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Polynomials-and-rational-expressions/197366: Perform the indicated operations and simplify. I got as an answer but do not think this is correct. 1 solutions Answer 147991 by jim_thompson5910(28598)   on 2009-05-22 16:06:36 (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 . In order to add/subtract these fractions, we need to get EVERY denominator equal to the LCD. Multiply the first fraction by FOIL Multiply the second fraction by FOIL Now that every denominator is equal, we can add/subtract the fractions. Combine the fractions. Distribute Combine like terms. Factor Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to In other words,

Quadratic_Equations/197330: Find b^2 - 4ac and the number of real solutions to equation -2x^(2)+5x-6=0 1 solutions Answer 147989 by jim_thompson5910(28598)   on 2009-05-22 15:58:54 (Show Source): You can put this solution on YOUR website! From we can see that , , and Start with the discriminant formula. Plug in , , and Square to get Multiply to get Subtract from to get Since the discriminant is less than zero, this means that there are two complex solutions. In other words, there are no real solutions.

Linear-systems/197356: Solve the following system of equations. X+9y=5 (1) X=4-9y (2) What is the solution of the system? 1 solutions Answer 147983 by jim_thompson5910(28598)   on 2009-05-22 15:25:18 (Show Source): You can put this solution on YOUR website! Start with the first equation. Plug in . Combine like terms on the left side Since the equation above is clearly NOT true, this means that there are no values of "y" that will satisfy the equation. So there are NO solutions. This means that the system is inconsistent.

Polynomials-and-rational-expressions/197362: I need help on factoring a trinomial. 1 solutions Answer 147982 by jim_thompson5910(28598)   on 2009-05-22 15:21:03 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out the GCF Now let's focus on the inner expression ------------------------------------------------------------ Looking at we can see that the first term is and the last term is where the coefficients are 1 and -48 respectively. Now multiply the first coefficient 1 and the last coefficient -48 to get -48. Now what two numbers multiply to -48 and add to the middle coefficient -2? Let's list all of the factors of -48: Factors of -48: 1,2,3,4,6,8,12,16,24,48 -1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -48 (1)*(-48) (2)*(-24) (3)*(-16) (4)*(-12) (6)*(-8) (-1)*(48) (-2)*(24) (-3)*(16) (-4)*(12) (-6)*(8) note: remember, the product of a negative and a positive number is a negative number Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2 First Number Second Number Sum 1 -48 1+(-48)=-47 2 -24 2+(-24)=-22 3 -16 3+(-16)=-13 4 -12 4+(-12)=-8 6 -8 6+(-8)=-2 -1 48 -1+48=47 -2 24 -2+24=22 -3 16 -3+16=13 -4 12 -4+12=8 -6 8 -6+8=2 From this list we can see that 6 and -8 add up to -2 and multiply to -48 Now looking at the expression , replace with (notice combines back to . So it is equivalent to ) Now let's factor by grouping: Group like terms Factor out the GCF of out of the first group. Factor out the GCF of out of the second group Since we have a common term of , we can combine like terms So factors to So this also means that factors to (since is equivalent to ) ------------------------------------------------------------ So our expression goes from and factors further to ------------------ Answer: So completely factors to

Linear-systems/197357: Solve by the substitution method 2x+5y=3 X=9-5y 1 solutions Answer 147980 by jim_thompson5910(28598)   on 2009-05-22 15:18:14 (Show Source): You can put this solution on YOUR website! Start with the given system Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute Combine like terms on the left side Subtract 18 from both sides Combine like terms on the right side Divide both sides by -5 to isolate y Divide Now that we know that , we can plug this into to find Substitute for each Multiply Subtract So our answers are and which form the ordered pair

Quadratic-relations-and-conic-sections/197361: (x-3)^2=12(y-6) circle ellipse hyperbola or parabola ??? 1 solutions Answer 147979 by jim_thompson5910(28598)   on 2009-05-22 15:15:29 (Show Source): You can put this solution on YOUR website! Take note that the equation is in the form which is the general form of a parabola. So is a parabola.

logarithm/197349: Simplify. log (subscript 6) 216^-3 1 solutions Answer 147976 by jim_thompson5910(28598)   on 2009-05-22 15:12:40 (Show Source): You can put this solution on YOUR website! ... Start with the given expression. ... Rewrite 216 as ... Multiply the exponents. ... Multiply ... Pull down the exponent. ... Evaluate the log base 6 of 6 to get 1 ... Multiply So

