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Exponential-and-logarithmic-functions/118725: xy(x²+3xy+9) 1 solutions Answer 86888 by jim_thompson5910(28593)   on 2008-01-05 15:56:18 (Show Source): You can put this solution on YOUR website! Start with the given expression Distribute among the terms in the parenthesis Multiply and to get Multiply and to get Multiply and to get ------------- Answer: So distributes to In other words,

Inequalities/118742: This question is from textbook algebra 1 how do you solve the equation -6r-10<3r-8? 1 solutions Answer 86883 by jim_thompson5910(28593)   on 2008-01-05 15:36:11 (Show Source): You can put this solution on YOUR website! Start with the given inequality Add 10 to both sides Subtract 3r from both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by -9 to isolate r (note: Remember, dividing both sides by a negative number flips the inequality sign) Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Coordinate-system/118744: What is the graph of x + y = 1 ? Thank you 1 solutions Answer 86882 by jim_thompson5910(28593)   on 2008-01-05 15:35:05 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Graphing Linear Equations Start with the given equation Subtract from both sides Multiply both sides by Distribute Multiply Rearrange the terms Reduce any fractions So the equation is now in slope-intercept form () where (the slope) and (the y-intercept) So to graph this equation lets plug in some points Plug in x=-8 Multiply Add So here's one point (-8,9) Now lets find another point Plug in x=-7 Multiply Add So here's another point (-7,8). Add this to our graph Now draw a line through these points So this is the graph of through the points (-8,9) and (-7,8) So from the graph we can see that the slope is (which tells us that in order to go from point to point we have to start at one point and go down -1 units and to the right 1 units to get to the next point), the y-intercept is (0,)and the x-intercept is (,0) . So all of this information verifies our graph. We could graph this equation another way. Since this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,). So we have one point (0,) Now since the slope is , this means that in order to go from point to point we can use the slope to do so. So starting at (0,), we can go down 1 units and to the right 1 units to get to our next point Now draw a line through those points to graph So this is the graph of through the points (0,1) and (1,0)

Quadratic_Equations/118752: Please help with this problem 3x^2 + x -4 = 0 What is the solution set ? Thank you 1 solutions Answer 86881 by jim_thompson5910(28593)   on 2008-01-05 15:33:34 (Show Source): You can put this solution on YOUR website! Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=3, b=1, and c=-4 Square 1 to get 1 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 3 to get 6 So now the expression breaks down into two parts or Lets look at the first part: Add the terms in the numerator Divide So one answer is Now lets look at the second part: Subtract the terms in the numerator Divide So another answer is So our solutions are: or Notice when we graph , we get: and we can see that the roots are and . This verifies our answer

expressions/118750: Please solve2/x - 1/5 = Thank you 1 solutions Answer 86880 by jim_thompson5910(28593)   on 2008-01-05 15:32:11 (Show Source): You can put this solution on YOUR website! Since there isn't a right side, we cannot solve. However, we can simplify. Start with the given expression Since the denominators are not equal, we need to get them to a common denominator. Since the LCD is , we need to get each denominator to Multiply by Combine the fractions Multiply 5 and 2 to get 10 Multiply by Combine the fractions Multiply x and 1 to get x Since the 2 fractions have the common denominator , we can combine them. In order to do that, just combine the numerators.

expressions/118748: Please help with this question - 4x - 15 < 25 is eqivalent to ? thank you 1 solutions Answer 86879 by jim_thompson5910(28593)   on 2008-01-05 15:25:57 (Show Source): You can put this solution on YOUR website! Do you want to solve for x? Start with the given inequality Add 15 to both sides Combine like terms on the right side Divide both sides by -4 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign) Divide -------------------------------------------------------------- Answer: So our answer is

Equations/118751: Please help with this question If x + 2/ x - 3 = 0 then x is = to Thank you 1 solutions Answer 86878 by jim_thompson5910(28593)   on 2008-01-05 15:24:49 (Show Source): You can put this solution on YOUR website! Start with the given equation Multiply both sides by Multiply Subtract 2 from both sides Combine like terms on the right side -------------------------------------------------------------- Answer: So our answer is

