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 Expressions-with-variables/267270: y=-x-3, x=-2 1 solutions Answer 196190 by jim_thompson5910(28593)   on 2010-02-08 18:12:37 (Show Source): You can put this solution on YOUR website!Hint: Plug in x=-2 (ie replace 'x' with -2) into to get to find 'y'.
 Equations/267268: I need to represent the following as an equation: "The sum of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?" The answer is 34. But, how do you represent the first 1/2 of the problem in an equation? I came up with several ways to represent the part of the equation that is the second half of the problem. I do not know how to represent "the sum of a certain two-digit number"...1 solutions Answer 196189 by jim_thompson5910(28593)   on 2010-02-08 18:11:07 (Show Source): You can put this solution on YOUR website!Let t = tens digit and u = units digit Any two digit number is of the form where 't' and 'u' are whole numbers. For example, the number 23 has a tens digit of 2 and a units digit of 3. So t=2 and u=3 which means that Because "The sum of the digits of a certain two-digit number is 7", we know that . So this the first equation. And since "Reversing its digits increases the number by 9", this tells us that . This is the second equation. I'll let you solve the system of equations.
 logarithm/267269: what is the log of 4x=31 solutions Answer 196187 by jim_thompson5910(28593)   on 2010-02-08 18:06:10 (Show Source): You can put this solution on YOUR website!Remember that can be rewritten as . In this case, this means that can be rewritten as . I'll let you take it from here.
 Linear_Equations_And_Systems_Word_Problems/267048: The line 3x + 15y = 3 is tangent to f(x) at (-4, 1). Find f'(-4).1 solutions Answer 196140 by jim_thompson5910(28593)   on 2010-02-08 14:40:35 (Show Source): You can put this solution on YOUR website!Simply find the slope of to find the slope of the tangent line (since is the tangent line).
 Quadratic_Equations/267146: what is the greatesr common factor of 10x^3-45x^2+20x1 solutions Answer 196138 by jim_thompson5910(28593)   on 2010-02-08 14:34:36 (Show Source): You can put this solution on YOUR website!The greatest common factor of is . This is the largest factor that evenly divides all three terms.
 Exponential-and-logarithmic-functions/266908: Simplify each number. 8^2/3 I know you puy parenthesis (8 and a fraction but I don't know what fraction.1 solutions Answer 196023 by jim_thompson5910(28593)   on 2010-02-07 22:36:25 (Show Source): You can put this solution on YOUR website! So
 Exponential-and-logarithmic-functions/266900: if {x^2-3x-40} divided by {x+5} x^2-3x-40 divided by x+5 x^2-5x -2x-40 -2x- 10 =30 x-2+30 x-30 I keep trying the problem to see were i made my mistake and i still can't seem to find were the error is? 1 solutions Answer 196009 by jim_thompson5910(28593)   on 2010-02-07 22:00:00 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where
 Linear-equations/266634: Find the X intercepts, and y intercepts. -x^2+5x+36 I know that I have to factor 36, to get my x intercepts, so I came up with (-6,0),(6,0) But my assignment tells me this is wrong. I believe that the y intercept would be (0,36), is this correct?1 solutions Answer 195928 by jim_thompson5910(28593)   on 2010-02-07 15:18:33 (Show Source): You can put this solution on YOUR website!To find the x-intercept(s), you need to set the expression equal to zero and solve for 'x' Set the expression equal to zero. 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 So this means that the x-intercepts are (-4,0) and (9,0) For the y-intercept, you are correct. The y-intercept is (0,36)
 Polynomials-and-rational-expressions/266446: The following problem is from my college algebra class using the book "Introduction to Algebra." A polynomial in x has a degree 3. The coefficient of x squared is 3 less than the coefficient of x to the 3rd.? The coefficient of x is three times the coefficient of x squared. The remaining coefficient is 2 more than the coefficient of x to the third. The sum of the coefficients is -4. What is the polynomial? I honestly don't even know where to begin, I started by using simple guesses and it got me nowhere. They assign us the most difficult question in the exercise set even though the text in no way prepares us for the answer. Please help!1 solutions Answer 195749 by jim_thompson5910(28593)   on 2010-02-06 20:26:45 (Show Source): You can put this solution on YOUR website!"A polynomial in x has a degree 3" means that the polynomial has a term (and that term has the largest exponent). Examples of 3rd degree polynomials are , , and . The most general 3rd degree polynomial is where a, b, c, d are all real numbers. Since "The coefficient of x squared is 3 less than the coefficient of x to the 3rd", this means that . Also, because "The coefficient of x is three times the coefficient of x squared", we know that . Furthermore, it's stated that "The remaining coefficient is 2 more than the coefficient of x to the third" which tells us that . Finally, since "The sum of the coefficients is -4", we get So we basically have the four equations , , , and I'll let you solve this system. The basic idea is to form an equation with one variable, solve for that variable, and then use that solution to find the value of another variable. You'll continue this process until you find all 4 variables. For example, plug , , and into to get . After that, plug into to get . Now we have an equation with a single variable to solve for.
