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Exponents/223460: x^11 divided by x^8 1 solutions Answer 167091 by jim_thompson5910(28696)   on 2009-10-07 21:24:35 (Show Source): You can put this solution on YOUR website! All we're doing to divide monomials with common bases is we're subtracting the exponents:

Equations/223419: please help me solve this equation: 1 solutions Answer 167086 by jim_thompson5910(28696)   on 2009-10-07 21:10:42 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract x from both sides. 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 . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the solutions are or

Equations/223448: This makes no sense to me : ( Please help. Not sure if I wrote it correctly but it reads p divided by p over 4= 5/2 p/ (p/4)= 5/2 1 solutions Answer 167085 by jim_thompson5910(28696)   on 2009-10-07 21:09:05 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply 'p' by the reciprocal of Multiply Simplify Since the equation is NEVER true for any value of 'p', this means that there are no solutions.

Graphs/223413: graph the equation y-3x=0 1 solutions Answer 167082 by jim_thompson5910(28696)   on 2009-10-07 21:06:57 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add 3x to both sides. Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is note: really looks like 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 1. This means that to go from point to point, we can go up 3 and over 1 So starting at , go up 3 units and to the right 1 unit 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

Equations/223408: x-6/7+4=15 1 solutions Answer 167080 by jim_thompson5910(28696)   on 2009-10-07 21:05:45 (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 right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is which approximates to .

Square-cubic-other-roots/223222: Write cube route of 16 in the form 2 to the k, k E Q 1 solutions Answer 166950 by jim_thompson5910(28696)   on 2009-10-07 16:42:28 (Show Source): You can put this solution on YOUR website! . So in this case,

Inequalities/223221: Solve 2y + 5 < -1. 1 solutions Answer 166949 by jim_thompson5910(28696)   on 2009-10-07 16:41:14 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is

Polynomials-and-rational-expressions/223218: On my math homework i have to do Factor each polynomial and the problem is 12x to the 2nd power y to the 2nd power and z + 40xy to the 3rd power z 1 solutions Answer 166945 by jim_thompson5910(28696)   on 2009-10-07 16:38:03 (Show Source): You can put this solution on YOUR website! Start with the given expression Take note that the GCF (greatest common factor) is Factor out the GCF Since we can't go on from here, this means that completely factors to

Probability-and-statistics/223217: Okay, I have been sitting here for an hour reading this problem. I am totally lost. Please help me. Bob can paint a house in 15 hours. If he hires Cindy to help they can do it in 9 hours. If Cindy does it alone, how long will it take her? 1 solutions Answer 166941 by jim_thompson5910(28696)   on 2009-10-07 16:30:08 (Show Source): You can put this solution on YOUR website! Check out this similar solution and this similar solution.

Proportions/223200: is 7 over 9 = 21 over 18 a proportion 1 solutions Answer 166938 by jim_thompson5910(28696)   on 2009-10-07 16:23:50 (Show Source): You can put this solution on YOUR website! What you're basically asking is if is true. Start with the given equation. Cross multiply. Multiply. Since the right side is the bigger of the two numbers, this means which also means that . ---------------------------- Answer So which means that the two fractions and are not in proportion to one another. So is NOT a proportion.

Linear-systems/223201: the problem says solve each system of equations by substitution. -3x+y=-4 -2x+3y=9 1 solutions Answer 166931 by jim_thompson5910(28696)   on 2009-10-07 16:07:40 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Start with the first equation. Add to both sides. Rearrange the terms. ------------------------------------------- Now plug in into the second 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. ------------------------------------------- Since we know that , we can use this to find . Go back to the first equation. Plug in . Multiply. Add to both sides. Combine like terms on the right side. So the answer is and . This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)

Equations/223189: hello i need help with solving equations with variables on both sides of the equations and so if possible could you help me like do the problem step by step fully so i will understand and know how to do it 8x + 5=-3(x+2) please help 1 solutions Answer 166930 by jim_thompson5910(28696)   on 2009-10-07 16:05:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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. ---------------------------------------------------------------------- Answer: So the answer is

Inequalities/223197: pleas help 6x+6-5x≤10 1 solutions Answer 166929 by jim_thompson5910(28696)   on 2009-10-07 16:04:01 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the answer is

