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Linear-systems/124659: Given f(x) = x2 + 5x + 2, find f(0). 1 solutions Answer 91369 by jim_thompson5910(28504)   on 2008-02-03 19:02:19 (Show Source): You can put this solution on YOUR website! Start with the given function. Plug in . In other words, replace each x with 0. Evaluate to get 0. Multiply 5 and 0 to get 0 Now combine like terms

Radicals/124660: Solve. x squared - 6x - 3 = 0 1 solutions Answer 91367 by jim_thompson5910(28504)   on 2008-02-03 19:01:10 (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=1, b=-6, and c=-3 Negate -6 to get 6 Square -6 to get 36 (note: remember when you square -6, you must square the negative as well. This is because .) 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 1 to get 2 So now the expression breaks down into two parts or Now break up the fraction or Simplify or So these expressions approximate to or So our solutions are: or Notice when we graph , we get: when we use the root finder feature on a calculator, we find that and .So this verifies our answer

Radicals/124661: Find the axis of symmetry of y = 2x squared + 8x - 7 1 solutions Answer 91366 by jim_thompson5910(28504)   on 2008-02-03 18:58:22 (Show Source): You can put this solution on YOUR website! To find the axis of symmetry, use this formula: From the equation we can see that a=2 and b=8 Plug in b=8 and a=2 Multiply 2 and 2 to get 4 Reduce So the axis of symmetry is

Expressions-with-variables/124663: Please help me figure out the value of y. Problem: 3y + 2 < 7 - 2y 1 solutions Answer 91364 by jim_thompson5910(28504)   on 2008-02-03 18:56:54 (Show Source): You can put this solution on YOUR website! Start with the given inequality Subtract 2 from both sides Add 2y to both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by 5 to isolate y Divide -------------------------------------------------------------- Answer: So our answer is

Graphs/124560: Hello, Please help! Solve by graphing: y= -3x+3 y= 2(x-2)-3 Thank you 1 solutions Answer 91291 by jim_thompson5910(28504)   on 2008-02-03 13:23:00 (Show Source): You can put this solution on YOUR website! Start with the second equation Distribute Combine like terms So our new system is Now let's graph the first equation (note: if you need help with graphing, check out this solver) Graph of Now let's plot the second graph Graph of (red) and (green) From the graph, we can see that the two lines intersect at (2,-3). So the solution is and

Graphs/124559: Hello, Please help solve 2x-5y=-3 y=-4x+1 Thank you 1 solutions Answer 91290 by jim_thompson5910(28504)   on 2008-02-03 13:14:12 (Show Source): You can put this solution on YOUR website! Start with the given system Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute Combine like terms on the left side Add 5 to both sides Combine like terms on the right side Divide both sides by 22 to isolate x Reduce Now that we know that , we can plug this into to find Substitute for each Simplify So our answer is and which also looks like

Polynomials-and-rational-expressions/124554: 6x^2+5xy-21y^2 1 solutions Answer 91284 by jim_thompson5910(28504)   on 2008-02-03 12:47:11 (Show Source): You can put this solution on YOUR website! Do you want to factor this? Looking at we can see that the first term is and the last term is where the coefficients are 6 and -21 respectively. Now multiply the first coefficient 6 and the last coefficient -21 to get -126. Now what two numbers multiply to -126 and add to the middle coefficient 5? Let's list all of the factors of -126: Factors of -126: 1,2,3,6,7,9,14,18,21,42,63,126 -1,-2,-3,-6,-7,-9,-14,-18,-21,-42,-63,-126 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -126 (1)*(-126) (2)*(-63) (3)*(-42) (6)*(-21) (7)*(-18) (9)*(-14) (-1)*(126) (-2)*(63) (-3)*(42) (-6)*(21) (-7)*(18) (-9)*(14) note: remember, the product of a negative and a positive number is a negative number Now which of these pairs add to 5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 5 First Number Second Number Sum 1 -126 1+(-126)=-125 2 -63 2+(-63)=-61 3 -42 3+(-42)=-39 6 -21 6+(-21)=-15 7 -18 7+(-18)=-11 9 -14 9+(-14)=-5 -1 126 -1+126=125 -2 63 -2+63=61 -3 42 -3+42=39 -6 21 -6+21=15 -7 18 -7+18=11 -9 14 -9+14=5 From this list we can see that -9 and 14 add up to 5 and multiply to -126 Now looking at the expression , replace with (notice adds up to . So it is equivalent to ) Now let's factor by grouping: Group like terms Factor out the GCF of out of the first group. Factor out the GCF of out of the second group Since we have a common term of , we can combine like terms So factors to So this also means that factors to (since is equivalent to ) ------------------------------- Answer: So factors to

