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# Recent problems solved by 'Nate'

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 Systems-of-equations/58447: The net weight of a bottle of olives is 216grams. Find the smallest number of bottles that must be purchased tohave at least 2kilograms of olives. Thanks!!!1 solutions Answer 40029 by Nate(3500)   on 2006-10-27 08:49:36 (Show Source): You can put this solution on YOUR website!How much does the total bottle weigh with the olive? I have no way of finding the olive's individual weight. Please do not respond in the comment area because I don't check there.
 Systems-of-equations/58448: For every 20ft. of chain link fencing, 80 support posts are used. How many suport posts will be needed for 45ft of chain link fence? Write the proportion that could be used to solve this problem, using the variable x thanks1 solutions Answer 40028 by Nate(3500)   on 2006-10-27 08:48:09 (Show Source): You can put this solution on YOUR website!x/45 = 80/20 x = 180
 Polynomials-and-rational-expressions/58436: Find all roots of f(x)=2x^4-17x^3+49x2-23x-91, given that 7/2 and -1 are roots Thank you1 solutions Answer 40027 by Nate(3500)   on 2006-10-27 08:46:09 (Show Source): You can put this solution on YOUR website!f(x) = 2x^4 - 17x^3 + 49x^2 - 23x - 91 (x + 1) is a factor: -1|....2....-17....49....-23....-91 ........2....-19....68.....-91....0 (x + 1)(2x^3 - 19x^2 + 68x - 91) = f(x) (x - 7/2) is a factor: 7/2|....2....-19....68....-91 .........2.....-12....26.....0 (x + 1)(x - 7/2)(2x^2 - 12x + 26) = f(x) (x + 1)(x - 7/2)2(x^2 - 6x + 13) = f(x) Don't Exist
 Graphs/58438: Graph y=(x-5)(2x+7)(3-x)^2(x-7)(x+2)^2, and label all intercepts ty1 solutions Answer 40025 by Nate(3500)   on 2006-10-27 08:36:09 (Show Source): You can put this solution on YOUR website!y-intercept y = (x - 5)(2x + 7)(3 - x)^2(x - 7)(x + 2)^2 y = (0 - 5)(2*0 + 7)(3 - 0)^2(0 - 7)(0 + 2)^2 y = (5)(7)(3)^2(7)(2)^2 = 35*9*7*4 = 8820 (0,8820) x-intercepts y = (x - 5)(2x + 7)(3 - x)^2(x - 7)(x + 2)^2 0 = (x - 5)(2x + 7)(3 - x)^2(x - 7)(x + 2)^2 x - 5 = 0 2x + 7 = 0 3 - x = 0 x - 7 = 0 x + 2 = 0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ x = 5 x = -7/2 x = 3 x = 7 x = -2 (5,0), (-7/2,0), (3,0), (7,0), (-2,0)
 Rational-functions/58393: A Go-ped traveled 9 miles in 24 minutes. How long would it take to go 27 miles? A.) 1 hour, 6 minutes B.) 1 hour, 12 minutes C.) 1 hour, 26 minutes D.) 1 hour 1 solutions Answer 40008 by Nate(3500)   on 2006-10-26 21:31:55 (Show Source): You can put this solution on YOUR website!Distance = Rate * Time Rate = Distance / Time Rate = 9 / 24 = 3 / 8 Distance = Rate * Time Time = Distance / Rate Time = 27 / (3 / 8) = 27(8 / 3) = 9 * 8 = 72 minutes 1 hour and 12 minutes B.)
