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Coordinate-system/139504: Find the domain of the function f(x)=1 _____ x-4 1 solutions Answer 101723 by jim_thompson5910(28536)   on 2008-05-01 11:40:42 (Show Source): You can put this solution on YOUR website! Start with the given function Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain. Add 4 to both sides Combine like terms on the right side Since makes the denominator equal to zero, this means we must exclude from our domain So our domain is: which in plain English reads: x is the set of all real numbers except So our domain looks like this in interval notation note: remember, the parenthesis excludes 4 from the domain If we wanted to graph the domain on a number line, we would get: Graph of the domain in blue and the excluded value represented by open circle Notice we have a continuous line until we get to the hole at (which is represented by the open circle). This graphically represents our domain in which x can be any number except x cannot equal 4

Equations/139536: -5(x-2)+3=5 1 solutions Answer 101722 by jim_thompson5910(28536)   on 2008-05-01 11:39:40 (Show Source): You can put this solution on YOUR website! Start with the given equation Distribute Combine like terms on the left side Subtract 13 from both sides Combine like terms on the right side Divide both sides by -5 to isolate x Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Coordinate-system/139503: Graph 3x-2y=-18 1 solutions Answer 101721 by jim_thompson5910(28536)   on 2008-05-01 11:38:59 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 3 and the run is 2. This means that to go from point to point, we can go up 3 and over 2 So starting at , go up 3 units and to the right 2 units to get to the next point Now draw a line through these points to graph So this is the graph of through the points and

Quadratic_Equations/139519: What do I solve this by factoring? 20x^2 + 13x + 2 Thanks! 1 solutions Answer 101720 by jim_thompson5910(28536)   on 2008-05-01 11:34:57 (Show Source): You can put this solution on YOUR website! Looking at we can see that the first term is and the last term is where the coefficients are 20 and 2 respectively. Now multiply the first coefficient 20 and the last coefficient 2 to get 40. Now what two numbers multiply to 40 and add to the middle coefficient 13? Let's list all of the factors of 40: Factors of 40: 1,2,4,5,8,10,20,40 -1,-2,-4,-5,-8,-10,-20,-40 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to 40 1*40 2*20 4*10 5*8 (-1)*(-40) (-2)*(-20) (-4)*(-10) (-5)*(-8) note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to 13? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 13 First Number Second Number Sum 1 40 1+40=41 2 20 2+20=22 4 10 4+10=14 5 8 5+8=13 -1 -40 -1+(-40)=-41 -2 -20 -2+(-20)=-22 -4 -10 -4+(-10)=-14 -5 -8 -5+(-8)=-13 From this list we can see that 5 and 8 add up to 13 and multiply to 40 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 ) Set the factorization equal to zero Now set each factor equal to zero: or or Now solve for x in each case -------------------------------- Answer: So our solutions are or

Quadratic_Equations/139520: What do I solve this by factoring? 49x^2 - 14x - 3 Thanks! 1 solutions Answer 101719 by jim_thompson5910(28536)   on 2008-05-01 11:33:05 (Show Source): You can put this solution on YOUR website! Looking at we can see that the first term is and the last term is where the coefficients are 49 and -3 respectively. Now multiply the first coefficient 49 and the last coefficient -3 to get -147. Now what two numbers multiply to -147 and add to the middle coefficient -14? Let's list all of the factors of -147: Factors of -147: 1,3,7,21,49,147 -1,-3,-7,-21,-49,-147 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -147 (1)*(-147) (3)*(-49) (7)*(-21) (-1)*(147) (-3)*(49) (-7)*(21) note: remember, the product of a negative and a positive number is a negative number Now which of these pairs add to -14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -14 First Number Second Number Sum 1 -147 1+(-147)=-146 3 -49 3+(-49)=-46 7 -21 7+(-21)=-14 -1 147 -1+147=146 -3 49 -3+49=46 -7 21 -7+21=14 From this list we can see that 7 and -21 add up to -14 and multiply to -147 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 ) Set the factorization equal to zero Now set each factor equal to zero: or or Now solve for x in each case ------------------------- Answer: So our solutions are or

Numeric_Fractions/139523: 4/5 = -11r - 2/3 1 solutions Answer 101718 by jim_thompson5910(28536)   on 2008-05-01 11:29:50 (Show Source): You can put this solution on YOUR website! Start with the given equation Multiply both sides by the LCM of 15. 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 Subtract 12 from both sides Add 165r to both sides Combine like terms on the right side Divide both sides by 165 to isolate r Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Graphs/139533: Graph the line with slope 1/2 passing through the point (-3,3) . 1 solutions Answer 101717 by jim_thompson5910(28536)   on 2008-05-01 11:28:24 (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 (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.