Equations/124533: Hi Can I have some finding an equation of the line through (3, 4) with slope 5/6? Thanks 1 solutions Answer 91274 by jim_thompson5910(28504)   on 2008-02-03 11:45:42 (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) Distribute Multiply and to get Add 4 to both sides to isolate y Combine like terms and to get (note: if you need help with combining fractions, check out this solver) ------------------------------------------------------------------------------------------------------------ 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.

Linear-equations/124478: This question is from textbook Introductory Algebra Graph on a plane. y > -1 1 solutions Answer 91237 by jim_thompson5910(28504)   on 2008-02-02 23:42:47 (Show Source): You can put this solution on YOUR website! In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (simply draw a horizontal line through ) 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) (note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)

Linear-equations/124483: Can someone help? I am understanding part of the problem but not the whole problem. I feel like I am missing something..thanks Solve each system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent..Thanks first equation second equation 1 solutions Answer 91236 by jim_thompson5910(28504)   on 2008-02-02 23:39:39 (Show Source): You can put this solution on YOUR website! Start with the given system Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute Combine like terms on the left side Subtract 25 from both sides Combine like terms on the right side Divide both sides by -3 to isolate x Divide Now that we know that , we can plug this into to find Substitute for each Simplify So our answer is and which also looks like So because we got a unique solution, this means that the system is independent. Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer. Graph of (red) and (green)

Inequalities/124485: This question is from textbook Algebra solve each inqualities by graphing. x>5 y<4 - 1 solutions Answer 91234 by jim_thompson5910(28504)   on 2008-02-02 23:38:01 (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 (simply draw a vertical line through ) 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 not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line Graph of with the boundary (which is the line in red) and the shaded region (in green) (note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line) --------------------------------------------------------------- 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 (simply draw a horizontal line through ) 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) (note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line) --------------------------------------------------------------- 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

Linear-systems/124486: 1000x+30y=500 x-2y=11 1 solutions Answer 91233 by jim_thompson5910(28504)   on 2008-02-02 23:36:57 (Show Source): You can put this solution on YOUR website! Do you want to solve by substitution? Start with the given system of equations: Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y. So let's isolate y in the first equation Start with the first equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce --------------------- Since , we can now replace each in the second equation with to solve for Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute to Multiply Multiply both sides by the LCM of 3. 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 Combine like terms on the left side Add 100 to both sides Combine like terms on the right side Divide both sides by 203 to isolate x Reduce -----------------First Answer------------------------------ So the first part of our answer is: Since we know that we can plug it into the equation (remember we previously solved for in the first equation). Start with the equation where was previously isolated. Plug in Multiply Combine like terms and reduce. (note: if you need help with fractions, check out this solver) -----------------Second Answer------------------------------ So the second part of our answer is: -----------------Summary------------------------------ So our answers are: and which form the point

Equations/124417: Please help. (2-9x^3)^2 1 solutions Answer 91176 by jim_thompson5910(28504)   on 2008-02-02 16:47:12 (Show Source): You can put this solution on YOUR website! Start with the given expression Expand. Remember something like 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: Now collect every term to make a single expression Now combine like terms Rearrange the terms in descending order --------------------- Answer: So foils and simplifies to In other words,

Equations/124403: Hi can I have some help finding an equation of the line with x-intercept -1 and y-intercept 8? 1 solutions Answer 91172 by jim_thompson5910(28504)   on 2008-02-02 16:12:47 (Show Source): You can put this solution on YOUR website! If the x-intercept is -1 and y-intercept is 8, then we have the point (-1,0) for the x-intercept and the point (0,8) for the y-intercept So let's find the equation of the line that goes through (-1,0) and (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.

