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 expressions/242940: how do you simplify (xy+ab^2)(xy-ab^2)1 solutions Answer 177957 by jim_thompson5910(28476)   on 2009-11-26 21:19:22 (Show Source): You can put this solution on YOUR website!You could use the difference of squares formula, but let's do it the long way. Start with the given expression. Now let's FOIL the expression. Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms:. Multiply the Outer terms:. Multiply the Inner terms:. Multiply the Last terms:. --------------------------------------------------- So we have the terms: , , , and Now add every term listed above to make a single expression. Now combine like terms. So FOILs to . In other words, . Note: recall that the difference of squares formula is . So you could have used this formula where in this case and
 logarithm/242934: Hello, Problem: log16^1/2. I tried solving and I got 4. What I'm not sure of is if its negative 4 or positive? I might be completly off, but learning what i have about logarithms I think I might be on the right track. Please let me know if its negative or positive, and my answer 4 is right. Thanks1 solutions Answer 177956 by jim_thompson5910(28476)   on 2009-11-26 21:16:19 (Show Source): You can put this solution on YOUR website! Start with the given expression. Use the change of base formula. Rewrite as Rewrite as Pull down the exponents using the identity Cancel out the common terms. Simplify So
 expressions/242938: can you help me simplify this problem? (x-2)(x^2-4x+3)1 solutions Answer 177953 by jim_thompson5910(28476)   on 2009-11-26 21:10:29 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Distribute. Multiply. Now combine like terms. So expands to . In other words, .
 Trigonometry-basics/242933: please help me: The range of F in F(x)=2sinx;-pi/2 HERE ARE THE POSSIBLE ANSWERS: a)-2<_F(x)<_2 b)-2<_F(x)<_0 c)F(x)<_21 solutions Answer 177946 by jim_thompson5910(28476)   on 2009-11-26 20:11:48 (Show Source): You can put this solution on YOUR website!If you graph , you get and you can see that the min y value is -2 while the max y value is 2. So the range is making the answer a) Another way you can do it is look at a table of values for 2*sin(x) and determine the max/min values.
 Equations/242931: I need to express the following problem in terms of B: a = 1/sq root of(1-B^2) I cannot figure out how to get rid of the square root since 1-b^2 simplifies to (1+B)(1-B)1 solutions Answer 177920 by jim_thompson5910(28476)   on 2009-11-26 19:13:56 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by . Divide both sides by 'a'. Square both sides. Square to get Subtract 1 from both sides. Multiply 1 by Combine the fractions. Divide both sides by -1. Distribute Take the square root of both sides. or Break up the plus/minus or Break up the square root. or Simplify the square roots in the denominator. So the solutions are: or
 logarithm/242902: Please help me solve this problem. If log(m)n=log(n)m, m not equal to n, m not equal to 1, n not equal to 1 and m.n>0, evaluate m.n. Please note (m) and (n) are subscripts (bases)1 solutions Answer 177918 by jim_thompson5910(28476)   on 2009-11-26 19:05:29 (Show Source): You can put this solution on YOUR website! Start with the given equation. Use the change of base formula on the left side. Use the change of base formula on the right side. Cross multiply Condense the terms. Get everything to one side Factor the left side using the difference of squares formula or Use the zero product property. or Get the term to the other side. or Use the identity to rewrite the right side (of the first equation) or Simplify or Now equate the arguments. Since we're told that , this means that the only solution is (which is the same as saying ) Now multiply n and m to get: . So the product of m and n is 1.
 Geometry_proofs/242906: given; CP bisects angle BCR and angle BPR prove; triangle BCP congruent to triangle RCP pls reply me back this my homework i will be waiting thank you1 solutions Answer 177915 by jim_thompson5910(28476)   on 2009-11-26 18:18:24 (Show Source): You can put this solution on YOUR website!If you draw the picture, you might get note: there's more than one way to draw it, but the idea should be the same. Here's how the proof would go:
 Exponential-and-logarithmic-functions/242917: 3^x+8=4x a. -30.551 b.30.551 c.31.721 d.29.381 I think the answer is b. please let me know1 solutions Answer 177907 by jim_thompson5910(28476)   on 2009-11-26 17:44:33 (Show Source): You can put this solution on YOUR website!If the equation is , then the approximate answer is which rounds to 30.551. So if that is the correct equation, then you have the correct answer.
