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# Recent problems solved by 'nerdybill'

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 Graphs/604847: Hello, Would u pls, check my answer? Factor the expression :c^2 + 4c + 4 My answer: (c + 2)^2 Thanks a lot, H.H 1 solutions Answer 381455 by nerdybill(7003)   on 2012-04-29 11:03:51 (Show Source): You can put this solution on YOUR website!You are correct. . You can check yourself... apply FOIL on (c + 2)(c + 2) and will get your original expression
 Linear-equations/604821: Just checking to see if I did this problem correctly. Find the equation of the line that goes through the points (-4,1) and (-1,4) I found the slope of -1/-1 or -1 y = x + b 4 = -1 + b 5 = b answer y = x + 5 ??1 solutions Answer 381425 by nerdybill(7003)   on 2012-04-29 08:19:18 (Show Source): You can put this solution on YOUR website!Your answer is correct. However, I'm not sure I followed how you got there. . slope of (-4,1) and (-1,4): m = (y2-y1)/(x2-x1) m = (4-1)/(-1-(-4)) m = (4-1)/(-1+4) m = 3/3 m = 1 . plug slope (above) and one point (-4,1) into "point-slope" form: y - y1 = m(x - x1) y - 1 = 1(x - (-4)) y - 1 = 1(x + 4) y - 1 = x + 4 y = x + 5
 Pythagorean-theorem/604717: A guy wire attached to the top of a 30-foot-long pole is anchored 10 feet from the base of the pole, as illustrated in the figure. Find the length of the guy wire to the nearest tenth of a foot1 solutions Answer 381376 by nerdybill(7003)   on 2012-04-28 20:55:21 (Show Source): You can put this solution on YOUR website!A guy wire attached to the top of a 30-foot-long pole is anchored 10 feet from the base of the pole, as illustrated in the figure. Find the length of the guy wire to the nearest tenth of a foot . Apply Pythagorean Theorem: Let x = length (feet) of wire then x^2 = 10^2 + 30^2 x^2 = 100 + 900 x^2 = 1000 x = 31.623 rounded to nearest tenth: x = 31.6 feet
 logarithm/604740: log8(2x-1)=01 solutions Answer 381375 by nerdybill(7003)   on 2012-04-28 20:52:34 (Show Source): You can put this solution on YOUR website!I'll assume you meant log base 8: log8(2x-1)=0 (2x-1)=8^0 2x-1=1 2x=2 x = 1
 Quadratic_Equations/604688: Rewrite the quadratic equation in standard form by completing the square. f(x)=x^2+8x+14 Answer (f(x)= (x, plus or minus ___)^2 plus or minus ____ I have worked this to x, 4 as well as x, -4. I have also come up with x, +8. Also for the second answer I have some up with +14 or sqrt 2.1 solutions Answer 381346 by nerdybill(7003)   on 2012-04-28 18:16:17 (Show Source): You can put this solution on YOUR website!Rewrite the quadratic equation in standard form by completing the square. f(x)=x^2+8x+14 . f(x)=x^2+8x+14 f(x)=(x^2+8x)+14 f(x)=(x^2+8x+16)+14-16 f(x)=(x+4)(x+4)-2 f(x)=(x+4)^2-2 (this is the standard form)
 logarithm/604691: Solve the logarithm equation log[4](x)+ log[4](6x-7)=log[4]5. Give the exact answer in the form of a fraction. x=____ I worked the problem and came up with two different fractions; I have x= 1/2 or x=5/3. 1 solutions Answer 381343 by nerdybill(7003)   on 2012-04-28 18:08:50 (Show Source): You can put this solution on YOUR website!log[4](x)+ log[4](6x-7)=log[4]5 log[4](x)(6x-7)=log[4]5 (x)(6x-7)=5 6x^2 - 7x = 5 6x^2 - 7x - 5 = 0 6x^2 - 10x + 3x - 5 = 0 (6x^2 - 10x) + (3x - 5) = 0 2x(3x - 5) + (3x - 5) = 0 (3x - 5)(2x+1) = 0 x = {5/3, -1/2} Since you can't take the log of a negative number, you can throw out -1/2 (extraneous) leaving: x = 5/3