Linear-systems/197355: Solve the system of equations by graphing. 7x-9y=-18 9y-7x=18 Is the system consistent or inconsistent? 1 solutions Answer 147974 by jim_thompson5910(28598)   on 2009-05-22 15:05:11 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: In order to graph these equations, we must solve for y first. Let's graph the first equation: Start with the first equation. Subtract from both sides. Divide both sides by to isolate . Rearrange the terms and simplify. Now let's graph the equation: Graph of . ------------------------------------------------------------------- Now let's graph the second equation: Start with the second equation. Add to both sides. Divide both sides by to isolate . Rearrange the terms and simplify. Now let's graph the equation: Graph of . ------------------------------------------------------------------- Now let's graph the two equations together: Graph of (red). Graph of (green) From the graph, we can see that one line is right on top of the other one, which means that they intersect an infinite number of times. So there are an infinite number of solutions. This means that the system of equations is consistent and dependent.

Rational-functions/197296: solve the equation 5/1+2e^-x = 4 please help me solve the equation 1 solutions Answer 147933 by jim_thompson5910(28598)   on 2009-05-21 20:46:38 (Show Source): You can put this solution on YOUR website! Start with the given equation Multiply both sides by Distribute Subtract 4 from both sides Combine like terms. Divide both sides by 8 Rewrite as Cross multiply Take the natural log of both sides (to eliminate the base "e" and isolate "x") So the solution is which approximates to

Polynomials-and-rational-expressions/197092: This question is from textbook Algebra and Trigonometry Structure and Method book 2 I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Laws of Logarithms Simplify 4^log base 2(2^ log base 2 of 5) 1 solutions Answer 147931 by jim_thompson5910(28598)   on 2009-05-21 20:33:39 (Show Source): You can put this solution on YOUR website! Remember, is one identity that is useful for simplifying logarithms. So (in this case, and ) This means that simplifies to In other words, ----------------------------------------------------------------- Now let's simplify ... Rewrite as ... Multiply the exponents. ... Rewrite the inner log using the identity ... Square 5 to get 25 ... Use the first identity given to simplify So =========================================================== Answer: This means that

Complex_Numbers/197291: How would I simplify this three problems. Please help me I have no idea how to even start. Any help would be greatly appreicated. (3)^1/2 + 2i (16)1/4 + 6 3 - (-9)^1/2 Thank you! 1 solutions Answer 147928 by jim_thompson5910(28598)   on 2009-05-21 20:08:48 (Show Source): You can put this solution on YOUR website! # 1 # 2 So # 3 So Note:

Complex_Numbers/197295: I have a correction. Simplify (16)^1/4 + 6 1 solutions Answer 147927 by jim_thompson5910(28598)   on 2009-05-21 20:04:35 (Show Source): You can put this solution on YOUR website! So

Equations/197288: I have an isosceles triangle. One vertex says (2x-3) (degree sign) and at the other end its (X+15)(degree sign) please solve for x thank you 1 solutions Answer 147920 by jim_thompson5910(28598)   on 2009-05-21 19:25:56 (Show Source): You can put this solution on YOUR website! Since the triangle is an isosceles triangle, this means that the base angles are equal. I'm assuming that the base angles are and . Since the base angles are equal, this means that So all you need to do is solve for "x". Once you have "x", you can use it to find the values of and .

Equations/197287: please help me solve 5x-3(x-4)=18 thank you 1 solutions Answer 147919 by jim_thompson5910(28598)   on 2009-05-21 19:17:49 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. 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

Equations/197286: please help. this is what the problem says 2x over 3 minus 5 =7 thank you 1 solutions Answer 147916 by jim_thompson5910(28598)   on 2009-05-21 19:08:54 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply EVERY term by the LCD to clear any fractions. Multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Equations/197285: please solve 2x over 3 -5-7 thank you 1 solutions Answer 147913 by jim_thompson5910(28598)   on 2009-05-21 19:02:31 (Show Source): You can put this solution on YOUR website! This isn't an equation, you cannot solve. Please repost with the correct problem.

Equations/197283: please solve 1.2x-2.4=1.5x+3 thank you 1 solutions Answer 147911 by jim_thompson5910(28598)   on 2009-05-21 18:55:29 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by 10 to clear out the decimals (ie make every number a whole number). Distribute and multiply. Add to 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

Functions/197280: find the range of the relation (-3,0)(-2,0)(1,4) the determine wheather the relation is a function 1 solutions Answer 147909 by jim_thompson5910(28598)   on 2009-05-21 18:48:16 (Show Source): You can put this solution on YOUR website! The range is {0,4} (the set of all outputs). Since every x value goes to only ONE y value, this means that this relation is a function.

