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 logarithm/293498: Simplify or solve for x. log base pi of e = x^2 I have the problem written out to look like pi^(x^2)=e I am not sure how to figure it out from there.1 solutions Answer 211869 by jim_thompson5910(28476)   on 2010-04-18 15:41:08 (Show Source): You can put this solution on YOUR website! Start with the given equation. Take the square root of both sides (don't forget about the plus/minus) or Break up the plus/minus to form two equations. So the solutions are or
 Linear-systems/293525: okai i have a question it said write the slope intercept of the linear equation her it is m=2,b=61 solutions Answer 211867 by jim_thompson5910(28476)   on 2010-04-18 15:36:14 (Show Source): You can put this solution on YOUR website! Start with the general slope-intercept equation Plug in m=2 and b=6 So the equation slope-intercept is
 Quadratic_Equations/293526: f(x)=x^2+5x+7'f(4) 1 solutions Answer 211865 by jim_thompson5910(28476)   on 2010-04-18 15:35:01 (Show Source): You can put this solution on YOUR website! Start with the given function. Plug in . Square to get . Multiply and to get . Multiply and to get . Combine like terms.
 Radicals/293367: negative radical negative 641 solutions Answer 211784 by jim_thompson5910(28476)   on 2010-04-18 01:21:02 (Show Source): You can put this solution on YOUR website! So Note:
 Quadratic_Equations/293365: i dont understand what is the solution of (3x-1)^2=5.1 solutions Answer 211783 by jim_thompson5910(28476)   on 2010-04-18 01:19:43 (Show Source): You can put this solution on YOUR website! Start with the given equation. Take the square root of both sides. or Break up the "plus/minus" to form two equations. or Add to both sides. or Divide both sides by 3. -------------------------------------- Answer: So the solutions are or .
 Linear-equations/293366: i need to graph x+6=2x-41 solutions Answer 211782 by jim_thompson5910(28476)   on 2010-04-18 01:17:57 (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 . To graph this, simply set up a number line and plot the point x=10 on the number line.
 Pythagorean-theorem/293363: Find the distance d(P1, P2) between the points P1 and P2. P1=(0,6); P2=(-2,6)1 solutions Answer 211781 by jim_thompson5910(28476)   on 2010-04-18 00:56:34 (Show Source): You can put this solution on YOUR website! Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the distance formula. Plug in , , , and . Subtract from to get . Subtract from to get . Square to get . Square to get . Add to to get . Take the square root of to get . So our answer is So the distance between the two points is 2 units. Note: If you plot the two points on a coordinate grid, you can easily count the number of spaces between the two points to be 6 units. However, this method only works if the two points have either the same x coordinate or the same y coordinate.
 Pythagorean-theorem/293358: use a Right triangle, find missing length for a. a= b=10 c=151 solutions Answer 211780 by jim_thompson5910(28476)   on 2010-04-18 00:51:03 (Show Source): You can put this solution on YOUR website!Remember, the Pythagorean Theorem is where "a" and "b" are the legs of a triangle and "c" is the hypotenuse. Start with the Pythagorean theorem. Plug in and Square to get . Square to get . Subtract from both sides. Combine like terms. Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense). Simplify the square root. ================================================================ Answer: So the solution is (which approximates to )
 Pythagorean-theorem/293359: A ladder that is 26 feet long is 10 feet from the base of a wall. How far up the wall does the ladder reach?1 solutions Answer 211779 by jim_thompson5910(28476)   on 2010-04-18 00:47:38 (Show Source): You can put this solution on YOUR website! We basically have this triangle set up: To find the unknown length, we need to use the Pythagorean Theorem. Remember, the Pythagorean Theorem is where "a" and "b" are the legs of a triangle and "c" is the hypotenuse. Since the legs are and this means that and Also, since the hypotenuse is , this means that . Start with the Pythagorean theorem. Plug in , , Square to get . Square to get . Subtract from both sides. Combine like terms. Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense). Take the square root of 576 to get 24. ================================================================ Answer: So the solution is which means that the ladder reaches 24 ft up the wall.
 Radicals/293344: how would you solve this proof? 1 solutions Answer 211778 by jim_thompson5910(28476)   on 2010-04-18 00:46:04 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD 4 to clear out the fractions. Rewrite as Combine the roots on the right side using the identity Distribute and multiply Rearrange the equation. We essentially have a nested radical on the left side. In general, we have an equation in the form . The goal from here is to square both sides, gather like terms, and equate rational and irrational parts. So let's do these next tasks. Start with the given equation. Square both sides. FOIL Square to get 6. Square to get 2. Combine like terms. Combine the roots on the right side using the identity Multiply Factor 12 into 4*3 (take note that 4 is a perfect square) Break up the root using the identity given above. Take the square root of 4 to get 2. Multiply From here, we can see that the two numbers are equal since the rational parts are equal and the irrational parts are equal. So this confirms that Note: Ideally, you'll only manipulate one side to transform it into the other. However, this is much more difficult to do with nested radicals. I find that algebraic manipulations suffice in this case. As a final check, you can use a calculator to find that both sides approximate to the value 0.258819045 (which helps verify the answer).