Expressions-with-variables/118749: write the equation of the line which contains (-3,1) and whose y intercept is -8 1 solutions Answer 86877 by jim_thompson5910(28593)   on 2008-01-05 15:22:23 (Show Source): You can put this solution on YOUR website! If the y-intercept is -8, then the line goes through the point (0,-8) First lets find the slope through the points (,) and (,) Start with the slope formula (note: is the first point (,) and is the second point (,)) Plug in ,,, (these are the coordinates of given points) Subtract the terms in the numerator to get . Subtract the terms in the denominator to get Reduce So the slope is ------------------------------------------------ Now let's use the point-slope formula to find the equation of the line: ------Point-Slope Formula------ where is the slope, and is one of the given points 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 to both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line which goes through the points (,) and (,) is: The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver) Graph of through the points (,) and (,) Notice how the two points lie on the line. This graphically verifies our answer.

Exponential-and-logarithmic-functions/118745: find each product. 3x²(2y+5x) 1 solutions Answer 86876 by jim_thompson5910(28593)   on 2008-01-05 15:20:47 (Show Source): You can put this solution on YOUR website! Start with the given expression Distribute among the terms in the parenthesis Multiply and to get Multiply and to get ------------- Answer: So distributes to In other words,

expressions/118747: If x - 3(x-2)= 4(x + 1)-8,then x = Please help 1 solutions Answer 86874 by jim_thompson5910(28593)   on 2008-01-05 15:10:49 (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 Subtract 6 from both sides Subtract 4x from both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by -6 to isolate x Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Inequalities/118741: This question is from textbook algebra 1 after you subtract 4 and are left with -d/3 < 6 how do you finish the problem? 1 solutions Answer 86871 by jim_thompson5910(28593)   on 2008-01-05 14:23:19 (Show Source): You can put this solution on YOUR website! Start with the given inequality Multiply both sides by 3 Multiply Divide both sides by -1 to isolate d (note: Remember, dividing both sides by a negative number flips the inequality sign) Divide -------------------------------------------------------------- Answer: So our answer is

Linear-equations/118701: My brain is on shut down from all my equations and this problem has me lost. Help Please!! Angela Solve the following system of linear inequalities by graphing. x – y <= 3 x + 2y ,=6 1 solutions Answer 86870 by jim_thompson5910(28593)   on 2008-01-05 14:09:29 (Show Source): You can put this solution on YOUR website! Start with the given system of inequalities In order to graph this system of inequalities, we need to graph each inequality one at a time. First lets graph the first inequality In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (note: if you need help with graphing, check out this solver) graph of Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,0) into the inequality Plug in and Simplify (note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.) Since this inequality is true, we simply shade the entire region that contains (0,0) Graph of with the boundary (which is the line in red) and the shaded region (in green) --------------------------------------------------------------- Now lets graph the second inequality In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (note: if you need help with graphing, check out this solver) graph of Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,0) into the inequality Plug in and Simplify Since this inequality is true, we simply shade the entire region that contains (0,0) Graph of with the boundary (which is the line in red) and the shaded region (in green) --------------------------------------------------------------- So we essentially have these 2 regions: Region #1 Graph of Region #2 Graph of When these inequalities are graphed on the same coordinate system, the regions overlap to produce this region. It's a little hard to see, but after evenly shading each region, the intersecting region will be the most shaded in. Here is a cleaner look at the intersection of regions Here is the intersection of the 2 regions represented by the series of dots

Exponential-and-logarithmic-functions/118710: find each product 2xy(3x²-xy+7) 1 solutions Answer 86869 by jim_thompson5910(28593)   on 2008-01-05 14:07:03 (Show Source): You can put this solution on YOUR website! Start with the given expression Distribute Multiply

Quadratic_Equations/118736: Please help to solve this problem. 3x^2 + x - 0 = Thanking you 1 solutions Answer 86868 by jim_thompson5910(28593)   on 2008-01-05 14:01:36 (Show Source): You can put this solution on YOUR website! Start with the given equation Remove the zero term on the left Factor the left side Now set each factor equal to zero: or or Now solve for x in each case So our answer is or Notice if we graph we can see that the roots are and . So this visually verifies our answer.