Quadratic_Equations/139521: How would I solve this using quadratic formula? f(x) = x^2 + 4 1 solutions Answer 101716 by jim_thompson5910(28536)   on 2008-05-01 11:26:57 (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 (note: since the polynomial does not have an "x" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like notice , , and ) Plug in a=1, b=0, and c=4 Square 0 to get 0 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 After simplifying, the quadratic has roots of or Notice if we graph the quadratic , we get graph of And we can see that there are no real roots To visually verify the answer, check out this page to see a visual representation of imaginary roots

Graphs/139531: This question is from textbook Essentials of College Mathematics I still haven't received an answer and I have class tomorrow. Could someone please help me with graphing this equation? What does the region look like and how do I graph it? 4x+3y=>24 3x+4y=>8 x=>0 y=>0 I would appreciate your help as soon as possible. Anne 1 solutions Answer 101715 by jim_thompson5910(28536)   on 2008-05-01 11:24:05 (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 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 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

Linear-equations/139482: Find the distance between (5,8) and (-4,5) 1 solutions Answer 101690 by jim_thompson5910(28536)   on 2008-04-30 23:56:39 (Show Source): You can put this solution on YOUR website! Start with the given distance formula where is the first point and is the second point Plug in , , , Evaluate to get 9. Evaluate to get 3. Square each value Add Simplify the square root (note: If you need help with simplifying the square root, check out this solver) So the distance approximates to which rounds to 9.49 So the distance between (5,8) and (-4,5) is approximately 9.49 units

Exponential-and-logarithmic-functions/139457: Find the largest value of x that satisfies: log(base5) (x^2) − log(base5) (x+2) = 2 x = THANKS A LOT! 1 solutions Answer 101689 by jim_thompson5910(28536)   on 2008-04-30 23:33:53 (Show Source): You can put this solution on YOUR website! Start with the given equation Combine the logs Use the relationship <===> to rewrite the equation Square 5 Multiply both sides by Distribute Get all terms to one side 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=-25, and c=-50 Negate -25 to get 25 Square -25 to get 625 (note: remember when you square -25, 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 So these expressions approximate to or So we can clearly see that is the largest value of x that satisfies the equation

Circles/139417: How do I solve for x with the information given? 1 solutions Answer 101688 by jim_thompson5910(28536)   on 2008-04-30 23:25:44 (Show Source): You can put this solution on YOUR website! Notice how the drawing has one angle that is not labeled. This angle and angle "x" are vertical angles. So this means that the unlabeled angle is also "x". So in the drawing write in this angle. Since there are 360 degrees in a circle, this means that the sum of these angles is 360. So we have the equation Combine like terms on the left side Subtract 260 from both sides Combine like terms on the right side Divide both sides by 2 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Quadratic_Equations/139443: Solve then graph. x + 8 > 2 The solution set is ? Help me figure this one out please. I would like to thank everyone who has helped me. I still have a couple weeks of needing your help. I must say I have learned a lot, but am still confused of a lot also...Thanks again everyone. 1 solutions Answer 101687 by jim_thompson5910(28536)   on 2008-04-30 23:20:30 (Show Source): You can put this solution on YOUR website! Start with the given inequality Subtract 8 from both sides Combine like terms on the right side -------------------------------------------------------------- Answer: So our answer is Now let's graph the solution set Start with the given inequality Plot the point on a number line Now plug in into the inequality Since is true, this means that we shade the entire region that is in. So shade to the right of . Note: there is a open circle at

Linear-systems/139472: This question is from textbook College Algebra How can I solve this system? 3x+4y=29 -x+2y=7 1 solutions Answer 101686 by jim_thompson5910(28536)   on 2008-04-30 23:17:40 (Show Source): You can put this solution on YOUR website! Let's solve this system using elimination 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 Multiply Subtract 20 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).

Exponential-and-logarithmic-functions/139463: This question is from textbook College Algebra Hello, I worked this problem and only got half credit. How can I work this as a systems of equations y=x^2-4 x-y=-2 This is what I did x=y-2 y=(y-2)^2-4 2y-4-4=0 1 solutions Answer 101685 by jim_thompson5910(28536)   on 2008-04-30 23:14:54 (Show Source): You can put this solution on YOUR website! Start with the given system Solve for x in the second equation Plug in Foil Subtract y from both sides Combine like terms Factor the right side Now set each factor equal to zero: or or Now solve for y in each case So our y-values are or Let's find x when Start with the second equation Plug in Subtract So when then Let's find x when Start with the second equation Plug in Subtract So when then ----------------------------------- Answer: So the solutions are (-2,0) or (3,5)