Polynomials-and-rational-expressions/223195: 16j^2 + 24j +9 1 solutions Answer 166928 by jim_thompson5910(28696)   on 2009-10-07 16:03:14 (Show Source): You can put this solution on YOUR website! I'm assuming you want to factor. Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is . Now multiply the first coefficient by the last term to get . Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ? To find these two numbers, we need to list all of the factors of (the previous product). Factors of : 1,2,3,4,6,8,9,12,16,18,24,36,48,72,144 -1,-2,-3,-4,-6,-8,-9,-12,-16,-18,-24,-36,-48,-72,-144 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*144 2*72 3*48 4*36 6*24 8*18 9*16 12*12 (-1)*(-144) (-2)*(-72) (-3)*(-48) (-4)*(-36) (-6)*(-24) (-8)*(-18) (-9)*(-16) (-12)*(-12) Now let's add up each pair of factors to see if one pair adds to the middle coefficient : First Number Second Number Sum 1 144 1+144=145 2 72 2+72=74 3 48 3+48=51 4 36 4+36=40 6 24 6+24=30 8 18 8+18=26 9 16 9+16=25 12 12 12+12=24 -1 -144 -1+(-144)=-145 -2 -72 -2+(-72)=-74 -3 -48 -3+(-48)=-51 -4 -36 -4+(-36)=-40 -6 -24 -6+(-24)=-30 -8 -18 -8+(-18)=-26 -9 -16 -9+(-16)=-25 -12 -12 -12+(-12)=-24 From the table, we can see that the two numbers and add to (the middle coefficient). So the two numbers and both multiply to and add to Now replace the middle term with . Remember, and add to . So this shows us that . Replace the second term with . Group the terms into two pairs. Factor out the GCF from the first group. Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis. Combine like terms. Or factor out the common term Condense --------------------------------------------- Answer: So factors to . Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

Numbers_Word_Problems/223183: what is the lowest number possible that when divided by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 always has one left over, or a remainder of one? thanks a bunch. 1 solutions Answer 166923 by jim_thompson5910(28696)   on 2009-10-07 15:58:04 (Show Source): You can put this solution on YOUR website! Well first off, if you divide ANY number by one, you'll ALWAYS get a remainder of 0 (since 1 goes into every number evenly). So I'm assuming that the set of numbers should be 2, 3, 4, 5, 6, 7, 8, 9, and 10 (otherwise, there is no answer). Note: I'm going to ignore the obvious answer of 1 and assume that this number is larger than each value in the group. Take note that 2, 3, 4, 5, 6, 7, 8, 9, and 10 all go into the LCM which is 2520. So 2520 divided by any number in this group leaves a remainder of 0. So just add 1 to this value to get 2521. This new number will leave a remainder of 1 if you divide it by any number in that group. So 2521 is the smallest number (except for 1) that leaves a remainder of 1 when dividing by these given numbers. Note: Other values that leave a remainder of 1 can be generated by adding on multiples of 2520.

Equations/223178: 1/7 = 14 - x one over seven equals fourteen minus x how did you come to the answer???? 1 solutions Answer 166918 by jim_thompson5910(28696)   on 2009-10-07 15:46:30 (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. Subtract from both sides. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the answer is which approximates to .

Equations/223180: i need help with solving equations with variables on both sides of the equation and here is the problem and if it is possible if you could explain it step by step how to do it that would be great so i will understand fully how to do it 11x-5=7(x-2)need help 1 solutions Answer 166917 by jim_thompson5910(28696)   on 2009-10-07 15:45:21 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. 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 . ---------------------------------------------------------------------- Answer: So the answer is which in decimal form is .

Square-cubic-other-roots/223169: please help me solve simplify: 1 solutions Answer 166916 by jim_thompson5910(28696)   on 2009-10-07 15:44:28 (Show Source): You can put this solution on YOUR website! Start with the given expression. Combine the roots. Multiply Break up the root. Factor Break up the root again. Take the square root of 400 to get 20. Take the square root of to get 'x'. So where

Linear-equations/223172: graph the equation y=4 1 solutions Answer 166915 by jim_thompson5910(28696)   on 2009-10-07 15:39:02 (Show Source): You can put this solution on YOUR website! The graph of y=4 is simply a horizontal line at y=4 and it looks like this Graph of (green horizontal line)

Quadratic-relations-and-conic-sections/223022: what is the graph of the equation 6x^2-24x-5y^2-10y-11=0? How do yo identify the solutions of the system of equations y^2-x^2=16 x^2-y^2=16 *Can you please show steps so i will know how to solve these kinds of problems in the future 1 solutions Answer 166914 by jim_thompson5910(28696)   on 2009-10-07 15:36:12 (Show Source): You can put this solution on YOUR website! # 1 From Wikipedia (see conic section article), if you have a conic of the form , then one of the following is possible: 1) If , then the equation represents an ellipse Special Case: if and , the equation represents a circle (which is a special case of an ellipse). or... 2) If , then the equation represents a parabola. or... 3) if , then the equation represents a hyperbola. Special Case: if (ie ), then the conic is a rectangular hyperbola. ------------------------------------------------------------ Now let's solve the problem at hand. Start with the given conic. Rearrange the conic into the form . By looking at the last equation, we see that , , , , and (just match up the corresponding coefficients). So in order to classify the given conic, we're going to use the formula and compare it to one of the cases described above. Start with the given formula. Plug in , , and . Square to get . Multiply to get . Combine like terms. So . Since , this means that the conic is an hyperbola. Here's a graph to verify that result: Graph of ====================================================================== # 2 Start with the first equation Add to both sides. -------- Move onto the second equation. Plug in Distribute Combine like terms. Since the equation is NEVER true for any value of 'x' or 'y', this means that there are no solutions to the system. Visually, this means that the two graphs will NEVER intersect (ie cross).