Linear-equations/118738: In a standard xy-coordinate system,the graph of the equation y = -3x + 8 is Thanking you 1 solutions Answer 86867 by jim_thompson5910(28593)   on 2008-01-05 13:59:37 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Graphing Linear Equations In order to graph we only need to plug in two points to draw the line So lets plug in some points Plug in x=0 Multiply Add So here's one point (0,8) Now lets find another point Plug in x=1 Multiply Add So here's another point (1,5). Add this to our graph Now draw a line through these points So this is the graph of through the points (0,8) and (1,5) So from the graph we can see that the slope is (which tells us that in order to go from point to point we have to start at one point and go down -3 units and to the right 1 units to get to the next point), the y-intercept is (0,)and the x-intercept is (,0) ,or (,0) We could graph this equation another way. Since this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,). So we have one point (0,) Now since the slope is , this means that in order to go from point to point we can use the slope to do so. So starting at (0,), we can go down 3 units and to the right 1 units to get to our next point Now draw a line through those points to graph So this is the graph of through the points (0,8) and (1,5)

Expressions-with-variables/118739: what are the x and y- intercept of the line -12x+6y=12 1 solutions Answer 86866 by jim_thompson5910(28593)   on 2008-01-05 13:58:21 (Show Source): You can put this solution on YOUR website! Start with the given equation Let's find the x-intercept To find the x-intercept, let y=0 and solve for x: Plug in Simplify Divide both sides by -12 Reduce So the x-intercept is (note: the x-intercept will always have a y-coordinate equal to zero) ------------------ Start with the given equation Now let's find the y-intercept To find the y-intercept, let x=0 and solve for y: Plug in Simplify Divide both sides by 6 Reduce So the y-intercept is (note: the y-intercept will always have a x-coordinate equal to zero) ------------------------------------------ So we have these intercepts: x-intercept: y-intercept:

Exponential-and-logarithmic-functions/118727: find each product (x-y)(x²-xy+y²) 1 solutions Answer 86865 by jim_thompson5910(28593)   on 2008-01-05 13:37:27 (Show Source): You can put this solution on YOUR website! Start with the given expression Expand the expression. Remember for something like it expands to Distribute Multiply Combine like terms Rearrange the terms So expands and simplifies to . In other words,

Exponential-and-logarithmic-functions/118729: Find each product. (x³+x²+1)(x²-x-5) 1 solutions Answer 86864 by jim_thompson5910(28593)   on 2008-01-05 13:33:34 (Show Source): You can put this solution on YOUR website! Start with the given expression Expand the expression. Remember for something like it expands to Distribute Multiply Combine like terms Now rearrange the terms in descending order So expands and simplifies to . In other words, If you need more help with multiplying polynomials, check out this Long Multiplication Calculator

Exponential-and-logarithmic-functions/118711: Find each product (3x-2)(2x²+3x-1) 1 solutions Answer 86863 by jim_thompson5910(28593)   on 2008-01-05 13:31:51 (Show Source): You can put this solution on YOUR website! Start with the given expression Expand the expression. Remember for something like it expands to Distribute Multiply Combine like terms Now rearrange the terms in descending order So expands and simplifies to . In other words, If you need more help with multiplying polynomials, check out this Long Multiplication Calculator

absolute-value/118682: what are the solutions to the absolute value equation /x+7/+5=17 ? /=absolute value bars choices: A 5 and -19 B 5 and -5 C 19 and -5 D 12 adn -5 1 solutions Answer 86810 by jim_thompson5910(28593)   on 2008-01-04 19:11:04 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract 5 from both sides. Break up the absolute value (remember, if you have , then or ) or Set the expression equal to the original value 12 and it's opposite -12 Now lets focus on the first equation Subtract 7 from both sides Combine like terms on the right side So our first solution is Now lets focus on the second equation Subtract 7 from both sides Combine like terms on the right side So our second solution is So this means the answer is or which means the answer is A)