 Travel_Word_Problems/604595: On Thursday September 8, 2011 Arkansas State Senator Bruce Holland was convicted of fleeing a police officer. He was reportedly going 110 miles per hour during a 17 mile chase. Rounding to the nearest minute, how long did the chase last? 1 solutions Answer 381287 by nerdybill(7003)   on 2012-04-28 11:49:52 (Show Source): You can put this solution on YOUR website!On Thursday September 8, 2011 Arkansas State Senator Bruce Holland was convicted of fleeing a police officer. He was reportedly going 110 miles per hour during a 17 mile chase. Rounding to the nearest minute, how long did the chase last? . Assuming he was traveling at 110 mph the entire time of the 17 mile chase (which, I'm sure he wasn't) then: 17/110 = .155 hours or, about 9 minutes
 Sequences-and-series/604590: I need help finding the vertex of the parabola: y= -6.25x²+ 150x + 7200? I have graphed it and found the vertex to be (12, 8100) but I need to be able to find it algebraically. I tried taking the derivative but I'm not sure I was doing that right or if thats how I should approach it. Please explain your steps, so that i can learn what and why you are doing what you do. Thanks in advance for all the help.1 solutions Answer 381284 by nerdybill(7003)   on 2012-04-28 11:40:24 (Show Source): You can put this solution on YOUR website!y= -6.25x²+ 150x + 7200 . The x-value of the vertex is at: x = -b/(2a) (from the "quadratic formula" w/o the radical) x = -150/(2(-6.25) x = -150/(-12.5) x = 150/12.5 x = 12 . To find the y-value, plug the above back into the equation: y= -6.25x²+ 150x + 7200 y= -6.25(12)²+ 150(12) + 7200 y= 8100
 Linear-equations/604571: how do i find the x and y intercepts and slope of the equation 3x = -21 solutions Answer 381276 by nerdybill(7003)   on 2012-04-28 11:09:00 (Show Source): You can put this solution on YOUR website!how do i find the x and y intercepts and slope of the equation 3x = -2 . 3x = -2 x = -2/3 This is simply a vertical line that crosses the x-axis at -2/3 . x-intercept is at (0,-2/3) y-intercept (none) runs parallel to the y-axis slope is undefined since it is a vertical line
 Rational-functions/604565: Can anyone help me figure this question out? Thanks! Simplify by removing factors of 1 48v^10x^4/18v^4x^21 solutions Answer 381274 by nerdybill(7003)   on 2012-04-28 11:06:30 (Show Source): You can put this solution on YOUR website!Simplify by removing factors of 1 48v^10x^4/18v^4x^2 (6*8)v^10x^4/(6*3)v^4x^2 8v^10x^4/3v^4x^2 8v^4v^6x^4/3v^4x^2 8v^6x^4/3x^2 8v^6x^2x^2/3x^2 8v^6x^2/3
 Rational-functions/604580: f(x)= 3(x^2+5) Find f^-1(x), f^-1(27)1 solutions Answer 381273 by nerdybill(7003)   on 2012-04-28 10:56:19 (Show Source): You can put this solution on YOUR website!f(x)= 3(x^2+5) Find f^-1(x), f^-1(27) . Find f^-1(x): y = 3(x^2+5) switch the variables and solve for y: x = 3(y^2+5) x/3 = y^2+5 x/3 - 5 = y^2 sqrt(x/3 - 5) = y or . finding f^-1(27): (that's plus or minus 2)
 Travel_Word_Problems/604575: Two cars leave town at the sime time traveling in opposite dirrections. One travels 70 mi/h and the other 55 mi/h. In how many hours will they be 250 miles apart?1 solutions Answer 381272 by nerdybill(7003)   on 2012-04-28 10:50:24 (Show Source): You can put this solution on YOUR website! Two cars leave town at the sime time traveling in opposite dirrections. One travels 70 mi/h and the other 55 mi/h. In how many hours will they be 250 miles apart? apply the distance formula of d=rt . Let x = time (hours) traveled then 70x + 55x = 250 125x = 250 x = 250/125 x = 2 hours
