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# Recent problems solved by 'Nate'

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 Linear-equations/68732: 1 solutions Answer 49255 by Nate(3500)   on 2007-02-03 18:45:29 (Show Source): You can put this solution on YOUR website!(x - 1)^2 = 12 x - 1 = +- sqrt(12) x = 1 +- sqrt(12)
 Systems-of-equations/69236: Could someone please help me add and simplify -2/x+2 + 3/x-2 Thanks so much for your help in advance!1 solutions Answer 49253 by Nate(3500)   on 2007-02-03 18:43:56 (Show Source): You can put this solution on YOUR website!-2(x - 2) / (x + 2)(x - 2) + 3(x + 2) / (x - 2)(x + 2) (-2x + 4) / (x^2 - 4) + (3x + 6)/(x^2 - 4) (-2x + 4 + 3x + 6) / (x^2 - 4) (x + 10) / (x^2 - 4)
 Geometric_formulas/69234: Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series? Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally.1 solutions Answer 49252 by Nate(3500)   on 2007-02-03 18:42:08 (Show Source): You can put this solution on YOUR website!Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Let's use an example: 2,4,6,8,10,12,14,16,etc. First Digit = 2 Second Digit = 4 (1,2) and (2,4) m = 2/1 y = 2x x = 3 y = 6 The line is linear. Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series? Let's use an example: 1,3,9,27,81,etc. (1,1) and (2,3) m = 2/1 y = 2x - 1 x = 3 y = 5 the value should be 9 Not Linear Quadratic? what is the vertex? let's leave that Exponential? (0,1/3) y = a*b^x 1/3 = a*1 y = (1/3)b^x 1 = (1/3)b 3 = b y = (1/3)(3^x) = 3^(x - 1) x = 3 y = 3^2 = 9 The line is exponential. The rest is self explanatory.
 Complex_Numbers/69137: subtract and simplify 2/(x+1)=3/(x-3)1 solutions Answer 49211 by Nate(3500)   on 2007-02-03 10:11:34 (Show Source): You can put this solution on YOUR website!2(x - 3) = 3(x + 1) 2x - 6 = 3x + 3 -9 = x
 Numeric_Fractions/69135: Mrs. Tate brings 5 1/2 pounds of candy to divide among ger 22 students. If the candy is divided equally, how many pounds of candy does each student recieve?1 solutions Answer 49210 by Nate(3500)   on 2007-02-03 10:07:50 (Show Source): You can put this solution on YOUR website!5.5/22 = 0.25 or 1/4 pounds each
 Complex_Numbers/69140: if x/2+y/5=1 sole for x1 solutions Answer 49209 by Nate(3500)   on 2007-02-03 10:06:23 (Show Source): You can put this solution on YOUR website!x/2 = 1 - y/5 x = 2 - 2y/5
 Linear-systems/69083: Is the ordered pair a solution of the solution? (1,19) y<_7x-13 y>3x+61 solutions Answer 49169 by Nate(3500)   on 2007-02-02 18:33:49 (Show Source): You can put this solution on YOUR website!y <_ 7x - 13 y <_ 7 - 13 y <_ -6 No y > 3x + 6 y > 3 + 6 y > 9 Yes
 Linear-equations/69084: Adult tickets for a play cost \$11.00 and child tickets cost \$10.00. If there were 23 people at a performance and the theater collected \$246.00 from ticket sales, how many children attended the play? Please help me to solve this 1 solutions Answer 49167 by Nate(3500)   on 2007-02-02 18:32:34 (Show Source): You can put this solution on YOUR website!a = number of adult tickets c = number of child tickets a + c = 23 or a = 23 - c 11a + 10c = 246 Plug: 11(23 - c) + 10c = 246 253 - 11c + 10c = 246 -c = -7 c = 7 a = 23 - 7 = 16 16 adult tickets and 7 child tickets
 Linear-equations/69085: Bob invested \$20,000, part at 14% and part at 13%. If the total interest at the end of the year is \$2,720, how much did he invest at 14%? Please help me on this 1 solutions Answer 49166 by Nate(3500)   on 2007-02-02 18:30:19 (Show Source): You can put this solution on YOUR website!P*R*T = I T = 1 P*R = I I + I = 2720 x*0.14 + (20,000 - x)*0.13 = 2720 0.14x + 2600 - 0.13x = 2720 0.01x = 120 x = \$12,000 in 14%
 Linear-equations/69086: Write the equation of the line that passes through point (-2,3) with a slope of -4. Please help1 solutions Answer 49165 by Nate(3500)   on 2007-02-02 18:26:43 (Show Source): You can put this solution on YOUR website!y - y1 = m(x - x1) y - 3 = -4(x + 2) y - 3 = -4x - 8 y = -4x - 5
 Linear-equations/69088: One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number. Please help1 solutions Answer 49164 by Nate(3500)   on 2007-02-02 18:25:37 (Show Source): You can put this solution on YOUR website!smaller number = x larger number = x + 12 x + 2x + 24 = 39 3x = 15 x = 5 Numbers are 5 and 17.