Expressions-with-variables/118677: How do you write an equation for the line (in slope-intercept form) with the given information: 1.is vertical and passes through (4, 11) 2.passs thrugh (7, -10) and (4, -16) 3.passes through (2, 18) and (4, 17) (P.s. they are seperate problems 123) 1 solutions Answer 86806 by jim_thompson5910(28593)   on 2008-01-04 17:04:47 (Show Source): You can put this solution on YOUR website! #1 All vertical lines are of the form where k is the x-coordinate of the points that the line goes through. So in this case, the equation of the line that passes through (4, 11) is ------------- #2 First lets find the slope through the points (,) and (,) Start with the slope formula (note: is the first point (,) and is the second point (,)) Plug in ,,, (these are the coordinates of given points) Subtract the terms in the numerator to get . Subtract the terms in the denominator to get Reduce So the slope is ------------------------------------------------ Now let's use the point-slope formula to find the equation of the line: ------Point-Slope Formula------ where is the slope, and is one of the given points 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 Subtract from both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line which goes through the points (,) and (,) is: The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver) Graph of through the points (,) and (,) Notice how the two points lie on the line. This graphically verifies our answer. ---------- #3 First lets find the slope through the points (,) and (,) Start with the slope formula (note: is the first point (,) and is the second point (,)) Plug in ,,, (these are the coordinates of given points) Subtract the terms in the numerator to get . Subtract the terms in the denominator to get So the slope is ------------------------------------------------ Now let's use the point-slope formula to find the equation of the line: ------Point-Slope Formula------ where is the slope, and is one of the given points So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Distribute Multiply and to get . Now reduce to get Add to both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line which goes through the points (,) and (,) is: The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver) Graph of through the points (,) and (,) Notice how the two points lie on the line. This graphically verifies our answer.

Linear_Equations_And_Systems_Word_Problems/118671: Write an equation that is parrallel and perpendicular to the given line. y=-1/3x+2 1 solutions Answer 86800 by jim_thompson5910(28593)   on 2008-01-04 14:46:54 (Show Source): You can put this solution on YOUR website! An equation that is parallel has the same slope. So the slope of this parallel line is . Now just replace the 2 with any number such as 5 to get: So one parallel line is Notice if we graph the two equations, we can see that they are parallel. So this verifies our answer. Graph of (red) and (green) ------------- An equation that is perpendicular has an negated inverted slope. Since the original slope is , the perpendicular slope is So the perpendicular slope is Now just replace the slope of with the new slope to get a perpendicular line. So one perpendicular line is Notice if we graph the two equations, we can see that they are perpendicular. So this verifies our answer. Graph of (red) and (green)

Angles/118669: Hello, I am a freshman student having problems in goemetry. It would be wonderful if I could have a little extra help on a few problems. I would greatly appreciate it. :) Here is my first problem. A calculation shows that an angle has a measure of 113.05 degrees. This angle can be written in the form A B', measured in degrees and minutes. What is the sum of A and B? Note: In the second sentence the A has a degree symbol after it. This is how far I got into the problem. 113 + ?/60 + ?/ 3600 1 solutions Answer 86798 by jim_thompson5910(28593)   on 2008-01-04 14:29:18 (Show Source): You can put this solution on YOUR website! Since the angle is 113.05 degrees, this means A=113 (just take the whole part of the number). Now take the decimal portion 0.05 and multiply it by 60 (since there are 60 minutes in a degree) to get . So this means that 0.05 degrees is 3 minutes which means B=3 So the sum of A and B is:

Numeric_Fractions/118668: If you have a negative improper fraction like -29/16 If you simplify that is it still a negative? 1 solutions Answer 86797 by jim_thompson5910(28593)   on 2008-01-04 14:22:57 (Show Source): You can put this solution on YOUR website! Well you can't reduce the fraction, but you can convert it to a mixed fraction. Start with the given improper fraction Break up into . Notice how is a multiple of . Break up the fraction. Reduce to get . Simplify. Remember is the same as . So the improper fraction is the mixed fraction . So the fraction is still negative

Rectangles/118667: What is the area of a rectangle with a length of 45 and diagonals of 51? 1 solutions Answer 86795 by jim_thompson5910(28593)   on 2008-01-04 13:13:33 (Show Source): You can put this solution on YOUR website! If we cut the rectangle in half along the diagonal, we get this triangle Since we can see that the triangle has legs of x and 45 with a hypotenuse of 51, we can use Pythagoreans theorem to find the unknown side. Pythagoreans theorem: where a and b are the legs of the triangle and c is the hypotenuse Plug in a=x, b=45, and c=51. Now lets solve for x Square each individual term Subtract 2025 from both sides Combine like terms Take the square root of both sides Simplify the square root So the width is 24 Now multiply 24 and 45 to get the area So the area of the rectangle is 1080

