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 Expressions-with-variables/200968: please help with step by step 5x^4+2x^3 over 2x^4+3x^3 multiply by 2x^3+x^2-3x over 5x^2-3x-21 solutions Answer 151206 by jim_thompson5910(28476)   on 2009-06-23 21:57:52 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words,
 Expressions-with-variables/200969: please help with step by step 5x^2-125 over x^3+5x^2 multiply 6x^2+2x over 5x-251 solutions Answer 151205 by jim_thompson5910(28476)   on 2009-06-23 21:54:05 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. Distribute So simplifies to . In other words,
 Polynomials-and-rational-expressions/200970: please help with step by step 21x^2-49x-42 over 4x^2-28x+48 divided by 21x+14 over 8x^2-32x1 solutions Answer 151203 by jim_thompson5910(28476)   on 2009-06-23 21:49:24 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the first fraction by the reciprocal of the second fraction . Factor to get . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words,
 Functions/200946: The following function computes the cost, C (in millions of dollars), of implementing a city recycling project when x percent of the citizens participate. C(X)=1.4x/100-x a)Using the model, find the cost if 60% of the citizens participate. b)Using the model, determine the percentage of participation that can be expected if $4 million is spent on this recycling project. Set up an equation and solve algebraically. Round to the nearest whole percent. 1 solutions Answer 151174 by jim_thompson5910(28476) on 2009-06-23 16:56:55 (Show Source): You can put this solution on YOUR website!Check out this previous solution.  Average/200943: What is the average (arithmetic mean) of 8, 7, 7, 5, 3, 2, and 2? A. 3 4/7 B. 4 5/6 C. 4 6/7 D. 5 E. 6 4/5 Please show me how to this step by step.Ireally need to know.Thank you so much! 1 solutions Answer 151168 by jim_thompson5910(28476) on 2009-06-23 16:29:47 (Show Source): You can put this solution on YOUR website!Simply add up the numbers and divide that sum by 7 (since there are 7 values) So the answer is C) Note: normally the mean is represented in decimal form.  Polynomials-and-rational-expressions/200942: x/x+1 + 5/x = 1/x^2+x1 solutions Answer 151165 by jim_thompson5910(28476) on 2009-06-23 15:39:37 (Show Source): You can put this solution on YOUR website! Start with the given equation. Factor the last denominator Multiply EVERY term by the LCD to clear out the fractions. Simplify Distribute Multiply Subtract 1 from both sides. Combine like terms. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Square to get . Multiply to get Subtract from to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the possible solutions are or However, recall that , this means that the only solution is ============================================================= Answer: So the solution is  Radicals/200938: This is 5 different problems I've been having problems with for a while. 4/sqrt5 4sqrtx^12/24sqrtx^12 15sqrt8x^16/5sqrt2x^4 (3sqrt5)(2sqrt10) (2sqrtx)(5sqrtx^3)1 solutions Answer 151157 by jim_thompson5910(28476) on 2009-06-23 14:13:34 (Show Source): You can put this solution on YOUR website!I'll do the first three to get you going in the right direction. # 1 Start with the given expression. Multiply both the numerator and denominator by Combine the roots. Multiply Take the square root of 25 to get 5 So # 2 Start with the given expression. Factor 24 to get 4*6 Cancel out the common terms. Simplify Combine the roots Divide Simplify So where # 3 Start with the given expression. Factor 15 into 5*3 Cancel out the common terms. Simplify Combine the roots. Factor 8 into 4*2 Cancel out the common terms. Simplify Divide the variable terms by subtracting the exponents. Subtract Factor into note: there are 6 terms. Break up the square root using the identity . Take the square root of to get . Take the square root of to get . Multiply. ================================================== Answer: So simplifies to In other words, where Edit: The other poster is correct in saying that "x" doesn't need to be non-negative, BUT recall that . If we assume that (ie it is NOT negative), then which simplifies things greatly. If "x" can be any number, then you must include the absolute value.  