 Finance/293349: I am having difficulty factoring (x^4 - 1). The following is my attempt, will someone please help me with this? Thanks, x16 – 1 (x4)4 – 1 (x4 – 1)(x4 + 1) (x2 – 1)(x4 + 1)(x4 – 1) (x2 – 1)(x2 + 1)(x4 – 1) (x+1)(x-1)(x2 + 1)(x4 + 1) 1 solutions Answer 211776 by jim_thompson5910(28476)   on 2010-04-18 00:21:47 (Show Source): You can put this solution on YOUR website!If the expression is , then . Let me know if you need help getting that answer.
 Quadratic_Equations/293099: (3v-2)(2v+1)=3v^2-11v-10 Thanks1 solutions Answer 211775 by jim_thompson5910(28476)   on 2010-04-18 00:18:56 (Show Source): You can put this solution on YOUR website! Start with the given equation. FOIL Get every term to the left side. Combine like terms. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "v": 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 solutions are or
 Linear-equations/293354: what is y=1/2x-41 solutions Answer 211774 by jim_thompson5910(28476)   on 2010-04-18 00:17:23 (Show Source): You can put this solution on YOUR website!I'm assuming that you want to graph this. 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 1 and the run is 2. This means that to go from point to point, we can go up 1 and over 2 So starting at , go up 1 unit and to the right 2 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
 Numeric_Fractions/293323: reduce each of the following rational numbers to simplest form 0/21 solutions Answer 211762 by jim_thompson5910(28476)   on 2010-04-17 21:27:02 (Show Source): You can put this solution on YOUR website! since zero divided by any number (except 0) is zero. We could also say something like or
 Graphs/293190: passes through points (-2,-3) and (3,3) 1 solutions Answer 211745 by jim_thompson5910(28476)   on 2010-04-17 19:59:27 (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 So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Rewrite as Distribute Multiply Subtract 3 from both sides. Combine like terms. note: If you need help with fractions, check out this solver. So the equation that goes through the points and is
 Distributive-associative-commutative-properties/293305: Is 10 X (9+5) = 10 + 5, or 10 X (9+5) = 10 X 9 + 10 X 5, or 10 X (9 +5) = 10 X 9 X 5, or 10 X (9 + 5) = 10 + 9 + 5 right? 1 solutions Answer 211744 by jim_thompson5910(28476)   on 2010-04-17 19:52:59 (Show Source): You can put this solution on YOUR website!What you're describing is the distributive property which is a X (b + c) = a X b + a X c ... where the 'X' means multiplication So 10 X (9+5) = 10 X 9 + 10 X 5 Notation note: since 'x' is used as a variable, we abandon the idea that 'x' is a multiplication symbol and instead turn to the * symbol.
 Equations/293302: How do you solve this equation? Log base 3 + Log base 3 9=11 solutions Answer 211741 by jim_thompson5910(28476)   on 2010-04-17 19:31:48 (Show Source): You can put this solution on YOUR website!Where are the variables? You need to have some unknowns to solve for.
 Miscellaneous_Word_Problems/293278: A school has 3333 lockers. The first student opens up every single locker. The second student closes every second locker starting with the second. The third student closes or opens every third locker starting with the third. The fourth student closes or opens every fourth locker starting with the fourth. This trend continues until all 3333 studnets have passed. How many lockers are open?1 solutions Answer 211731 by jim_thompson5910(28476)   on 2010-04-17 18:28:35 (Show Source): You can put this solution on YOUR website!Hint: Look at a smaller set of lockers. How many lockers (and which ones specifically) are open when there are only 10 lockers involved? Then find out how many (and which ones specifically) are open when 100 lockers are considered. Keep doing this until you start to see a pattern. If you're having trouble seeing a pattern, try smaller increments (ie go from 10 to 20, then to 30, etc...)