Polynomials-and-rational-expressions/118666: x^2+3x+1 _________ x-3 1 solutions Answer 86794 by jim_thompson5910(28593)   on 2008-01-04 13:08:02 (Show Source): You can put this solution on YOUR website! Let's simplify this expression using synthetic division Start with the given expression First lets find our test zero: Set the denominator equal to zero Solve for x. so our test zero is 3 Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero. 3 | 1 3 1 | Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1) 3 | 1 3 1 | 1 Multiply 3 by 1 and place the product (which is 3) right underneath the second coefficient (which is 3) 3 | 1 3 1 | 3 1 Add 3 and 3 to get 6. Place the sum right underneath 3. 3 | 1 3 1 | 3 1 6 Multiply 3 by 6 and place the product (which is 18) right underneath the third coefficient (which is 1) 3 | 1 3 1 | 3 18 1 6 Add 18 and 1 to get 19. Place the sum right underneath 18. 3 | 1 3 1 | 3 18 1 6 19 Since the last column adds to 19, we have a remainder of 19. This means is not a factor of Now lets look at the bottom row of coefficients: The first 2 coefficients (1,6) form the quotient and the last coefficient 19, is the remainder, which is placed over like this Putting this altogether, we get: So which looks like this in remainder form: remainder 19 You can use this online polynomial division calculator to check your work

Polynomials-and-rational-expressions/118657: 5y^3(y^5)^2 ___________ 10y^5(y^2)^6 1 solutions Answer 86793 by jim_thompson5910(28593)   on 2008-01-04 13:05:53 (Show Source): You can put this solution on YOUR website! Start with the given expression Multiply the exponents Multiply Multiply the monomials by adding the exponents Add Now divide the monomials by subtracting the exponents Subtract Now reduce to get Now rewrite as So simplifies to . In other words,

Quadratic_Equations/118664: explain why a^0 =1 for any nonzero value of a. 1 solutions Answer 86791 by jim_thompson5910(28593)   on 2008-01-04 12:57:07 (Show Source): You can put this solution on YOUR website! Remember, when you multiply expressions like and , you simply add the exponents. So Now when you divide, just undo the multiplication by dividing. In other words, Now if you divide 2 equal expressions, then you will always get 1 (ie ). So something like So this shows why for any nonzero value of a. Now I'll let you think this question over: why does "a" have to be nonzero?

Complex_Numbers/118661: what is the difference of two squares mean 1 solutions Answer 86789 by jim_thompson5910(28593)   on 2008-01-04 12:11:10 (Show Source): You can put this solution on YOUR website! In this case, a square is a term that is squared. For instance, the variable x is a term and is a square. So if we have x and y, then and are both squares. Now subtract one from the other to get a difference of squares: note: this also works for numbers. For instance, 25 is a perfect square that can be written as . So if we have it's the same as which is also a difference of squares.

Linear-systems/118644: please help raising rabbits. Before Roland sold two female rabbits half of his rabbits were female. If x represents his orginal number of rabbits, then 1/2x -2= 1/3(x-2). Thank you 1 solutions Answer 86762 by jim_thompson5910(28593)   on 2008-01-04 00:54:42 (Show Source): You can put this solution on YOUR website! Do you want to solve for x? Start with the given equation Multiply both sides by the LCM of 6. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver) Distribute and multiply the LCM to each side Distribute Add 12 to both sides Subtract 2x from both sides Combine like terms on the left side Combine like terms on the right side -------------------------------------------------------------- Answer: So our answer is

Polynomials-and-rational-expressions/118595: subtract 3k^-4m-7 from k2-5k+3 1 solutions Answer 86761 by jim_thompson5910(28593)   on 2008-01-04 00:45:04 (Show Source): You can put this solution on YOUR website! Start with the given expression Distribute the negative Group like terms Combine like terms