 Average/266441: 2x-5x-7 1 solutions Answer 195739 by jim_thompson5910(28593)   on 2010-02-06 19:49:15 (Show Source):
 Equations/266430: 5-9x=140-44x1 solutions Answer 195717 by jim_thompson5910(28593)   on 2010-02-06 18:51:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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. ---------------------------------------------------------------------- Answer: So the solution is which approximates to .
 Equations/266377: How do you solve: 2y/3-4=y/6-1 Thanks1 solutions Answer 195692 by jim_thompson5910(28593)   on 2010-02-06 16:36:12 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. 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
 Graphs/266311: How do you solve: Write an equation of a line which contains the points (3,-2) and (3,6) Thank you1 solutions Answer 195690 by jim_thompson5910(28593)   on 2010-02-06 14:59:42 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Remember, you cannot divide by zero. So this means that the slope is undefined. Since the slope is undefined, this means that the equation of the line through the points and is .
 Polynomials-and-rational-expressions/266222: The two's are exponents I couldn't make them small. The -1 is also a exponent (b4)(b-6)-1 (b2)-2)1 solutions Answer 195628 by jim_thompson5910(28593)   on 2010-02-05 22:08:16 (Show Source): You can put this solution on YOUR website! So --------------- So
 Angles/266221: (< -stands for angle)-----.< a is supplementary to < b .what is the sum of ,1 solutions Answer 195625 by jim_thompson5910(28593)   on 2010-02-05 22:05:00 (Show Source): You can put this solution on YOUR website!By definition, supplementary angles add to 180 degrees. So
 Polynomials-and-rational-expressions/266157: Give exaxt and approximate sollutions to three decimal places... y^2 - 10y + 25=161 solutions Answer 195623 by jim_thompson5910(28593)   on 2010-02-05 21:59:17 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract 16 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 "y": 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
 Polynomials-and-rational-expressions/266175: solve for x. x^2 + 12x + 4 = 01 solutions Answer 195613 by jim_thompson5910(28593)   on 2010-02-05 21:03:34 (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 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) Break up the fraction. Reduce. or Break up the expression. So the solutions are or
 Inverses/266204: Please evaluate the following function or inverse; then write the ordered pair. f(x)=3x+1 and f^-1=(x-1)/3 f(2) = ( ) ( , ) Thank you for your help!1 solutions Answer 195611 by jim_thompson5910(28593)   on 2010-02-05 21:02:08 (Show Source): You can put this solution on YOUR website! Start with the given function. Plug in Multiply Add So the ordered pair is (2,7)
 Equations/266169: My question is regarding multiplying fractions and canceling out terms. The problem is (a+b)/2*(10x+2)/b^2-a^2. I have no idea where to even start because I know that I can't cancel out anything when it's in this form. Help please! 1 solutions Answer 195591 by jim_thompson5910(28593)   on 2010-02-05 19:18:55 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Combine the fractions. Rewrite (in the denominator) as Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words,
 Equations/266123: 2r^2+10r+11=01 solutions Answer 195553 by jim_thompson5910(28593)   on 2010-02-05 17:02:30 (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 "r": Start with the quadratic formula Plug in , , and 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
 Surface-area/266118: Show that (-1,-1), (9,4), (20,6), and (10,1) are the vertices of a rhombus, and then find the area of the rhombus.1 solutions Answer 195543 by jim_thompson5910(28593)   on 2010-02-05 16:21:50 (Show Source): You can put this solution on YOUR website!Hint: find the distances between each vertex (excluding the vertices that are opposite one another). If those distances are equal, then the figure is a rhombus.