Divisibility_and_Prime_Numbers/200927: How many whole numbers between 1 to 200 are divisible by 6 and not by 10 ?1 solutions Answer 151156 by jim_thompson5910(28476) on 2009-06-23 13:49:35 (Show Source): You can put this solution on YOUR website!Just list all the multiples of 6 and take off any numbers that are multiples of 10. So here are all the numbers from 1 to 200 that are are divisible by 6 and not by 10: 6, 12, 18, 24, 36, 42, 48, 54, 66, 72, 78, 84, 96, 102, 108, 114, 126, 132, 138, 144, 156, 162, 168, 174, 186, 192, 198 There are 27 numbers here.  Inequalities/200909: Solve: (5/7)<=(x-5/3)<2 1 solutions Answer 151155 by jim_thompson5910(28476) on 2009-06-23 13:32:56 (Show Source): You can put this solution on YOUR website! Start with the given compound inequality. Multiply EVERY term by the LCD to clear out any fractions. Simplify Multiply Add to all sides. Combine like terms on the left side. Combine like terms on the right side. Divide all sides by 21. Reduce. So the solution is  Exponential-and-logarithmic-functions/200907: find y' when y=ln(x+2)/(x^2+1) this problem has the big ( around all) thanks for help 1 solutions Answer 151154 by jim_thompson5910(28476) on 2009-06-23 13:27:30 (Show Source): You can put this solution on YOUR website!I'm assuming that the problem is right??? Recall that if , then In your case, , which means that and Now derive f and g to get: and Now plug these functions into the formula to get: Now multiply every term by the inner LCD x+2 and simplify you could perform more simplifications, but that would only change how the answer looks.  Linear-equations/200921: This question is from textbook Geometry given points R (-2,3) and S (5,1) find the slop of every line perpendicular to RS. please show all your work for full credit. A.Slope of RS B.Slope of Perendicular lines1 solutions Answer 151153 by jim_thompson5910(28476) on 2009-06-23 13:15:49 (Show Source): You can put this solution on YOUR website!A) Note: is the first point R and is the second point S . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get So the slope of the line that goes through the points R and S is ------------------------------------------------------------- B) Now simply flip the fraction to get . Finally, change the sign to get . So the slope of ANY perpendicular line to segment RS is  Travel_Word_Problems/200936: This question(200898) is in your data base but i am not positive if it is correct. I was told there is a answer. Could somebody else PLEASE look at this problem again and work it to verify if it is correct or wrong. I would really appreciate it..Thanks Question: A biker can travel 18 mph with no wind. The same rider can bicycle 8 mi against the wind in the same time it takes to bicycle 12 miles with the wind. What is the speed of the wind? 1 solutions Answer 151152 by jim_thompson5910(28476) on 2009-06-23 13:13:16 (Show Source): You can put this solution on YOUR website!Let w = speed of the wind (in mph) First, let's set up the equation involving the trip against the wind: Start with the distance-rate-time formula Plug in and (the wind slows him down, so you must subtract "w" from 18) Divide both sides by . Rearrange the equation ----------------------------------- Go back to the distance-rate-time formula Plug in and (the wind speeds him up, so you must add "w" to 18) Divide both sides by . Rearrange the equation ------------------------------------- Now recall that he "can bicycle 8 mi against the wind in the same time it takes to bicycle 12 miles with the wind". So this means that the times "t" are the same variable. This means that we can plug one equation into another: Start with the given equation. Plug in Cross multiply Distribute. Subtract from both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. Divide (either use a calculator or long division) ---------------------------------------------------------------------- Answer: So the solution is which means that the speed of the wind is 3.6 mph. Note: if you are expecting a whole number for an answer, I would verify that you have the correct problem written down.  Numbers_Word_Problems/200929: The number 9 can be written as the sum of 9 consecutive integers. What is the product of these 9 integers ?1 solutions Answer 151150 by jim_thompson5910(28476) on 2009-06-23 13:00:44 (Show Source): You can put this solution on YOUR website!Let x = first integer So x+1 is the next integer, x+2 is the next integer after that, etc... So because "The number 9 can be written as the sum of 9 consecutive integers", this means that Start with the given equation. Remove the parenthesis. