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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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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(28715)   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

Equations/222853: -5X+2=2 1 solutions Answer 166757 by jim_thompson5910(28715)   on 2009-10-06 21:37:34 (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

Complex_Numbers/222848: how do i know if i get the right answer? a lot of times on tests, i don't know if i have the right answer or not, usually on the more difficult questions. here's one question: (2+3i)+(-4+5i)-(9-3i)/3. the slash is dividing. the answer is -5-9i i beleive. what i wanna know, is how do you expand this question? how is it solved? thanks. 1 solutions Answer 166755 by jim_thompson5910(28715)   on 2009-10-06 21:34:12 (Show Source): You can put this solution on YOUR website! If the expression is , then... Start with the given expression. Break up the fraction Reduce. Distribute Combine like terms. So

Equations/222844: Solve equation. Did I do this right? 11-5(3-x)=-2(x+3)+6x I got x=-2 1 solutions Answer 166753 by jim_thompson5910(28715)   on 2009-10-06 21:30:42 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. Add to 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 So you are correct.

Linear-equations/222842: How can 12 - 6 = -6 This is a problem I got from my algebra teacher today. 12 - 6 = -n she said the answer is -6 How can that be true when in elementary school I learned that 12 - 6 = 6. Thanks 1 solutions Answer 166751 by jim_thompson5910(28715)   on 2009-10-06 21:29:21 (Show Source): You can put this solution on YOUR website! What she meant by "the answer is -6" is that the value of satisfies the equation . Take note that the left side is simply 6 (since 12-6=6). So the equation then becomes . Now plug in to get and now simplify . Since this is a true equation, this verifies the answer. Note: none of this means that (since this isn't even true anyway).

logarithm/222790: Let (((log(a,X))))=C and (((log(b,X))))=D. Find the general statement that expresses (((log(ab,X))))in term of C and D. I already know the answer is (CD)/(C+D) I cannot figure out how to write a proof for this question. I know all of the logarithmic principles as well but I can only come up with either (C)(D) as my answer or (C+D). I can't get a fraction. 1 solutions Answer 166740 by jim_thompson5910(28715)   on 2009-10-06 21:16:27 (Show Source): You can put this solution on YOUR website! I found that it helps to work backwards for a bit to find out how to go forward. In this case, I broke down to get: (used the change of base formula here) (used the identity ) Then I realized that I needed to find substitutions for and (to somehow get 'x' in there). So I figured I'd solve for those respective expressions like so: Start with the first equation. Use the change of base formula. Multiply both sides by . Divide both sides by C. So this means --------------------- Start with the second equation. Use the change of base formula. Multiply both sides by Divide both sides by D. So this means ------------------------------------------- Now let's get back to the main problem: Start with the given expression. Use the change of base formula. Use the identity to break up the denominator. Now here's where the substitutions come into play: Plug in and From here, it's just boils down to algebraically simplifying the expression: Multiply the first inner fraction by . Multiply the second inner fraction by . Combine the lower fractions. Multiply by the reciprocal of the lower fraction. Multiply Factor out the GCF from the denominator. Cancel out the common terms. Simplify Rearrange the terms (trivial, but I figured that I'd match the book). So this means where and

Proportions/222784: In the Dicovering Algebra: An Investigative approach, there is a question that says Find the value of the unknown number in each proportion? The problem is 52/91=42/s. So do i inverse it. Swich it up like this: 91/52=s/42? or keep it the same? 1 solutions Answer 166720 by jim_thompson5910(28715)   on 2009-10-06 20:24:02 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by s Multiply both sides by 91 Multiply Divide both sides by 52 Reduce. So our answer is which in decimal form is

Equations/222726: what is the answer to written form i have tried to get rid of one of the X's but i dont remember how 1 solutions Answer 166714 by jim_thompson5910(28715)   on 2009-10-06 19:54:08 (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

Square-cubic-other-roots/222738: square root of 72x^2 y^3 please help, im stuck. thank you. 1 solutions Answer 166712 by jim_thompson5910(28715)   on 2009-10-06 19:49:56 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor into Factor into Break up the square root using the identity . Take the square root of to get . Take the square root of to get . Take the square root of to get . Rearrange and multiply the terms. ================================================== Answer: So simplifies to In other words, where every variable is non-negative.

Linear-equations/222729: how to put -2x+3y=8 into slope-intercept form 1 solutions Answer 166706 by jim_thompson5910(28715)   on 2009-10-06 19:37:16 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. 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

Quadratic_Equations/222686: Multiply. (b+(1/3))(b+(1/3)) Thank you! 1 solutions Answer 166699 by jim_thompson5910(28715)   on 2009-10-06 18:54:51 (Show Source): You can put this solution on YOUR website! 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: , , , Now add every term listed above to make a single expression. Now combine like terms. So FOILs to . In other words, .

Polynomials-and-rational-expressions/222692: Factor completely. 64r^2-121 Thank you!! 1 solutions Answer 166698 by jim_thompson5910(28715)   on 2009-10-06 18:48:59 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as . Notice how we have a difference of squares where in this case and . So let's use the difference of squares formula to factor the expression: Start with the difference of squares formula. Plug in and . So this shows us that factors to . In other words .