 Polynomials-and-rational-expressions/266087: how do i factor n^3+5n^2-4n-20 as a polynomial1 solutions Answer 195537 by jim_thompson5910(28593)   on 2010-02-05 16:15:07 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms Now factor to get (use the difference of squares formula). So factors to In other words,
 Radicals/266108: Subtract and simplify 3√27 - 5 3√81 solutions Answer 195536 by jim_thompson5910(28593)   on 2010-02-05 16:12:14 (Show Source): You can put this solution on YOUR website! So
 Divisibility_and_Prime_Numbers/265387: Will n! +2, n! +3,..., n! +n for n>=2 always be a sequence of n-1 composite numbers? Why?1 solutions Answer 195142 by jim_thompson5910(28593)   on 2010-02-04 00:11:08 (Show Source): You can put this solution on YOUR website!Take note that 2 is a factor of n! if n>=2. Why? Let's say that n=5, then n!=5!=5*4*3*2*1. For any other value of n>=2, 2 will always be a factor of n! Likewise, 3 is a factor of n! if n>=3. Notice that if n=2, then you only have one term. Similarly, 4 is a factor of n!+4 for n>=4 (if n<4 then you have at most two terms). This idea generalizes to the fact that n is a factor of n!. This is trivial since n!=n(n-1)...(2)(1) for any value of n. Because of the facts stated above, we can factor out the GCFs to get the new sequence: 2((n-1)!+1), 3((n-1)!+1), 4((n-1)!+1), ... n((n-1)!+1), Since each term in the sequence is a product of two factors (other than 1 or itself), this means that each term is a composite number for any value of n.
 Square-cubic-other-roots/265314: what is square root of 54x1 solutions Answer 195126 by jim_thompson5910(28593)   on 2010-02-03 22:40:28 (Show Source): You can put this solution on YOUR website! So where
 Inequalities/265318: graphing inequalities, I understand step one, but no further. Example: 3x+7y > 7 change to equals 3x+7y=7 So where do I go from here and how do I get the numbers( ?,?) to plug ion and be able to graph these questions? I hope that makes sense.1 solutions Answer 195110 by jim_thompson5910(28593)   on 2010-02-03 21:12:18 (Show Source): You can put this solution on YOUR website!I'll help you graph Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is -3 and the run is 7. This means that to go from point to point, we can go down 3 and over 7 So starting at , go down 3 units and to the right 7 units to get to the next point Now draw a line through these points to graph So this is the graph of through the points and I'll leave it to you to graph (ie apply the proper shading)
 Polynomials-and-rational-expressions/265322: how do you solve 2b^2+13b-7 using trinomials1 solutions Answer 195108 by jim_thompson5910(28593)   on 2010-02-03 21:10:14 (Show Source): You can put this solution on YOUR website!I'm assuming that you mean Start with the given equation Factor the left side (note: if you need help with factoring, check out this solver) Now set each factor equal to zero: or or Now solve for b in each case So our answers are or
 test/265255: c^2 + 9c + 14 = 0 help me solve1 solutions Answer 195107 by jim_thompson5910(28593)   on 2010-02-03 21:09:31 (Show Source): You can put this solution on YOUR website! Start with the given equation Factor the left side (note: if you need help with factoring, check out this solver) Now set each factor equal to zero: or or Now solve for c in each case So our answers are or
 Equations/265204: Solve and check 7r-(2r+8)=321 solutions Answer 195052 by jim_thompson5910(28593)   on 2010-02-03 18:50:51 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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. ---------------------------------------------------------------------- Answer: So the solution is