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is which means that the first integer is -3 So the 9 consecutive integers are: -3, -2, -1, 0, 1, 2, 3, 4, 5 If you multiply them together, you'll get 0 (since 0 is being multiplied here).  Radicals/200934: what if the radical expression is not a rational expression, for example what if I had √12 + √108? How would I begin on simplifying it? Afterall, there is no denominator other than 1. 1 solutions Answer 151149 by jim_thompson5910(28476) on 2009-06-23 12:54:53 (Show Source): You can put this solution on YOUR website! Start with the given expression Simplify to get . Note: If you need help with simplifying square roots, check out this solver. Simplify to get . Since we have the common term , we can combine like terms Factor out the GCF Combine like terms. So simplifies to . In other words, You can verify this with a calculator.  Quadratic_Equations/200869: a(a+1)-3(a+1)=a+11 solutions Answer 151109 by jim_thompson5910(28476) on 2009-06-22 19:34:21 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute Subtract "a" from both sides. Subtract 1 from both sides. Combine like terms. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "a": Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the solutions are or  Quadratic_Equations/200858: This question is from textbook Elementary and Intermediate Algebra Throwing a wrench. An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The height of the wrench above the ground after t seconds is given by S(t) = -16t2 - 32t + 128. a) What is the height of the wrench after 1 second? b) How long does it take for the wrench to reach the ground? 1 solutions Answer 151105 by jim_thompson5910(28476) on 2009-06-22 18:09:15 (Show Source): You can put this solution on YOUR website!a) Start with the given function. Plug in . Square to get . Multiply and to get . Multiply and to get . Combine like terms. So the wrench is 80 feet in the air after 1 second. ----------------------------------------------------------------------- b) Start with the given function. Plug in (ie make the height equal to zero). Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "t": Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the possible solutions are or But remember that a negative time value doesn't make much sense. So we'll ignore So the only solution is which means that it takes 2 seconds for the wrench to hit the ground.  Expressions-with-variables/200859: In writing out an answer, for example: m more than nineteen. Will it be the variable first or the number? Is their a rule when putting which first?1 solutions Answer 151103 by jim_thompson5910(28476) on 2009-06-22 18:07:55 (Show Source): You can put this solution on YOUR website!There isn't a rule, but it's conventional to place the variable first like so . Why? Well later you'll learn about polynomials and you'll find that the constant terms are placed last. Note: the expression is the exact same expression (ie for all values of "m").  Radicals/200827: Please walk me through each step in solving this problem: Square root of 25x - 25 minus square root of 9x-9. (Sorry, I cannot product the square root symbol). They say the answer is 2times square root of x-11 solutions Answer 151087 by jim_thompson5910(28476) on 2009-06-22 14:08:06 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor out the GCF 25 from the first radicand Factor out the GCF 9 from the second radicand Break up the roots using the identity Take the square root of 25 to get 5 Take the square root of 9 to get 3 Factor out the GCF Combine like terms. So where  Radicals/200828: Please walk me through each step in solving this problem: Simplify by collecting like radical terms, if possible: 3times the cube root of y^5 + 4 times cube root of y^2 + cube root of 8y^6. They say the answer is (3y+4)times cube root of y^2 + 2y^2. Sorry I cannor provide the symbol for square root.1 solutions Answer 151086 by jim_thompson5910(28476) on 2009-06-22 14:04:35 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite 8 as Rewrite as Rewrite as Break up the roots using the identity Evaluate the cube root of to get 2 Evaluate the cube root of to get "y" Multiply Factor out the from the first two terms. note: this step isn't necessary, but your book does it. ======================================================= Answer: So simplifies to In other words, Polynomials-and-rational-expressions/200829: Divide: (x^3-2x^2+8) / (x+2) 1 solutions Answer 151085 by jim_thompson5910(28476) on 2009-06-22 13:54:52 (Show Source): You can put this solution on YOUR website! Let's simplify this expression using synthetic division Start with the given expression First lets find our test zero: Set the denominator equal to zero Solve for x. so our test zero is -2 Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.