 Linear-equations/69089: The length of a rectangle is 8 in, more than twice its width. If the perimeter of the rectangle is 64in, find the width of the rectangle. Please help1 solutions Answer 49163 by Nate(3500)   on 2007-02-02 18:24:20 (Show Source): You can put this solution on YOUR website!width = w length = 2w + 8 2*length + 2*width = perimeter 2(2w + 8) + 2(w) = 64 4w + 16 + 2w = 64 6w = 48 w = 8 width = 8in length = 24in
 Trigonometry-basics/69005: what is the area of a 2ft wide walk around the outside of a garden that is 30ft long and 20ft wide?1 solutions Answer 49122 by Nate(3500)   on 2007-02-01 21:44:06 (Show Source): You can put this solution on YOUR website!width = 2 + 20 + 2 = 24 length = 2 + 30 + 2 = 34 area of whole area = 24*34 area of garden = 20*30 area of walk = 24*34 - 20*30 area of walk = 816 - 600 = 216ft^2
 Quadratic_Equations/69007: Solve the following equation for x: x^2 + 5 = 21 Express your answer(s) in both "simplified radical" form, and in decimal form. I came up with x=4 and x=sqrt16. Would this be correct.1 solutions Answer 49121 by Nate(3500)   on 2007-02-01 21:40:04 (Show Source): You can put this solution on YOUR website!x^2 + 5 = 21 x^2 = 16 x = +- 4
 Quadratic_Equations/69008: Solve the following equation for x: 5(x – 2)^2 = 3 Express your answer(s) in both "simplified radical" form, and in decimal form. I came up with x=2+or-sqrt(3/5). Could someone please check this one for me. Thanks.1 solutions Answer 49120 by Nate(3500)   on 2007-02-01 21:38:53 (Show Source): You can put this solution on YOUR website!5(x – 2)^2 = 3 (x – 2)^2 = 3/5 x - 2 = +- sqrt(3/5) x = 2 +- sqrt(3/5) x = 2 +- sqrt(3)/sqrt(5) x = 10/5 +- sqrt(15)/5 x = (10 +- sqrt(15))/5 x = 2.77 or x = 1.23
 Polynomials-and-rational-expressions/69009: This question is from textbook heath algebra 1 what is the FOIL method?1 solutions Answer 49119 by Nate(3500)   on 2007-02-01 21:33:38 (Show Source): You can put this solution on YOUR website!First Outer Inner Last Multiply the first terms Multiply the outer terms Multiply the inner terms Multiply the las terms (x + 1)(2x - 2) 2x^2 + 2x - 2x - 2 2x^2 - 2
 Proportions/68280: Here is a question: At an Italian restaurant there is a jug of heterogeneous oils that are composed of 20 liters of 93% oil type and 10 liters of pure neutral liquid. Now, the 93% oils are on the bottom while the neutral liquid is less dense. How much of the oils must I take out of the bottom, so that when I shake the jug up, I get a heterogeneous solution of 64%?1 solutions Answer 48569 by Nate(3500)   on 2007-01-27 21:08:53 (Show Source): You can put this solution on YOUR website!First, let us find the solution's percentage of oil content: (20(93%) + 10(0%))/(30) = ? (20(0.93) + 10(0.00))/30 = ? 18.6/30 = 0.62 or 62% On the contrary, you would have to add oils to get a solution of 64% .... (18.6 + x(0.93))/(30 + x) = 0.64 18.6 + 0.93x = 19.2 + 0.64x 0.29x = 0.6 x = about 2.1 liters of 93% oils must be added
