the same job in 1 ½ hours.,,<< TRANSLATION: Tony's rate is 1 pool per 1½ hour Tony's rate is 1 pool per 90 minutes Tony's rate = 1/90 pool per minute Now Jim's rate + Sue's rate + Tony's rate = their combined rate becomes 1/30 + 1/45 + 1/90 = 1/x Get the LCD of all the denominators 30, 45, 90, and x, which is 90x. Multiply through by 90x (90x)(1/30) + (90x)(1/45) + (90x)(1/90) = (90x)(1/x) 3x + 2x + x = 90 6x = 90 x = 90/6 x = 15 minutes Edwin ```
 Travel_Word_Problems/7354: John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time? 1 solutions Answer 4084 by AnlytcPhil(1278)   on 2005-08-16 12:20:29 (Show Source): You can put this solution on YOUR website!John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time? ` Learn these three equivalent equations: ` DISTANCE = RATE × TIME ` RATE = DISTANCE/TIME ` TIME = DISTANCE/RATE ` You are asked "how fast". That's asking for a RATE, so use the middle one above. ` RATE = DISTANCE/TIME ` The distance = 28 miles and the time = 30 minutes or .5 hour. ` RATE = 28 miles/(.5 hour) = 28/(.5) miles/hour = 56 miles/hour. ` Edwin
 Money_Word_Problems/6356: A=\$6000 P= \$1000 interest is 12% compounded quarterly Find # of interest periods1 solutions Answer 3407 by AnlytcPhil(1278)   on 2005-08-01 09:50:30 (Show Source): You can put this solution on YOUR website!A=\$6000 P= \$1000 interest is 12% compounded quarterly Find # of interest periods ` The formula is ` A = P(1+r/n)nt ` Where ` A = ending amount = 6000 P = beginning amount = 1000 r = annual rate expressed as a decimal = .12 n = number of interest periods per year = 4 ` ` (since it's quarterly) t = number of years (which we find first) ` A = P(1+r/n)nt ` Taking logs of both sides ` logA = log[P(1+r/n)nt] ` logA = logP + log(1+r/n)nt ` logA = logP + nt[log(1+r/n)] ` logP + nt[log(1+r/n)] = logA ` nt[log(1+r/n)] = logA - logP ` nt[log(1+r/n)] `` logA - logP -------------- = ------------- `n[log(1+r/n)] ` n[log(1+r/n)] ` nt[log(1+r/n)] `` logA - logP -------------- = ------------- `n[log(1+r/n)] ` n[log(1+r/n)] ` ` ` ` ` ` ` ` ``` logA - logP ` ` ` ` ` ` `t = ------------- ` ` ` ` ` ` ` `` n[log(1+r/n)] ` ` ` ` ` ` ` ` ``` log6000 - log1000 ` ` ` ` ` ` `t = -------------------- ` ` ` ` ` ` ` ` ` `4[log(1+.12/4)] ` ` ` ` ` ` ` ` ``` 3.77815125 - 3 ` ` ` ` ` ` `t = -------------------- ` ` ` ` ` ` ` ` ` `4[log(1.03)] ` ` ` ` ` ` ` ` `` ` .7781512504 ` ` ` ` ` ` `t = --------------- ` ` ` ` ` ` ` ` ` `.0513488988 ` ` ` ` ` ` ` ` `` ` .77815125 ` ` ` ` ` ` `t = --------------- ` ` ` ` ` ` ` ` ` `.0513488988 ` ` ` ` ` ` ` `t = 15.15419548 years ` Multiply by 4 to get the number of interest periods ` Answer = 60.61678192 which means that 60 interest periods will yield slightly less that \$6000, or \$5891.60 and 61 interest period will yield slightly more than \$6000, or \$6068.40. ` Edwin J
 Linear-equations/6348: please help me solve this. write an equation of a line given (x1,y1)=(12,7) and (x2,y2)=(-4,5) 1 solutions Answer 3404 by AnlytcPhil(1278)   on 2005-08-01 07:51:08 (Show Source): You can put this solution on YOUR website!write an equation of a line given (x1,y1)=(12,7) and (x2,y2)=(-4,5) Now use That will do as a final answer if you only want the slope-intercept form, or, you can multiply through by 8 and get rid of fractions and to get it in standard form Ax + By = C and since the standard form requires that A be positive, we multiply thru by -1 Edwin
 Travel_Word_Problems/6314: Your help is greatly appreciated. Here is my problem: A boy can drive a motorboat 45 miles downstream in the same amount of time that he can drive 27 miles upstream. What is the speed of the current in the river if the speed of the boat in still water is 12 mph1 solutions Answer 3392 by AnlytcPhil(1278)   on 2005-07-31 20:02:14 (Show Source): You can put this solution on YOUR website!A boy can drive a motorboat 45 miles downstream in the same amount of time that he can drive 27 miles upstream. What is the speed of the current in the river if the speed of the boat in still water is 12 mph. ` Let x = the speed of the current. Make a DRT chart ` ` ` ` ` ` `|`Distance | Rate `| ` Time ` downstream | ` ` ` ` `|` ` ` `| ` ` ` `` upstream ` | ` ` ` ` `|` ` ` `| ` ` ` `` ` Fill in the given distances ` ` ` ` ` ` `|`Distance | Rate `|` ` Time ` downstream | ` `45 ` `|` ` ` `|` ` ` ` `` upstream ` | ` `27 ` `|` ` ` `|` ` ` ` `` ` Now fill in the rates. The rate downstream is the sum of the rate of the boat if in still water + the rate of the current, or 12+x. The rate upstream is the difference of the rate of the boat if in still water - the rate of the current, or 12-x. ` ` ` ` ` ` `|`Distance | Rate `|` ` Time ` downstream | ` `45 ` `|`12+x `|` ` ` ` `` upstream ` | ` `27 ` `|`12-x `|` ` ` ` `` ` Now fill in the times using Time = Distance/Rate ` ` ` ` ` ` `|`Distance | Rate `|` ` Time ` downstream | ` `45 ` `|`12+x `| 45/(12+x) upstream ` | ` `27 ` `|`12-x `| 27/(12-x) ` >>...downstream in the same amount of time...upstream...<< ` The key words are "same amount of time". "Same" means "equal", so we set the two times equal to each other ` ` ` ` ` ` ` ` ` ` ` Can you solve this equation? If not post again. ` ` ` ` ` ` ` ` ` ` Answer: x = 3 mph. ` Checking: This means the boat never went 12 mph because there was no still water. It went 15 mph upstream and 9 mph downstream. The time to go 45 miles downstream at 15 mph was 3 hours. The time to go 27 miles upstream at 9 mph was also 3 hours. ` Edwin J