 expressions/242921: If y=y3, then y3(y3-y)=1 solutions Answer 177906 by jim_thompson5910(28476)   on 2009-11-26 17:42:27 (Show Source): You can put this solution on YOUR website!If , then . So if , then
 Exponential-and-logarithmic-functions/242919: Express as a difference of logarithms log base b 5/w Is log base b 5-log base b w the answer?1 solutions Answer 177905 by jim_thompson5910(28476)   on 2009-11-26 17:41:05 (Show Source): You can put this solution on YOUR website!You are correct. Good job.
 Exponential-and-logarithmic-functions/242916: Solve the exponenetial equation 3^(1+2x)=243 a)2 b)-2 c)6 d)81 I think the answer is A Please let me know. thanks1 solutions Answer 177904 by jim_thompson5910(28476)   on 2009-11-26 17:39:36 (Show Source): You can put this solution on YOUR website!You are correct. Note how . So becomes . Equate the exponents to get and solve for 'x' to get ---> which is the answer.
 Exponential-and-logarithmic-functions/242918: simplify log base a a8 a.a^8 b.8log base a a c. 1 d.8 I chose d. Is this correct?1 solutions Answer 177903 by jim_thompson5910(28476)   on 2009-11-26 17:37:19 (Show Source): You can put this solution on YOUR website!You are correct. Recall that . So in this case, . In other words,
 Proofs/242905: How do I solve these proofs? Number one 1.~B v[(C>D)&(E>D)] 2. B&(C v E) /therefore, D Number two 1. W&(A&M) 2. (A&W)>([(N v(R v H)] 3. ~N & (~P&~H) /therefore, R Number three 1. (O&T)>(S&M) 2. R>~M 3. T&R 4. O&S /therefore, V Number 4. last one 1. F>W /therefore, (F&S)>W 1 solutions Answer 177901 by jim_thompson5910(28476)   on 2009-11-26 17:35:32 (Show Source): You can put this solution on YOUR website!# 1 1. ~B v [(C -> D) & (E -> D)] 2. B & (C v E) /therefore D -------------------------------- 3. (C v E) & B 2 Commutation 4. B 2 Simplification 5. C v E 3 Simplification 6. ~~B 4 Double Negation 7. (C -> D) & (E -> D) 1,6 Disjunctive Syllogism 8. D v D 7,5 Constructive Dilemma 9. D 8 Tautology  ============================================== # 2  1. W & (A & M) 2. (A & W) -> [N v (R v H)] 3. ~N & ( ~P & ~H ) /therefore, R ---------------------------------- 4. (W & A) & M 1 Association 5. W & A 4 Simplification 6. A & W 5 Commutation 7. N v (R v H) 2,6 Modus Ponens 8. ~N 3 Simplification 9. ( ~P & ~H ) & ~N 3 Commutation 10. ~P & ~H 9 Simplification 11. ~H & ~P 10 Commutation 12. ~H 11 Simplification 13. R v H 7,8 Disjunctive Syllogism 14. H v R 13 Commutation 15. R 14,12 Disjunctive Syllogism  ============================================== # 3 1. (O & T)>(S & M) 2. R -> ~M 3. T & R 4. O & S /therefore, V ---------------------------------- 5. R & T 3 Commutation 6. R 5 Simplification 7. O 4 Simplification 8. T 3 Simplification 9. O & T 7,8 Conjunction 10. S & M 1,9 Modus Ponens 11. M & S 10 Commutation 12. M 11 Simplification 13. ~~M 12 Double Negation 14. ~R 2,13 Modus Tollens 15. R & ~R 6,14 Conjunction 16. F 15 Contradiction 17. F v V 16 Addition 18. V 17 Tautology  note: the truth value of R & ~R is ALWAYS false (since R can't be both true and false at the same time). I'm denoting 'false' as the letter 'F'. Also, the truth value of F v V is dependent on the truth value of V (since F is a constant). So F v V is equivalent to V ============================================== # 4 1. F -> W /therefore, (F & S) -> W --------------------------------------- 2. ~F v W 1 Material Implication 3. (~F v W) v ~S 2 Addition 4. ~F v (W v ~S) 3 Association 5. ~F v (~S v W) 4 Commutation 6. (~F v ~S) v W 5 Association 7. ~(F & S) v W 6 De Morgan's Law 8. (F & S) -> W 7 Material Implication 
 Equations/242824: Solve 6y^2+5y-14=0 thank you1 solutions Answer 177792 by jim_thompson5910(28476)   on 2009-11-25 20:51:12 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "y": Start with the quadratic formula Plug in , , and 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/242799: solve the equation (3m-6)^2 + 3(3m-6)-10=0 Thank you1 solutions Answer 177767 by jim_thompson5910(28476)   on 2009-11-25 19:29:47 (Show Source): You can put this solution on YOUR website! Start with the given equation. Let Replace each '3m-6' with 'z' Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "z": Start with the quadratic formula Plug in , , and 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 in terms of z are or Since , this means that or . Solving for 'm' gets us the final solutions or