 Polynomials-and-rational-expressions/604572: Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial. f(x)=14-x^21 solutions Answer 381271 by nerdybill(7003)   on 2012-04-28 10:45:27 (Show Source): You can put this solution on YOUR website!Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial. f(x)=14-x^2 Ordered in highest to lowest degree: f(x) = -x^2+14 . It is a "quadratic". Leading term: -x^2 Leading coefficient: -1 Degree: 2
 Functions/604578: State the domain of the rational function. g(x)= x-8/x+31 solutions Answer 381269 by nerdybill(7003)   on 2012-04-28 10:41:27 (Show Source): You can put this solution on YOUR website!State the domain of the rational function. g(x)= x-8/(x+3) . The "domain" specifies all possible values of x. In this case, you just want to make sure the denominator is not zero because dividing by zero is undefined. So, we set the denominator to zero to find the value x can't take: x+3=0 x = -3 So, the domain is all real numbers except -3. Or, you can state it like: (-oo, -3) U (-3, +oo) where oo stands for infinity
 Functions/604574: For the function find the maximum number of real zeros that the function can have, the maximum number of x-intercepts that the function can have, and the maximum number of turning points that the graph of the function can have. f(x)=5x^3+8x^2-2x+91 solutions Answer 381267 by nerdybill(7003)   on 2012-04-28 10:35:03 (Show Source): You can put this solution on YOUR website!For the function find the maximum number of real zeros that the function can have, the maximum number of x-intercepts that the function can have, and the maximum number of turning points that the graph of the function can have. f(x)=5x^3+8x^2-2x+9 . Max number of real zeros: 3 Max number of x-intercepts: 3 max turning points: 3-1 = 2
 Travel_Word_Problems/604568: An airliner travels 35 miles in 4 minutes. What is its speed in miles per hour? 1 solutions Answer 381264 by nerdybill(7003)   on 2012-04-28 09:55:51 (Show Source): You can put this solution on YOUR website!35 miles in 4 minutes: 35/4 miles/min * 60 min/hr (35*60)/4 2100/4 525 miles per hour (mph)
 Geometry_Word_Problems/604554: suppose that 500 people attended the play if adults were charged 10 dollars and children were charged 7 dollars determine how many adults and children attended if they raised a total of 4472 dollars1 solutions Answer 381263 by nerdybill(7003)   on 2012-04-28 09:53:34 (Show Source): You can put this solution on YOUR website! suppose that 500 people attended the play if adults were charged 10 dollars and children were charged 7 dollars determine how many adults and children attended if they raised a total of 4472 dollars . Let x = number of adults then 500-x = number of children . 10x + 7(500-x) = 4472 10x + 3500-7x = 4472 3x + 3500 = 4472 3x = 972 x = 324 (adults) . Children: 500-x = 500-324 = 176