 Rational-functions/58396: 3/5 = 36/60 True or False ? 1 solutions Answer 40007 by Nate(3500)   on 2006-10-26 21:29:41 (Show Source): You can put this solution on YOUR website!(3) / (5) ~> (3*12) / (5 * 12) ~> (36) / (60) True
 Expressions-with-variables/58382: I cannot solve x^4-5x^2-8=0 My professor told me to substitute y for x but I still cannot fathom what is going on. I have tried for the past several hours please help. 1 solutions Answer 40002 by Nate(3500)   on 2006-10-26 21:23:25 (Show Source): You can put this solution on YOUR website!Depending on your math status, I could lead you onto what your professor was indicating. y = x^2 leads to ~> (x^2)^2 - 5(x^2) - 8 = 0 (y)^2 - 5(y) - 8 = 0 y^2 - 5y - 8 = 0 Now, we have the partial answer. Since the original equation supported , we must have the variable equal something to develop the answer. About: x = 2.5050 x = -2.5050
 Rational-functions/58384: State the degree of the following polynomial. 8x3 + 6x2y + 4xy3 - 2y4 1 solutions Answer 39998 by Nate(3500)   on 2006-10-26 21:14:52 (Show Source):
 Polynomials-and-rational-expressions/58336: 2x^2-12x=1481 solutions Answer 39959 by Nate(3500)   on 2006-10-26 18:40:24 (Show Source): You can put this solution on YOUR website!x^2 - 6x = 74 (x - 3)^2 = 74 + 9 = 83 x - 3 = +- sqrt(83) x = 3 +- sqrt(83)
 Linear-equations/58350: This question is from textbook Connected Math 2 How do you find the slope?1 solutions Answer 39957 by Nate(3500)   on 2006-10-26 18:37:43 (Show Source): You can put this solution on YOUR website!Dependes: for a linear line or from derivitives? Linear Line: m = (y2 - y1)/(x2 - x1) for (x1,y1) and (x2,y2)
 Geometry_proofs/58347: Directions: Set up and complete a proof of the statement. If a triangle is isosceles, the triangle formed by its base and the angle bisectors of its base angles is also isosceles.1 solutions Answer 39955 by Nate(3500)   on 2006-10-26 18:35:17 (Show Source): You can put this solution on YOUR website!Define: Big Triangle: ABC where A is the top part, B is the bottom left, and C is the bottom right Small Triangle: Top part is labled D 1. AB = AC; < ABC = < ACB ........ 1. given 2. 2 * < DBC = < ABC and 2 * < DCB = < ACB ..... 2. definition of angle bisector 3. 2 * < DBC = < ABC and 2 * < DCB = < ABC ..... 3. substitution 4. 2 * < DBC = 2 * < DCB ................. 4. transitive property 5. < DBC = < DCB ................... 5. division 6. DB = DC ....................... 6. opposite segements of congruent angles are congruent 7. triangle DBC is isoceles ...... 7. definition of isoceles triangles I am sorry if it is quite long; I just like to make things clear.
 Exponential-and-logarithmic-functions/58335: This question is from textbook Algebra 2 9z-4=6.281 solutions Answer 39944 by Nate(3500)   on 2006-10-26 17:25:19 (Show Source): You can put this solution on YOUR website!9z = 10.28 z = 10.28/9
 Miscellaneous_Word_Problems/58158: A metallurgist has one alloy containing 20% copper and another containing 70% copper. How many pounds of alloy must he use to make 50 pounds of the a third alloy containing 50% copper? Thank you for taking the time to help!1 solutions Answer 39943 by Nate(3500)   on 2006-10-26 17:18:36 (Show Source): You can put this solution on YOUR website!x = amount of 20% copper y = amount of 70% copper *Remember: x = 50 - y (0.2x + 0.7y)/50 = 0.5 0.2x + 0.7y = 25 0.2(50 - y) + 0.7y = 25 10 - 0.2y + 0.7y = 25 0.5y = 15 y = 30 x = 50 - y = 50 - 30 = 20 30 pounds of 70% copper 20 pounds of 20% copper
 Money_Word_Problems/58319: Michael's Coffee Shop sells a special blend called Mike's Favorite. For the blend, Michael mixes Hazelnut Coffee, which sells for \$7.50 per pound, with Cinnamon Coffee, which sells for \$6.75 per pound. How much of each flavor must he use to create 10 pounds of Mike's Favorite blend if he sells it for \$7.00?1 solutions Answer 39942 by Nate(3500)   on 2006-10-26 17:12:43 (Show Source): You can put this solution on YOUR website!h = the amount of pounds of hazelnut coffee c = the amount of pounds of cinnamon coffee *Remember: c = 10 - h (7.5h + 6.75c)/10 = 7 7.5h + 6.75c = 70 7.5h + 6.75(10 - h) = 70 7.5h + 67.5 - 6.75h = 70 0.75h = 2.5 h = 3 1/3 c = 10 - h = 10 - 3 1/3 = 6 2/3
 Geometry_proofs/58317: Prove that the diagonals of a parallelogram bisect each other.1 solutions Answer 39941 by Nate(3500)   on 2006-10-26 17:08:17 (Show Source): You can put this solution on YOUR website!Just graph a square on a cartesian coordinate plain. P(1,1), N(-1,1), S(-1,-1), and M(1,-1) The points that make the diagonals: (-1,1) and (1,-1) <~> (1,1) and (-1,-1) Slope of (-1,1) and (1,-1) m = (-1 - 1)/(1 + 1) = -2/2 = -1 Slope of (1,1) and (-1,-1) m = (1 + 1)/(1 + 1) = 2/2 = 1 The slope of one is the inverse of it's negative counterpart. The lines are perpendicular. Now, you may have to put that in a proof; I do not if your school wants you to do so.