Sequences-and-series/222944: 31+34+37+.....+325+328= the numbers go up in three's. what is the sum of the question above 1 solutions Answer 166858 by jim_thompson5910(28696)   on 2009-10-07 11:21:54 (Show Source): You can put this solution on YOUR website! Hint: Use the formula to find the sum of the series

Linear-systems/222939: solve the system of equations 4x + 5y = -41 3x - 2y = 21 1 solutions Answer 166855 by jim_thompson5910(28696)   on 2009-10-07 11:17:55 (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. Multiply the both sides of the second equation by 5. 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. Notice how the y terms cancel out. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So our answer is and . Which form the ordered pair . This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)

Linear-equations/222940: Find an equation of the line with the given slope and containing the given point. Slope= 2/3; (-3,3) 1 solutions Answer 166854 by jim_thompson5910(28696)   on 2009-10-07 11:16:55 (Show Source): You can put this solution on YOUR website! If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Distribute Multiply and to get Add 3 to both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line with a slope of which goes through the point (,) is: which is now in form where the slope is and the y-intercept is Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver) Graph of through the point (,) and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.

Equations/222955: Solve for the equation: 3t-2(t+3)=t 1 solutions Answer 166853 by jim_thompson5910(28696)   on 2009-10-07 11:16:17 (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. Subtract from both sides. Combine like terms on the left side. Simplify. Since this equation is never true for any t value, this means that there are no solutions.

Polynomials-and-rational-expressions/223020: Write each polynomial in descending order of the variable x. 5xy^2+3x^2y-9-2x^3 1 solutions Answer 166851 by jim_thompson5910(28696)   on 2009-10-07 11:13:25 (Show Source): You can put this solution on YOUR website! First, write the term that has the largest exponent for 'x'. That would be . Now add on the next term that has the second largest exponent for 'x'. That would be . So far, we have . Now add on the next term has the third largest exponent for 'x', which is to get . Now finally add on the last term -9 to get So the answer is

Equations/223017: how do do the problem -1=5-z-z where do i start? 1 solutions Answer 166850 by jim_thompson5910(28696)   on 2009-10-07 11:10:51 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the right side. Subtract from both sides. Combine like terms. Rearrange the equation. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is

Probability-and-statistics/223002: There are 3 blue and 5 red balloons, what are the odds that you pick one blue balloon? 1 solutions Answer 166847 by jim_thompson5910(28696)   on 2009-10-07 11:07:00 (Show Source): You can put this solution on YOUR website! P(blue) = n(blue)/n(total) = 3/(5+3)=3/8=0.375 note: n(blue) means "number of blue" So there's a 37.5% chance that you'll select a blue balloon.

logarithm/223004: Here is the problem using natural logarithm: 23=3ln(x-1)+14 What we did was the following: 23=3ln(x-1)+14 subtract 14 from both sides 9=3ln(x-1) divide both sides by 3 3=ln(x-1) x-1=e^3 add 1 to both sides x=e^3+1 Please help!!! It's driving us nuts!! 1 solutions Answer 166846 by jim_thompson5910(28696)   on 2009-10-07 11:05:01 (Show Source): You can put this solution on YOUR website! If the original problem is and your answer is , then you are correct. Check: Start with the given equation Plug in Combine like terms. Pull down the exponent. Evaluate the natural log of 'e' to get 1. Multiply Add. Since the equation is true, this verifies the solution.

Equations/223012: -3x-6(x-4)=9 1 solutions Answer 166845 by jim_thompson5910(28696)   on 2009-10-07 11:00:29 (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 answer is which approximates to .

Systems-of-equations/222888: find all of the ordered pairs, (x,y) of integers that satisfy all four of the given equations: 5*x*3*y=180, x^2+y^2=40, 8*x-8*y=32, 12x/4y=1 The ordered pair has to satisfy all equations and i have to find all of them. for example, if x=5 and y=9, that ordered pair needs to work for every equation. I'm guessing since it says find all of them, there is probably more than one. 1 solutions Answer 166775 by jim_thompson5910(28696)   on 2009-10-06 22:36:06 (Show Source): You can put this solution on YOUR website! I think they gave your 4 equations just to scare you a bit. It turns out that the four equations , , , and are a hyperbola, a circle, and two straight lines respectively. Since and are equations of lines, you need to satisfy all 4 equations, and the intersection of two lines is either going to give you a) no solutions, b) infinite solutions, or c) 1 solution, this means that your best bet is to solve the system Note: you should find that there is only one solution to the system of two equations above, which would mean that there is only one solution to the given system of four equations.

Linear-systems/222851: How do you sove this equation? absolute value (7x-4)-4=-11 1 solutions Answer 166761 by jim_thompson5910(28696)   on 2009-10-06 21:39:25 (Show Source): You can put this solution on YOUR website! Start with the given equation Add 4 to both sides. Since the equation is never true (note: remember, the absolute value of any number is always positive), there are no solutions to This means that there are no solutions to the equation