Rational-functions/197269: solve the equation 1/x-2 - 4/x^2-4 = 5 please help me solve this equation 1 solutions Answer 147906 by jim_thompson5910(28598)   on 2009-05-21 18:25:18 (Show Source): You can put this solution on YOUR website! Ignore the previous post (there is a solution). Start with the given equation. Factor the second denominator Take note that or (these values cause a division by zero) Simplify FOIL Distribute Combine like terms. Get everything to one side. Combine like terms. Notice we have a quadratic 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 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 However, recall that we stated that (this values causes a division by zero). So is NOT a solution. =============================================================== Answer: So the only solution is

Equations/197221: 7/8x - 1/4 + 3/4x = 1/16 + x 1 solutions Answer 147902 by jim_thompson5910(28598)   on 2009-05-21 18:14:55 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply EVERY term by the LCD to clear any fractions. Multiply. Combine like terms on the left side. Add to 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 which in decimal form is .

Equations/197277: please solve one half x + x over 3 = 5 over 6 thank you 1 solutions Answer 147899 by jim_thompson5910(28598)   on 2009-05-21 18:12:23 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply EVERY term by the LCD to clear any fractions. Distribute and multiply. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Linear-systems/197239: solve by the elimination method 2x+3y=1 4x+6y=2 1 solutions Answer 147893 by jim_thompson5910(28598)   on 2009-05-21 18:00:13 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the first equation by -2. Distribute and multiply. So we have the new system of equations: 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. Since is always true, this means that there are an infinite number of solutions. So the system is consistent and dependent.

Equations/197271: please solve this problem. 8x+3=6x-13 thank you 1 solutions Answer 147892 by jim_thompson5910(28598)   on 2009-05-21 17:58:38 (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

Rational-functions/197262: solve the equation 2lnx+5=7 please help me solve this equation 1 solutions Answer 147891 by jim_thompson5910(28598)   on 2009-05-21 17:57:54 (Show Source): You can put this solution on YOUR website! Is the equation ???? Start with the given equation. Divide both sides by 2. Rewrite the equation using the property: ====> Subtract 5 from both sides. So the solution is which approximates to -------------------------------------------------------------- OR.... Is the equation ???? Start with the given equation. Subtract 5 from both sides. Combine like terms. Divide both sides by 2. Reduce Rewrite the equation using the property: ====> Simplify So the solution is which approximates to Note:

Equations/197270: Please solve 2x+7x+6=51 thank u 1 solutions Answer 147890 by jim_thompson5910(28598)   on 2009-05-21 17:53:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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

Quadratic_Equations/197253: can you help me with these problems?? thank you so much 1.) 2.) 3.) 4.) 1 solutions Answer 147889 by jim_thompson5910(28598)   on 2009-05-21 17:52:16 (Show Source): You can put this solution on YOUR website! I'll do the first two to get you started... # 1 Start with the given equation. Notice we have a quadratic 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 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 solutions are or # 2 Start with the given equation. Notice we have a quadratic 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 Rewrite as Add to to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) Break up the fraction. Reduce. or Break up the expression. So the solutions are or which approximate to or

Rational-functions/197267: solve the equation 5/2x-3 = 2x/x+4 please help me solve this equation 1 solutions Answer 147887 by jim_thompson5910(28598)   on 2009-05-21 17:49:22 (Show Source): You can put this solution on YOUR website! Start with the given equation. Cross multiply Distribute Get all terms to the right side Combine like terms. Notice we have a quadratic 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 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

Equations/197266: Solve this equation please. 2x+1=13 thank you 1 solutions Answer 147886 by jim_thompson5910(28598)   on 2009-05-21 17:46:23 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Quadratic_Equations/197254: Quadratic equation: x^2-12=0 1 solutions Answer 147885 by jim_thompson5910(28598)   on 2009-05-21 17:45:41 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice we have a quadratic 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 . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) Break up the fraction. Reduce. or Break up the expression. So the solutions are or which approximate to or

Rational-functions/197261: solve the equation 4log3(-2x)=10 please help me solve this equation 1 solutions Answer 147884 by jim_thompson5910(28598)   on 2009-05-21 17:43:15 (Show Source): You can put this solution on YOUR website! Start with the given equation. Divide both sides by 4. Reduce Rewrite the equation using the property: ====> Divide both sides by -2. Rearrange the equation Convert to radical form and simplify Simplify the square root. So the solution is which approximates to

Exponential-and-logarithmic-functions/197260: solve the equation 2^5x=8^x+6 please help me solve this equation 1 solutions Answer 147882 by jim_thompson5910(28598)   on 2009-05-21 17:38:30 (Show Source): You can put this solution on YOUR website! Start with the given equation. Rewrite as Multiply the exponents. Since the bases are equal, this means that the exponents are equal. Distribute. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is