 Graphs/68265: This question is from textbook An Incremental Development PLease help! Complete the square as an aid in graphing : y = -x^2 + 8x - 121 solutions Answer 48565 by Nate(3500)   on 2007-01-27 20:55:18 (Show Source): You can put this solution on YOUR website!y = -x^2 + 8x - 12 -y = x^2 - 8x + 12 -y - 12 = x^2 - 8x -y - 12 + 16 = (x - 4)^2 -y + 4 = (x - 4)^2 -y = (x - 4)^2 - 4 y = -(x - 4)^2 + 4
 Functions/68266: This question is from textbook If f(x)=-1, what is x? What point(s) areon the graph of f. 1 solutions Answer 48563 by Nate(3500)   on 2007-01-27 20:52:18 (Show Source): You can put this solution on YOUR website!f(x) = -1 + 0x x is any real number y = -1 is a horizontal line So all x points are all reals, but all f(x) points are -1.
 Numbers_Word_Problems/68268: This question is from textbook An Incremental Development The sum of the digits of a two-digit counting number was 9. When the digits were reversed, the new number was 45 less than the original number. What was the original number?1 solutions Answer 48561 by Nate(3500)   on 2007-01-27 20:48:51 (Show Source): You can put this solution on YOUR website!Two Digit Number: 10a + b a + b = 9 or a = 9 - b 10b + a = 10a + b - 45 Plug: 10b + 9 - b = 10(9 - b) + b - 45 9b + 9 = 90 - 10b + b - 45 9b + 9 = 45 - 9b 18b = 36 b = 2 a = 7 Number: 72
 Travel_Word_Problems/68203: Ching leaves San Francisco and travels toward Los Angeles at 50 mi/h. An hour later, Phil leaves Los Angeles and travels toward San Francisco at 60 mi/h. If the two cities are 380 miles apart, how many hours will it take for Ching to meet Phil?1 solutions Answer 48509 by Nate(3500)   on 2007-01-27 11:21:19 (Show Source): You can put this solution on YOUR website!At the start, the total distance between the two was 380: 380 Then, Ching drives for 50 miles for 50mi/h: 330 - 50x Then, Phil travels 60 mi/h: 330 - 50x - 60x = 0 -110x = -330 x = 3 3 hours
 absolute-value/68202: An 800 g solution of acid and water contains 128 g of acid. What percent of the solution is acid?1 solutions Answer 48508 by Nate(3500)   on 2007-01-27 11:16:24 (Show Source): You can put this solution on YOUR website!amount of acid / total amount = acidity 128 / 800 0.16 or 16%
 Evaluation_Word_Problems/68204: Translate the following statement into an algebraic equation. Let x represent the number. 6 times a number is 14 more than that number. 1 solutions Answer 48507 by Nate(3500)   on 2007-01-27 11:12:19 (Show Source): You can put this solution on YOUR website!6x = 14 + x 5x = 14 x = 14/5
 Mixture_Word_Problems/68002: Dimitruis skipped lunch today to get some sun in the school courtyard. Lying on the grass and looking up at an angle of 22 he could see the top of the flagpole which was about 100 ft away. How tall is the flagpole? 1 solutions Answer 48352 by Nate(3500)   on 2007-01-25 15:59:39 (Show Source): You can put this solution on YOUR website!..|\ ..|..\ h|....\ ..|......\ ..|...22\ ...... 100 ft tan(22degrees) = h/100 100*tan(22) = h About 40 feet