Parallelograms/139411: I know I'm solving for x, so I think I set up the equation like (2x+5)+(3x+1)+(13)+(5x-7)=? My problem is that I don't know what I set it to equal to. 1 solutions Answer 101657 by jim_thompson5910(28536)   on 2008-04-30 20:10:37 (Show Source): You can put this solution on YOUR website! Since the diagonals of a rectangle are equal, this means that we have the equation Remove the parenthesis Combine like terms on the left side Combine like terms on the right side Add 2 to both sides Subtract 3x from both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by 4 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Functions/138844: k. What price would you sell the tile sets at to realize this profit (hint, use the demand equation from part a)? 1 solutions Answer 101293 by jim_thompson5910(28536)   on 2008-04-27 16:46:55 (Show Source): You can put this solution on YOUR website! From part a), we found the demand equation where x is the number of units sold and p is the price. To find the demand simply plug in (remember, we max out the profit when 28 tiles are sold) Start with the given equation Plug in Add So the price should be set at $34

Trigonometry-basics/138826: Write as a sum Write as a product 1 solutions Answer 101283 by jim_thompson5910(28536)   on 2008-04-27 14:46:01 (Show Source): You can put this solution on YOUR website! 1) Start with the given expression Use the Product-to-Sum formula Add/Subtract Distribute So 2) Are you sure that it's ? There are no corresponding sum-to-product identities for mixed the trig functions sine and cosine. Double check your assignment.

Trigonometry-basics/138824: Solve 1 solutions Answer 101281 by jim_thompson5910(28536)   on 2008-04-27 14:38:55 (Show Source): You can put this solution on YOUR website! Start with the given equation Let . So this means that Replace with u and with 2u Rewrite as Replace with Square Factor out Now use the zero product property: ...or... Now let's solve : Take the square root of both sides ...or... Take the arcsine of both sides Since , this means ...or... However, since is not in the interval [0,2), it is not a solution. So the first solution is -------------------------------------------------------------------- Now let's solve : Subtract 1 from both sides Divide both sides by -4 Take the square root of both sides: ...or... So let's solve the first part : ...or... ...or... However since our interval is positive, the negative answer is not in the interval. So another part of the solution is --------------------- Now let's solve the second part : ...or... ...or... So another part of the solution is =============================================== Answer: So all together our solutions are:

Trigonometry-basics/138823: Find the exact value of 1 solutions Answer 101279 by jim_thompson5910(28536)   on 2008-04-27 14:35:46 (Show Source): You can put this solution on YOUR website! let so Substitute "2u" in for "u" Multiply Take the arccosine of the cosine of to get Replace with Add 1 to both sides Divide both sides by 2 Take the square root of both sides Simplify Rationalize the denominator if necessary So

Trigonometry-basics/138821: Prove the identity: (x is theta) 1 solutions Answer 101276 by jim_thompson5910(28536)   on 2008-04-27 14:25:07 (Show Source): You can put this solution on YOUR website! Note: I'm only manipulating the left side. I'm not touching the right side. I'm only showing it for comparison. Start with the given equation Break up to get Expand using the sum-difference formulas Replace with . Replace with . Factor out Rearrange the terms Factor out 2 Replace with Replace with Distribute Combine like terms Distribute So we've just proven that is an identity.

Trigonometry-basics/138819: Prove the identity: (x is theta) 1 solutions Answer 101275 by jim_thompson5910(28536)   on 2008-04-27 14:16:58 (Show Source): You can put this solution on YOUR website! Note: I'm only manipulating the left side. I'm not touching the right side. I'm only showing it for comparison. Start with the given equation Expand by using the Sum-Difference Formulas Foil Combine like terms Replace with . Replace with Distribute Combine like terms So we've just proven that is an identity.

Trigonometry-basics/138815: Prove the identity: (x is theta) 1 solutions Answer 101273 by jim_thompson5910(28536)   on 2008-04-27 14:08:28 (Show Source): You can put this solution on YOUR website! Note: I'm only manipulating the left side. I'm not touching the right side. I'm only showing it for comparison. Start with the given equation Replace with Simplify Multiply both the numerator and denominator by the LCD . This will clear out the denominators in both the numerator and the denominator. Distribute and multiply Replace with 1 Simplify So we've just proven that is an identity.

Trigonometry-basics/138801: Graph and the period and phase shift 1 solutions Answer 101260 by jim_thompson5910(28536)   on 2008-04-27 12:41:30 (Show Source): You can put this solution on YOUR website! Graph of (not the best graph, but it gives you an idea of what it looks like) Remember the general form is where the period is , and the phase shift is So in this case... the period is , the phase shift is

Trigonometry-basics/138798: Graph and find amplitude, period and phase shift 1 solutions Answer 101259 by jim_thompson5910(28536)   on 2008-04-27 12:36:21 (Show Source): You can put this solution on YOUR website! Graph of Remember the general form is where the amplitude is , the period is , and the phase shift is So in this case... the amplitude is , the period is , the phase shift is