Equations/124400: Please help. (x^2+x+6)(x-6) Thank you. 1 solutions Answer 91171 by jim_thompson5910(28504)   on 2008-02-02 16:09:19 (Show Source): You can put this solution on YOUR website! Start with the given expression Rearrange the terms Expand the expression. Remember something like 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

Graphs/124412: Solve each of the following systems of linear inequalities graphically. 10. 2x + y ≤ 8 x + y ≥ 3 x ≥ 0 y ≥ 0 1 solutions Answer 91170 by jim_thompson5910(28504)   on 2008-02-02 15:58:09 (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 not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line Graph of with the boundary (which is the line in red) and the shaded region (in green) --------------------------------------------------------------- Now lets graph the third 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 (simply draw a vertical line through ) graph of (note:the graph is the line that is overlapping the y-axis. So it may be hard to see) Now lets pick a test point, say (1,0). 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 (1,0) into the inequality Plug in and Simplify Since this inequality is true, we simply shade the entire region that contains (1,0) Graph of with the boundary (which is the line in red) and the shaded region (in green) --------------------------------------------------------------- Now lets graph the fourth 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 (simply draw a horizontal line through ) graph of (note:the graph is the line that is overlapping the x-axis. So it may be hard to see) Now lets pick a test point, say (0,1). 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 (0,1) into the inequality Plug in and Simplify Since this inequality is true, we simply shade the entire region that contains (0,1) Graph of with the boundary (which is the line in red) and the shaded region (in green) --------------------------------------------------------------- So we essentially have these 4 regions: Region #1 Graph of Region #2 Graph of Region #3 Graph of Region #4 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 4 regions represented by the series of dots

Graphs/124411: Solve each of the following systems of linear inequalities graphically. 9. x – 2y ≥ -2 x + 2y ≤ 6 x ≥ 0 y ≥ 0 1 solutions Answer 91169 by jim_thompson5910(28504)   on 2008-02-02 15:55:28 (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) --------------------------------------------------------------- Now lets graph the third 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 (simply draw a vertical line through ) graph of (note:the graph is the line that is overlapping the y-axis. So it may be hard to see) Now lets pick a test point, say (1,0). 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 (1,0) into the inequality Plug in and Simplify Since this inequality is true, we simply shade the entire region that contains (1,0) Graph of with the boundary (which is the line in red) and the shaded region (in green) --------------------------------------------------------------- Now lets graph the fourth 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 (simply draw a horizontal line through ) graph of (note:the graph is the line that is overlapping the x-axis. So it may be hard to see) Now lets pick a test point, say (0,1). 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 (0,1) into the inequality Plug in and Simplify Since this inequality is true, we simply shade the entire region that contains (0,1) Graph of with the boundary (which is the line in red) and the shaded region (in green) --------------------------------------------------------------- So we essentially have these 4 regions: Region #1 Graph of Region #2 Graph of Region #3 Graph of Region #4 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 4 regions represented by the series of dots

Graphs/124410: Solve each of the following systems by substitution. 8. 3x – y = -15 x = y -7 1 solutions Answer 91168 by jim_thompson5910(28504)   on 2008-02-02 15:52:15 (Show Source): You can put this solution on YOUR website! Start with the given system Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute Combine like terms on the left side Add 21 to both sides Combine like terms on the right side Divide both sides by 2 to isolate y Divide Now that we know that , we can plug this into to find Substitute for each Simplify So our answer is and which also looks like Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer. Graph of (red) and (green)

Graphs/124409: Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. 7. -3x + y = 8 3x – 2y = -10 1 solutions Answer 91167 by jim_thompson5910(28504)   on 2008-02-02 15:50:19 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for y. In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for , we would have to eliminate (or vice versa). So lets eliminate . In order to do that, we need to have both coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated. So to make the coefficients equal in magnitude but opposite in sign, we need to multiply both coefficients by some number to get them to an common number. So if we wanted to get and to some equal number, we could try to get them to the LCM. Since the LCM of and is , we need to multiply both sides of the top equation by and multiply both sides of the bottom equation by like this: Multiply the top equation (both sides) by Multiply the bottom equation (both sides) by Distribute and multiply Now add the equations together. In order to add 2 equations, group like terms and combine them Combine like terms and simplify Notice how the x terms cancel out Simplify Divide both sides by to isolate y Reduce Now plug this answer into the top equation to solve for x Start with the first equation Plug in Subtract 2 from both sides Combine like terms on the right side Divide both sides by -3 to isolate x Divide So our answer is and which also looks like Now let's graph the two equations (if you need help with graphing, check out this solver) From the graph, we can see that the two equations intersect at . This visually verifies our answer. graph of (red) and (green) and the intersection of the lines (blue circle).