(note: remember if a polynomial goes from to there is a zero coefficient for . This is simply because really looks like  -2 | 1 -2 0 8 | Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)  -2 | 1 -2 0 8 | 1 Multiply -2 by 1 and place the product (which is -2) right underneath the second coefficient (which is -2)  -2 | 1 -2 0 8 | -2 1 Add -2 and -2 to get -4. Place the sum right underneath -2.  -2 | 1 -2 0 8 | -2 1 -4 Multiply -2 by -4 and place the product (which is 8) right underneath the third coefficient (which is 0)  -2 | 1 -2 0 8 | -2 8 1 -4 Add 8 and 0 to get 8. Place the sum right underneath 8.  -2 | 1 -2 0 8 | -2 8 1 -4 8 Multiply -2 by 8 and place the product (which is -16) right underneath the fourth coefficient (which is 8)  -2 | 1 -2 0 8 | -2 8 -16 1 -4 8 Add -16 and 8 to get -8. Place the sum right underneath -16.  -2 | 1 -2 0 8 | -2 8 -16 1 -4 8 -8 Since the last column adds to -8, we have a remainder of -8. This means is not a factor of Now lets look at the bottom row of coefficients: The first 3 coefficients (1,-4,8) form the quotient and the last coefficient -8, is the remainder, which is placed over like this Putting this altogether, we get: So which looks like this in remainder form: remainder -8  Numbers_Word_Problems/200848: in x years from now, Robert will be k years old. How old was Robert m years ago? The possible answers are: a) x-(k+m) b) k-x c) k-x-m d) x-(k-m) e) k+m-x Thank you for helping me!1 solutions Answer 151084 by jim_thompson5910(28476) on 2009-06-22 13:52:32 (Show Source): You can put this solution on YOUR website!Let r=Robert's age right now So if "in x years from now, Robert will be k years old", this means that we simply add "x" to "r" to get "k" like so: . Now solve for "r" to get . So Robert's age right now (in terms of "k" and "x") is Now just subtract off "m" more years from to get So the answer is C) k-x-m ----------------------------------------------------------------------- Note: if this doesn't make any sense, just plug in some values. Let's say that Robert is 12 years old. So . In two years, he will be 14 (which means k=14). So this means that we'll make . Now how old was Robert 5 years ago (note: m=5) So plug in , and into to get: So he was 7 years old 5 years ago (from his current age of 12)  Linear-systems/200854: The Jurassic Zoo charges$28.00 for each adult admission and $12.00 for each child. The total bill for 254 people from a school trip was$3864.00. How many adults and how many children went to the zoo?1 solutions Answer 151082 by jim_thompson5910(28476)   on 2009-06-22 13:23:18 (Show Source): You can put this solution on YOUR website!Let a = # of adults that attended c = # of children that attended Since a total of 254 people attended, this means that . Also, because "The Jurassic Zoo charges $28.00 for each adult admission and$12.00 for each child" and "The total bill for 254 people from a school trip was \$3864.00", we know that So we have the system of equations: In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for "a", we would have to eliminate "c" (or vice versa). So lets eliminate "c". In order to do that, we need to have both "c" coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero and cancel out. So to make the "c" coefficients equal but opposite, we need to multiply both "c" coefficients by some number to get them to an equal number. So if we wanted to get 1 and 12 to some equal number, we could try to get them to the LCM 12. However, we want one number equal to 12 and the other equal to -12. Because one "c" coefficient is already equal to 12, we need to multiply both sides of the first equation by -12 (to get the "c" coefficient equal to -12). Start with the first equation. Multiply the both sides of the first equation by -12. Distribute and multiply. So we have the new system of equations: Take note that the "c" coefficients are equal but opposite. Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ============================================================================ Answer: So the solutions are and . This means that 51 adults attended and 203 children attended.