 Geometric_formulas/67418: This question is from textbook Advanced mathematics Write the quadratic equation with a lead coefficient of 1 whose roots are 1+3i and 1-3i. Could someone show me how to this step-by-step, please?1 solutions Answer 47978 by Nate(3500)   on 2007-01-21 08:50:06 (Show Source): You can put this solution on YOUR website!Say you have these for roots: (x - 5)(x + 1) or x^2 - 4x - 5 Your roots would be 5 and -1 because you would take the opposite (negative value) of the value in the parenthesis. (x - (1 + 3i))(x - (1 - 3i)) (x - 1 - 3i)(x - 1 + 3i) x^2 - x - 3xi - x + 1 + 3i + 3xi - 3i + 9 x^2 - 2x + 10 Check: x^2 - 2x = -10 (x - 1)^2 = -9 x - 1 = +- 3i x = 1 +- 3i
 Complex_Numbers/67434: Find the 4 roots of the equation: x^4+kx^2+1=0 k^2<41 solutions Answer 47976 by Nate(3500)   on 2007-01-21 08:43:31 (Show Source): You can put this solution on YOUR website!figure that p = x^2 for now: (x^2)^2 + k(x^2) + 1 = 0 p^2 + kp + 1 = 0 p^2 + kp = -1 (p + k/2)^2 = -1 + k^2/4 p + k/2 = +- sqrt(k^2/4 - 1) p = -k/2 +- sqrt(k^2/4 - 1) x^2 = -k/2 +- sqrt(k^2/4 - 1) x = +- sqrt(-k/2 +- sqrt(k^2/4 - 1)) ~~~~~~ k^2 < 4 -2 < k < 2
 Travel_Word_Problems/67435: The Jones family drove to Disneyland at 50 miles per hour and returned on the same route at 40mph. Find the distance to Disneyland if the total driving time was 7.2 hours. 1 solutions Answer 47975 by Nate(3500)   on 2007-01-21 08:38:39 (Show Source): You can put this solution on YOUR website!distance = 50*t distance = 40*(7.2 - t) 50t = 40(7.2 - t) 50t = 288 - 40t 90t = 288 t = 3.2 distance = 50*t or 160 miles
 Geometric_formulas/67381: This question is from textbook Advanced mathematics Find the standard form of the equation of a circle whose center is (2,1) and whose radius is 3.1 solutions Answer 47926 by Nate(3500)   on 2007-01-20 18:32:22 (Show Source): You can put this solution on YOUR website!(x - 2)^2 + (y - 1)^2 = 9
 Geometric_formulas/67388: This question is from textbook Advanced mathematics The latitud of Cambridge is 42.4 degrees north of the equator. If the diameter of the earth is 7920 miles, how far is Cambridge from the equator?1 solutions Answer 47925 by Nate(3500)   on 2007-01-20 18:31:13 (Show Source): You can put this solution on YOUR website!Circumference = 2(pi)r C = 7920(pi) 360 degrees make a circle 7920(pi)/360 22(pi) miles to one degree 22(pi)*42.4 about 2,930 miles
 Radicals/67325: For the function, y = 1/ x - 2 a.)Give the y values for x = -2, -1, 0, 1, 2, 3 b.) Using these points, draw a curve show your graph here: 1 solutions Answer 47892 by Nate(3500)   on 2007-01-19 23:23:15 (Show Source): You can put this solution on YOUR website! x: -2 ......... -1 .......... 0 ....... 1 ....... 2 ........... 3 y: -0.25 .. -0.33 .. -0.5 ... -1 .. undefined . 1 ~ ~ ~ ~
 logarithm/67311: This question is from textbook An Incremental Development Please help to simplify solve for x : log5(x + 3) + log5 4 = log5 36 1 solutions Answer 47890 by Nate(3500)   on 2007-01-19 23:19:28 (Show Source):