 decimal-numbers/242787: -(-3) to the third power?1 solutions Answer 177757 by jim_thompson5910(28476)   on 2009-11-25 18:34:12 (Show Source): You can put this solution on YOUR website! So
 logarithm/242790: w^2 - 3w + 5 = 01 solutions Answer 177747 by jim_thompson5910(28476)   on 2009-11-25 17:56:25 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "w": Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) or Break up the expression. So the solutions are or
 Complex_Numbers/242786: square root of p^2-3p+16 (the square root ends on top of 16)=p+11 solutions Answer 177746 by jim_thompson5910(28476)   on 2009-11-25 17:55:46 (Show Source): You can put this solution on YOUR website! Start with the given equation. Square both sides. FOIL Subtract from both sides. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Linear_Algebra/242759: solve the system for all soulutions usin any suitable method y=3x+2 and x-2y=111 solutions Answer 177713 by jim_thompson5910(28476)   on 2009-11-25 15:44:18 (Show Source): You can put this solution on YOUR website! Start with the second equation. Plug in Distribute. Combine like terms on the left side. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. Go back to the first equation. Plug in Multiply Add So the solutions are and giving us the ordered pair (-3,-7)
 Polynomials-and-rational-expressions/242760: I sent this problem earlier but after receiving a response quickly realized I entered the wrong problem, can u please help me with this one? I have no clue where to start. Thanks in advance!! Solve: (x+2)(x-2)(x+1)>0 a)the solution set is b)solution is all real numbers c)there is no solution1 solutions Answer 177712 by jim_thompson5910(28476)   on 2009-11-25 15:41:48 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Set the left side equal to zero Set each individual factor equal to zero: , or Solve for x in each case: , or So our critical values are , and Now set up a number line and plot the critical values on the number line So let's pick some test points that are near the critical values and evaluate them. Let's pick a test value that is less than (notice how it's to the left of the leftmost endpoint). This corresponds to the left most interval () So let's pick Start with the given inequality Plug in Evaluate and simplify the left side Since the inequality is false, this means that the interval does not work. So this interval is not in our solution set and we can ignore it. --------------------------------------------------------------------------------------------- Let's pick a test value that is in between and . This corresponds to the left middle interval () So let's pick Start with the given inequality Plug in Evaluate and simplify the left side Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set. So part our solution in interval notation is () --------------------------------------------------------------------------------------------- Let's pick a test value that is in between and . This corresponds to the right middle interval () So let's pick Start with the given inequality Plug in Evaluate and simplify the left side Since the inequality is false, this means that the interval does not work. So this interval is not in our solution set and we can ignore it. --------------------------------------------------------------------------------------------- Let's pick a test value that is greater than (notice how it's to the right of the rightmost endpoint). This corresponds to the right most interval () So let's pick Start with the given inequality Plug in Evaluate and simplify the left side Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set. So part our solution in interval notation is () --------------------------------------------------------------------------------------------- Summary: So the solution in interval notation is: () ()