Functions/138710: "A company calculates it's profit by finding the difference between revenue and cost. The cost function of producing x hammers is C(x) = 4x+170. If each hammer is sold for $10, the revenue function for selling x hammers is R (x) = 10x." 1.) How many hammers must be sold to make a profit? 2.) How many hammers must be sold to make a profit of $100? 1 solutions Answer 101212 by jim_thompson5910(28536)   on 2008-04-26 17:58:25 (Show Source): You can put this solution on YOUR website! 1) The profit function is defined by: Profit = Revenue - Cost So in function notation it looks like: So in our case: Plug in and Distribute the negative Combine like terms Set the right side greater than zero. Remember we're looking for positive profit. Add 170 to both sides Divide both sides by 6 Divide Round to the nearest whole number. A third of a hammer can't be sold. So when , we'll have positive profit. So more than 29 hammers must be sold to gain a profit. 2) We're still using the profit function. So Since we want a profit of $100, simply plug in . Start with the profit function Plug in Add 170 to both sides Divide both sides by 6 So when , we'll have a profit of $100. So 45 must be sold to make a profit of $100.

Graphs/138691: Is the equation symmetric about the x-axis? 1 solutions Answer 101206 by jim_thompson5910(28536)   on 2008-04-26 14:41:38 (Show Source): You can put this solution on YOUR website! Remember, if , then the equation is symmetric about the x-axis. So in this case, we only need to replace y with negative y and see if the equations are equivalent. Start with the given equation Replace each "y" with negative y Raise -y to the fourth power to get . Raise -y to the second power to get Since the first equation is equivalent to the last equation, this shows that graph is symmetric about the x-axis For visual proof, here's the graph: From the graph, we can see that equation is symmetric about the x-axis

Graphs/138688: The demand equation is given as and the supply as . Find the equilibrium price. 1 solutions Answer 101205 by jim_thompson5910(28536)   on 2008-04-26 14:31:24 (Show Source): You can put this solution on YOUR website! Start with the given system Now move onto the second equation Plug in Multiply both sides by the LCD 50x Distribute and multiply Subtract 625000 from both sides. Factor the left side (note: if you need help with factoring, check out this solver) Now set each factor equal to zero: or or Now solve for x in each case So our answer is or However, a negative number of jackets does not make sense. So the only solution is Now plug into the second equation So our solution is and So when 500 jackets are sold, the supply will equal the demand at $25.

Graphs/138687: Graph the two equations and and find the solutions 1 solutions Answer 101203 by jim_thompson5910(28536)   on 2008-04-26 14:21:22 (Show Source): You can put this solution on YOUR website! Start with the given equation Solve for y or Break up the right side Now let's graph Graph of Now let's graph Graph of Now graph Graph of Now graph the three equations together (note: the first two equations make up ) Graph of (red). Graph of (green). Graph of (blue) From the graph, we can see that there are no intersections. So there are no solutions.

Graphs/138686: Graph the two equations and and find the solutions 1 solutions Answer 101201 by jim_thompson5910(28536)   on 2008-04-26 14:12:50 (Show Source): You can put this solution on YOUR website! First graph Graph of Now graph Graph of Now graph the two equations together Graph of (red. Graph of (green) From the graph, we can see that the two equations intersect at the points (-2,1) and (1,4) So this means that the solutions are and OR and

Graphs/138685: A cost function is given as . Find the cost of producing 100 boxes 1 solutions Answer 101199 by jim_thompson5910(28536)   on 2008-04-26 14:00:53 (Show Source): You can put this solution on YOUR website! Since we're trying to find , our test zero is 100 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. 100 | 1/2 -8 -80 200 | Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1) 100 | 1/2 -8 -80 200 | 1/2 Multiply 100 by 1/2 and place the product (which is 50) right underneath the second coefficient (which is -8) 100 | 1/2 -8 -80 200 | 50 1/2 Add 50 and -8 to get 42. Place the sum right underneath 50. 100 | 1/2 -8 -80 200 | 50 1/2 42 Multiply 100 by 42 and place the product (which is 4200) right underneath the third coefficient (which is -80) 100 | 1/2 -8 -80 200 | 50 4200 1/2 42 4120 Add 4200 and -80 to get 4120. Place the sum right underneath 4200. 100 | 1/2 -8 -80 200 | 50 4200 1/2 42 4120 Multiply 100 by 4120 and place the product (which is 412000) right underneath the fourth coefficient (which is 200) 100 | 1/2 -8 -80 200 | 50 4200 412000 1 42 4120 Add 412000 and 200 to get 412200. Place the sum right underneath 412000. 100 | 1/2 -8 -80 200 | 50 4200 412000 1/2 42 4120 412200 Since the last column adds to 412200, we have a remainder of 412200. ------------------------------------ Answer: So according to the remainder theorem, So the cost to produce 100 boxes is $412,200