 Geometry_Word_Problems/58324: The base of a ladder is 3 feet away from the wall. The top of the ladder is 14 feet from the floor. Find the length of the ladder to the nearest thousandth. Thanks~ ac1 solutions Answer 39939 by Nate(3500)   on 2006-10-26 17:02:26 (Show Source): You can put this solution on YOUR website!............................./..|..... ............................/...|..... .........................../....|..... .....................c../......|.14ft ......................../.......|..... ....................../.........|..... ..................../...........|..... ................../_3ft__|..... ~~~~~~~~~~~~~~~~ a^2 + b^2 = c^2 14^2 + 3^2 = c^2 196 + 9 = c^2 205 = c^2 sqrt(205) = c = about 14.318ft
 Radicals/58325: It says simplify: 5\/(radical sign)252 Did I do this right? 5\/7*36= 5*\/7*\/36=5*49*61 solutions Answer 39937 by Nate(3500)   on 2006-10-26 16:54:11 (Show Source): You can put this solution on YOUR website!5*sqrt(252) 5*sqrt(2*126) 5*sqrt(2*2*63) 5*sqrt(2*2*3*21) 5*sqrt(2*2*3*3*7) 5(2)(3)*sqrt(7) 30*sqrt(7)
 Functions/58326: A=P+Prt1 solutions Answer 39936 by Nate(3500)   on 2006-10-26 16:52:22 (Show Source): You can put this solution on YOUR website!Total amount after interest = principle + principle*rate*time
 Radicals/58327: It says to simplify: 9\/(radical sign)2-\/8 Is this correct? I got: 9\/2-\/4*2=9\/2-2\/2 7\/2 I appreciate your imput! Thank you CH1 solutions Answer 39935 by Nate(3500)   on 2006-10-26 16:51:19 (Show Source): You can put this solution on YOUR website!9*sqrt(2) - sqrt(8) 9*sqrt(2) - 2*sqrt(2) sqrt(2)(9 - 2) 7*sqrt(2)
 Linear-equations/58329: Finding the slope and y-intercept for each line that has a slope and y-intercept. The problem is x+2y=31 solutions Answer 39933 by Nate(3500)   on 2006-10-26 16:50:11 (Show Source): You can put this solution on YOUR website!Put the equation in slope intercept form for easy access to information. x + 2y = 3 2y = -x + 3 y = -x/2 + 3/2 slope-intercept form: y = mx + b where m is the slope and b is the y-intercept -1/2 = slope 3/2 = y-intercept
 Numeric_Fractions/58330: This question is from textbook Algebra 1 54 divided by negative one half1 solutions Answer 39931 by Nate(3500)   on 2006-10-26 16:48:15 (Show Source): You can put this solution on YOUR website!54/(-1/2) 54(-2) -108
 Linear_Algebra/58328: A shoe mfg. makes outdoor and indoor soccer shoes. There is a two- step manufactoring processes for both kinds of shoes. Each pair of outdoor shoes require 2 hours of processing in step one, 1 hour in tep two, and produces a profit of \$20 for the company. Indoor shoes require 1 hour of processing step one, 3 hour in step two and produces a profit of \$15 for each pair. The company has 40 hours of labor per day avaiable for step one and 60 hours of labor per day available for step two. How many pairs of each type of shoe can be produced per day to maximize profit.1 solutions Answer 39930 by Nate(3500)   on 2006-10-26 16:47:24 (Show Source): You can put this solution on YOUR website!How can a company have 40 hours or 60 hours of labor per day when a day is 24 hours?
 Functions/58332: This question is from textbook Algerbra 1 can u solve the problem for me1 solutions Answer 39928 by Nate(3500)   on 2006-10-26 16:44:52 (Show Source): You can put this solution on YOUR website!I most likely can.