 Polynomials-and-rational-expressions/242758: Directions are to Solve and I don't even know where to start. I thought to set the equation equal to zero, but very confused, can someone please help me?? w^2 - 7w - 18 = 01 solutions Answer 177706 by jim_thompson5910(28476)   on 2009-11-25 15:31:04 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "w": 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/242738: 3x^2+14x-24=01 solutions Answer 177703 by jim_thompson5910(28476)   on 2009-11-25 15:26:50 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 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
 Exponents-negative-and-fractional/242757: what is negative 3 to the fourth1 solutions Answer 177702 by jim_thompson5910(28476)   on 2009-11-25 15:26:00 (Show Source): You can put this solution on YOUR website! Simply put,
 Polynomials-and-rational-expressions/242743: Desperate for help, I understand how to start but I am getting very confused the answer I arrived at was 4y- 39/(y+6)(y-6), but I don't think it's right, please help!!! Perform the indicated operations and simplify: y-3/y-6-y+1/y+6+y-42/y^2-361 solutions Answer 177701 by jim_thompson5910(28476)   on 2009-11-25 15:25:08 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor the last denominator. Take note that the LCD is Multiply the first fraction by to get that denominator equal to the LCD. Multiply the second fraction by to get that denominator equal to the LCD. FOIL. Combine the fractions. Distribute. Combine like terms. Factor the numerator. Cancel out the common terms. Simplify. So where or
 Equations/242466: 6(2x+8)-5(x-7)=5x+91+x 3(3x+1)=5-5(3x-3) 2-8(x+3)<-38-3(x+8)+3x1 solutions Answer 177481 by jim_thompson5910(28476)   on 2009-11-24 15:12:40 (Show Source): You can put this solution on YOUR website!#1 Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is # 2 Start with the given equation. Distribute. Combine like terms on the right side. 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 . ---------------------------------------------------------------------- Answer: So the solution is which approximates to . # 3 Start with the given inequality. Distribute. Combine like terms on the left side. Combine like terms on the right side. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 expressions/242461: evaluate the factorial expression 409!/408!1 solutions Answer 177478 by jim_thompson5910(28476)   on 2009-11-24 14:56:57 (Show Source): You can put this solution on YOUR website!Because 409! and 408! are huge numbers, we can't directly calculate them. However, we can note that 409!=409*408! So (409!)/(408!)=(409*408!)/(408!)=409 or in short, (409!)/(408!)=409
 Polynomials-and-rational-expressions/242463: Multiply. thanks (7m + 9)(8m^2 + m + 7) 1 solutions Answer 177477 by jim_thompson5910(28476)   on 2009-11-24 14:55:02 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Distribute. Multiply. Now combine like terms. So expands to . In other words, .
 Polynomials-and-rational-expressions/242287: find the roots of 2x squared -5x+1=01 solutions Answer 177366 by jim_thompson5910(28476)   on 2009-11-23 23:07:19 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . or Break up the expression. So the solutions are or which approximate to or
 Equations/242074: how do you solve something like this 6-b=5b+30?1 solutions Answer 177226 by jim_thompson5910(28476)   on 2009-11-23 16:03:27 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 logarithm/242094: I need help on how to solve a logarithmic Equation. The question is 3 Log (base 2) x+1 = 7 When I tried putting this equation into exponential form, I got 2^7 = (x+1)^3. However, when I solved for this, I did not end up with the answer that is needed. I ended up looking up the answer in the back of the book so that i could see if i could backtrack from there, but it was simply 4. Thanks, dmc93x@yahoo.com1 solutions Answer 177224 by jim_thompson5910(28476)   on 2009-11-23 16:00:07 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract 1 from both sides. Combine like terms. Divide both sides by 3. Reduce Convert to exponential form. Square 2 to get 4. So the solution is
 Linear_Equations_And_Systems_Word_Problems/241772: The quotient of a number and 3 is 161 solutions Answer 177065 by jim_thompson5910(28476)   on 2009-11-22 18:12:50 (Show Source): You can put this solution on YOUR website!"The quotient of a number and 3 is 16" translates to . I'll let you take it from here.