Graphs/124408: Solve each of the following systems by graphing. 6. 4x + 3y = 12 x + y = 2 1 solutions Answer 91166 by jim_thompson5910(28504)   on 2008-02-02 15:47:33 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: In order to graph these equations, we need to solve for y for each equation. So let's solve for y on the first equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets graph (note: if you need help with graphing, check out this solver) Graph of So let's solve for y on the second equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets add the graph of to our first plot to get: Graph of (red) and (green) From the graph, we can see that the two lines intersect at the point (,) (note: you might have to adjust the window to see the intersection)

Graphs/124407: Solve each of the following systems by graphing. 5. x – y = 8 x + y = 2 1 solutions Answer 91165 by jim_thompson5910(28504)   on 2008-02-02 15:45:48 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: In order to graph these equations, we need to solve for y for each equation. So let's solve for y on the first equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets graph (note: if you need help with graphing, check out this solver) Graph of So let's solve for y on the second equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets add the graph of to our first plot to get: Graph of (red) and (green) From the graph, we can see that the two lines intersect at the point (,) (note: you might have to adjust the window to see the intersection)

Graphs/124405: Evaluate each function for the value specified 4. f (x)= x^3 + 2x^2 - 7x+ 9; find (a) f (-2), (b) f (0), and (c) f (2). 1 solutions Answer 91164 by jim_thompson5910(28504)   on 2008-02-02 15:42:50 (Show Source): You can put this solution on YOUR website! a) Let's evaluate Start with the given function. Plug in . In other words, replace each x with -2. Evaluate to get -8. Evaluate to get 4. Multiply 2 and 4 to get 8 Multiply -7 and -2 to get 14 Now combine like terms -----------Now let's evaluate another value--------- b) Let's evaluate Start with the given function. Plug in . In other words, replace each x with 0. Evaluate to get 0. Evaluate to get 0. Multiply 2 and 0 to get 0 Multiply -7 and 0 to get 0 Now combine like terms -----------Now let's evaluate another value--------- c) Let's evaluate Start with the given function. Plug in . In other words, replace each x with 2. Evaluate to get 8. Evaluate to get 4. Multiply 2 and 4 to get 8 Multiply -7 and 2 to get -14 Now combine like terms

Graphs/124404: Evaluate each function for the value specified 3. f (x) = -2x^3 + 5x^2 - x - 1; find (a) f (-1), (b) f (0), and (c) f (2). 1 solutions Answer 91163 by jim_thompson5910(28504)   on 2008-02-02 15:40:41 (Show Source): You can put this solution on YOUR website! a) Let's evaluate Start with the given function. Plug in . In other words, replace each x with -1. Evaluate to get -1. Evaluate to get 1. Multiply -2 and -1 to get 2 Multiply 5 and 1 to get 5 Multiply -1 and -1 to get 1 Now combine like terms -----------Now let's evaluate another value--------- b) Let's evaluate Start with the given function. Plug in . In other words, replace each x with 0. Evaluate to get 0. Evaluate to get 0. Multiply -2 and 0 to get 0 Multiply 5 and 0 to get 0 Multiply -1 and 0 to get 0 Now combine like terms -----------Now let's evaluate another value--------- c) Let's evaluate Start with the given function. Plug in . In other words, replace each x with 2. Evaluate to get 8. Evaluate to get 4. Multiply -2 and 8 to get -16 Multiply 5 and 4 to get 20 Multiply -1 and 2 to get -2 Now combine like terms

Graphs/124402: Graph each of the following inequalities 2. 4x + 3y > 12 1 solutions Answer 91162 by jim_thompson5910(28504)   on 2008-02-02 15:38:12 (Show Source): You can put this solution on YOUR website! 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 not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line Graph of with the boundary (which is the line in red) and the shaded region (in green) (note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)

Graphs/124401: Graph each of the following inequalities 1. x – y ≥ 4 1 solutions Answer 91161 by jim_thompson5910(28504)   on 2008-02-02 15:36:01 (Show Source): You can put this solution on YOUR website! 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 not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line Graph of with the boundary (which is the line in red) and the shaded region (in green)