 Probability-and-statistics/58334: Two dice are rolled. What are the number of ways an 8 can appear from the throw of the dice?1 solutions Answer 39927 by Nate(3500)   on 2006-10-26 16:44:19 (Show Source): You can put this solution on YOUR website!There is a total of five ways. 6 : 2 2 : 6 5 : 3 3 : 5 4 : 4 This tells you the number of possibilities: f(x) = -|x - 7| + 6 f(8) = -|8 - 7| + 6 = -|1| + 6 = -1 + 6 = 5
 Equations/57671: by what number must you multiply each side of the equation to produce the equivalent equation x+25? 2/5 x=10 a. 1/5 b. 5/2 c. 4 d. 51 solutions Answer 39383 by Nate(3500)   on 2006-10-23 15:31:59 (Show Source): You can put this solution on YOUR website!2x/5 = 10 is 2x/5 - 10 = 0 What times -10 gives us 25? -10x = 25 x = -5/2 Answer: None of the above; I think you typed something wrong.
 Graphs/57461: This question is from textbook Beginning Algebra Can someone help me on this problem? I need to graph the following iequality: 4x + y > 4 - (there is a line under the >) I have to send this through the computer and not on paper. Can someone help me on this? I would appreciate it allot. Thanks, Sher1 solutions Answer 39225 by Nate(3500)   on 2006-10-22 11:31:08 (Show Source): You can put this solution on YOUR website!If you have anymore questions like these, you could just do this: >= meaning it is greater than or equal to .... we know the difference. 4x + y >= 4 y >= -4x + 4 solid line with shading above
 Graphs/57462: This question is from textbook Beginning Algebra Can someone help me on this problem? I need to graph the following inequality: 3x - 4y < 12 I have to send this through the computer and not on paper. Can someone show me how it looks and worked out? Thanks, I would appreciate it. Sher1 solutions Answer 39224 by Nate(3500)   on 2006-10-22 11:29:13 (Show Source): You can put this solution on YOUR website!3x - 4y < 12 -4y < -3x + 12 y > 3x/4 - 3 It is a dotted line with shading above the line.
 Systems-of-equations/57470: Hi! I need some help factoring this problem out and then simplyfying my answer. x^2+2x-15 --------- x^2-9 ------- x^2+6x+5 --------- x^2+4x+31 solutions Answer 39222 by Nate(3500)   on 2006-10-22 11:25:41 (Show Source): You can put this solution on YOUR website!I hope this is how you wanted it: ~~~~ ~~~~ ~~~~ ~~~~ ~~~~
 Functions/57465: This question is from textbook Beginning Algebra Can someone help me on this problem? I need to rewrite the following equation as a function of x. -3x + 4y = 11 Thank you, Ashley1 solutions Answer 39221 by Nate(3500)   on 2006-10-22 11:21:36 (Show Source): You can put this solution on YOUR website!-3x + 4y = 11 4y = 3x + 11 y = 3x/4 + 11/4 f(x) = 3x/4 + 11/4 or f(x) = 0.75x + 2.75
 Functions/57469: This question is from textbook Beginning Algebra Can someone help me on this problem? If the inventor charges \$4 per unit, then her profit for producing and selling x units is given by the function: P(x) = 2.25x - 7000 (a) What is her profit if she sells 2000 units? (b) What is her profit if she sells 5000 units? (c) What is the break-even point for sales? Thanks, Ashley1 solutions Answer 39219 by Nate(3500)   on 2006-10-22 11:18:35 (Show Source): You can put this solution on YOUR website!(a) What is her profit if she sells 2000 units? P(x) = 2.25x - 7000 P(x) = 2.25(2000) - 7000 = -2500 She loses \$2,500 (tough break) (b) What is her profit if she sells 5000 units? P(x) = 2.25x - 7000 P(x) = 2.25(5000) - 7000 = 4250 She makes a profit of \$4,250 (c) What is the break-even point for sales? P(x) = 2.25x - 7000 0 = 2.25x - 7000 7000 = 2.25x 7000/2.25 = 3111 1/9
 Coordinate-system/57466: This question is from textbook Beginning Algebra Can someone help me graph this problem. I have to put it on the computer and send. I need to graph the following function: f(x) = 2x - 5 Thanks, Ashley1 solutions Answer 39218 by Nate(3500)   on 2006-10-22 11:14:46 (Show Source): You can put this solution on YOUR website!You can plot points; you can follow slope-intercept rule; you can do a lot to make a graph.