 Problems-with-consecutive-odd-even-integers/293274: the 1st and 3rd of three consective integers are odd integers are added, the result is 69 less than five times the second integer. Find the third integer familiarize with steps x = odd integer x + 2 = 2nd Odd Integer x + 4 = 3rd Odd integer Translate x + (x + 4) is 1st PLUS 3rd integer 69 - 5(x + 2) is 69 less than 5 times the 2nd integer the 1st odd integer plus the 3rd consective odd integer [x + (x+4)] equals the sum of 69 less than 5(x + 2) the 2nd integer x + (x + 4 ) = 69 - 5(x + 2) 2x + 4 = 69 - 5x - 10 2x + 4 = 59 - 5x 2x = 55 - 5x 7x = 55 This does not get me a whole number to test the answer for odd consective integers. Where have I gone wrong? 1 solutions Answer 211728 by jim_thompson5910(28476)   on 2010-04-17 18:08:44 (Show Source): You can put this solution on YOUR website!Your error lies in the translation. The first one is fine, but the second expression should be . So your equation should be
 Linear-equations/293276: What is the y-intercept of the line with the equation 4x + 9y = -108?1 solutions Answer 211727 by jim_thompson5910(28476)   on 2010-04-17 18:06:21 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point
 Trigonometry-basics/293273: I am stuck on this problem where I need to solve for X. (tan^-1) 2x= -pi/6 If anyone could help it would be much appreciated!1 solutions Answer 211724 by jim_thompson5910(28476)   on 2010-04-17 18:02:07 (Show Source): You can put this solution on YOUR website! ... Start with the given equation. ... Take the tangent of both sides to eliminate the inverse tangent. ... Break up the tangent into sine over cosine ... Evaluate the sine of to get ... Evaluate the cosine of to get ... Multiply the first fraction by the reciprocal of the second fraction. ... Multiply and simplify ... Rationalize the denominator of the fraction on the right side. ... Divide both sides by 2. So the solution is Edit: Take note that (just do a bit of algebraic manipulation)
 Inverses/293269: Solve using inverse operations -6=3+3x and -a+5=01 solutions Answer 211720 by jim_thompson5910(28476)   on 2010-04-17 17:22:04 (Show Source): You can put this solution on YOUR website!# 1 Start with the given equation. Add to both sides. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ------------------------ Answer: So the solution is ============================================================ # 2 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
 Graphs/293265: Write the following equation in function form. Then graph it. 2y+3x=21 solutions Answer 211718 by jim_thompson5910(28476)   on 2010-04-17 17:10:14 (Show Source): You can put this solution on YOUR website!First we must solve for y: Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. Now replace 'y' with f(x) to get So the function is 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 2. This means that to go from point to point, we can go down 3 and over 2 So starting at , go down 3 units and to the right 2 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
 Inequalities/293227: please solve 2x +6>x+191 solutions Answer 211708 by jim_thompson5910(28476)   on 2010-04-17 16:20:03 (Show Source): You can put this solution on YOUR website! Start with the given inequality. 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
 Graphs/293237: How would I graph the equation f(x)=-3(x+1)^2? I know the vertex is (-1,0)and the equation of the line of symmetry is -1. I just can't figure out how it should look on a graph (parabola opening up or down)?1 solutions Answer 211706 by jim_thompson5910(28476)   on 2010-04-17 16:17:57 (Show Source): You can put this solution on YOUR website!For any quadratic in the form , if (ie 'a' is positive), then the parabola will open up. On the other hand, if , then the parabola will open down. Note: if , then the graph is a flat line (and not a parabola)
 Equations/293258: what is the answer to this 5t^2 + 3t -9 =0 what is t? Thanx 1 solutions Answer 211705 by jim_thompson5910(28476)   on 2010-04-17 16:14:08 (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 "t": 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) or Break up the expression. So the solutions are or
 Functions/293257: Write the equation(S) in function form, please. 5x-y=-1 and 2y+3x=2 Thanks a bunch- curious learner1 solutions Answer 211703 by jim_thompson5910(28476)   on 2010-04-17 16:12:48 (Show Source): You can put this solution on YOUR website!# 1 First we must solve for y: Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. Now replace 'y' with f(x) to get So the function is ================================================================== # 2 Again, we must solve for y: Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. Now replace 'y' with f(x) to get So the function is
 Rectangles/293259: i am just practicing here. This is my question: The length of a rectangle is 2 ft. more than the width. The perimeter of the rectangle is 20 feet. Find the length. Tell me if this is the correct way. P= 2L + 2L P= 2*(2) + 20 P= 4 + 20 P= 24 L= 6 because 24 divided by 4 = 6(answer) 1 solutions Answer 211702 by jim_thompson5910(28476)   on 2010-04-17 16:08:56 (Show Source): You can put this solution on YOUR website!I'm not sure how you got that answer (it's the correct answer) since your steps are incorrect. Let L = length and W = width Recall that the perimeter of a rectangle is . Since the length is 2 ft more than the width, we can say that Start with the given equation. Plug in and Distribute. Combine like terms. Subtract 4 from both sides. Combine like terms. Divide both sides by 4 to isolate W. Reduce. So the width is ft and the length is ft
 Quadratic_Equations/293152: PLEASEEE I NEED HELP WITH THIS ONE> Quadratic equation....please dont say 2.665 and -2.65. BUt here is the equation 18x^2-128 (FOIL)(WITH 4 SPACES)I THINK. pleasehelp it is for carneigie learning online. I am a freshman and this is the only problem i cant figure out1 solutions Answer 211601 by jim_thompson5910(28476)   on 2010-04-17 00:25:34 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor out the GCF . Now factor to get (use the difference of squares formula) So factors to In other words,
 Average/293151: Please solve 5/4x+1/8x=5/8+x Please solve this problem1 solutions Answer 211600 by jim_thompson5910(28476)   on 2010-04-17 00:09:20 (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. Combine like terms on the left side. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is .
 expressions/293145: Evaluate z+y/5 for z=22 and y=13 z+y/5= Please evaluate, I am almost done with my test and I need some help with this problem. Thank you1 solutions Answer 211599 by jim_thompson5910(28476)   on 2010-04-16 23:30:43 (Show Source): You can put this solution on YOUR website!Simply plug in z=22 and y=13 and simplify to get So when z=22 and y=13