Linear-equations/124397: Hi! Can I have some help on finding an equation of the line through (1, 5) with slope 2? 1 solutions Answer 91160 by jim_thompson5910(28504)   on 2008-02-02 14:52:51 (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) Distribute Multiply and to get Add 5 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/124398: This question is from textbook College Algebra Sullivan I need to see the solution worked out in steps. Thank you X^3-9X+=0 1 solutions Answer 91159 by jim_thompson5910(28504)   on 2008-02-02 14:52:01 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out the GCF Now set each factor equal to zero: or or Now solve for x in : So our solutions are: ,, or

Quadratic_Equations/124353: solve the equation by completing the square. t^2-12t+20=0. how do i solve it? 1 solutions Answer 91149 by jim_thompson5910(28504)   on 2008-02-02 12:09:08 (Show Source): You can put this solution on YOUR website! note: I'm going to use x instead of t Start with the given equation Subtract from both sides Take half of the x coefficient to get (ie ). Now square to get (ie ) Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation Now factor to get Now add to both sides to isolate y Combine like terms Now we're done with completing the square Now to solve for x, let Add to both sides Reduce Take the square root of both sides Simplify the square root Add to both sides So the solution breaks down to or Combine like terms or So our answers are or Notice if we graph , we can see that the roots are and . So this visually verifies our answer.

Functions/124378: Can someone please help me with this problem? The last line of synthetic division for (2x^4-5x^3+7x^2-3x+1)/(x-3) gives coefficients for the quotient of 2,1,8,21. Is this true or false? I thought the answer was false. Am I right please help!!! 1 solutions Answer 91148 by jim_thompson5910(28504)   on 2008-02-02 12:02:03 (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 | 2 -5 7 -3 1 | Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 2) 3 | 2 -5 7 -3 1 | 2 Multiply 3 by 2 and place the product (which is 6) right underneath the second coefficient (which is -5) 3 | 2 -5 7 -3 1 | 6 2 Add 6 and -5 to get 1. Place the sum right underneath 6. 3 | 2 -5 7 -3 1 | 6 2 1 Multiply 3 by 1 and place the product (which is 3) right underneath the third coefficient (which is 7) 3 | 2 -5 7 -3 1 | 6 3 2 1 Add 3 and 7 to get 10. Place the sum right underneath 3. 3 | 2 -5 7 -3 1 | 6 3 2 1 10 Multiply 3 by 10 and place the product (which is 30) right underneath the fourth coefficient (which is -3) 3 | 2 -5 7 -3 1 | 6 3 30 2 1 10 Add 30 and -3 to get 27. Place the sum right underneath 30. 3 | 2 -5 7 -3 1 | 6 3 30 2 1 10 27 Multiply 3 by 27 and place the product (which is 81) right underneath the fifth coefficient (which is 1) 3 | 2 -5 7 -3 1 | 6 3 30 81 2 1 10 27 Add 81 and 1 to get 82. Place the sum right underneath 81. 3 | 2 -5 7 -3 1 | 6 3 30 81 2 1 10 27 82 Since the last column adds to 82, we have a remainder of 82. This means is not a factor of Now lets look at the bottom row of coefficients: Looking at the last line, we see the coefficients: 2,1,10, and 27 So the coefficients for the quotient are not 2,1,8, and 21 So the answer is false and you are correct.

Graphs/124382: Graph the solution to the inequality │y – 1│< 2 1 solutions Answer 91147 by jim_thompson5910(28504)   on 2008-02-02 11:56:32 (Show Source): You can put this solution on YOUR website! Start with the given inequality Break up the absolute value (remember, if you have , then and ) and Break up the absolute value inequality using the given rule Combine the two inequalities to get a compound inequality Add 1 to all sides ---------------------------------------------------- Answer: So our answer is which looks like this in interval notation if you wanted to graph the solution set, you would get Graph of the solution set in blue and the excluded values represented by open circles

Square-cubic-other-roots/124320: Thanks for your help ^4 sqrt 81 1 solutions Answer 91115 by jim_thompson5910(28504)   on 2008-02-01 21:14:28 (Show Source): You can put this solution on YOUR website! Start with the given expression Rewrite the radical expression using exponent notation Factor into Rewrite the expression using the identity Convert the expression back to radical notation Take the square root of 81 to get 9 Take the square root of 9 to get 3 So