 Angles/604567: the measure of the supplement of an angle is 40 less than 3 times its complement, find the measure of the angle, its supplement and its complement, please give me the formula and how you figured it out. thanks so much.1 solutions Answer 381262 by nerdybill(7003)   on 2012-04-28 09:49:12 (Show Source): You can put this solution on YOUR website! the measure of the supplement of an angle is 40 less than 3 times its complement, find the measure of the angle, its supplement and its complement, please give me the formula and how you figured it out. thanks so much. . Let x = the angle then 90-x = the complement 180-x = the supplement . From: "the supplement of an angle is 40 less than 3 times its complement" we get our equation: 180-x = 3(90-x) - 40 180-x = 270-3x - 40 180-x = 230-3x 180+2x = 230 2x = 50 x = 25 degrees (the angle) . The complement: 90-x = 90-25 = 65 degrees . The supplement: 180-x = 180-25 = 155 degrees
 Equations/604542: lisa can sweep the paths around her home in 30 minutes. Her sister Tania takes 20 minutes to do the same job. If they work together, how long will it take to complete the job?1 solutions Answer 381261 by nerdybill(7003)   on 2012-04-28 09:45:08 (Show Source): You can put this solution on YOUR website! lisa can sweep the paths around her home in 30 minutes. Her sister Tania takes 20 minutes to do the same job. If they work together, how long will it take to complete the job? . Let x = time (minutes) it takes for both then x(1/30 + 1/20) = 1 multiplying both sides by 60 (common denominator) we get: x(2 + 3) = 60 x(5) = 60 x = 60/5 x = 12 minutes
 logarithm/604562: what is one less than 3000 in base 5. Please show step by step1 solutions Answer 381260 by nerdybill(7003)   on 2012-04-28 09:42:47 (Show Source): You can put this solution on YOUR website! what is one less than 3000 in base 5. Please show step by step . Begin by converting 3000 base 5 to base 10: 3*5^3 3*125 375 one less than the above is then: 374 . Or, you could do the math in base 5: 3000-1 = 2444 in base 5 converting to base 10 2*5^3 + 4*5^2 + 4*5 + 4 2*125 + 4*25 + 4*5 + 4 250 + 100 + 20 + 4 374
 Linear_Equations_And_Systems_Word_Problems/604444: you order 2 tacos and 2 enchiladas for \$4.80. you friend order 3 tacos and 1 enchiladas for \$4. how much does each cost1 solutions Answer 381161 by nerdybill(7003)   on 2012-04-27 18:43:35 (Show Source): You can put this solution on YOUR website! you order 2 tacos and 2 enchiladas for \$4.80. you friend order 3 tacos and 1 enchiladas for \$4. how much does each cost . Let t = cost of a taco and e = cost of an enchilada . 2t + 2e = 4.80 3t + e = 4.00 . multiply bottom equation by -2 and add both equations together: 2t + 2e = 4.80 -6t - 2e = -8.00 ------------------- -4t = -3.20 t = -3.20/(-4) t = \$0.80 (or 80 cents for a taco) . enchilada: 3t + e = 4.00 3(0.80) + e = 4.00 2.40 + e = 4.00 e = 4.00 - 2.40 e = \$1.60
 Rational-functions/604442: evaluate v(s)=s^3+3s^2-4s-2 when s = -21 solutions Answer 381160 by nerdybill(7003)   on 2012-04-27 18:38:58 (Show Source): You can put this solution on YOUR website!evaluate v(s)=s^3+3s^2-4s-2 when s = -2 . substitute the s for -2 in the equation: v(s)=s^3+3s^2-4s-2 v(-2)=(-2)^3+3(-2)^2-4(-2)-2 v(-2)=-8+3(4)-(-8)-2 v(-2)=-8+12+8-2 v(-2)=4+8-2 v(-2)=12-2 v(-2)=10
 Volume/604379: how can I find the base of a figure if the volume is 210 ft³ and the height is 14 ft?1 solutions Answer 381155 by nerdybill(7003)   on 2012-04-27 16:48:53 (Show Source): You can put this solution on YOUR website! how can I find the base of a figure if the volume is 210 ft³ and the height is 14 ft? . Volume = "area of base" * " height" plug in what was given: 210 = b(14) 210/14 = b 15 square feet = b (base area)
 test/604410: log(2x+5)=31 solutions Answer 381153 by nerdybill(7003)   on 2012-04-27 16:45:48 (Show Source): You can put this solution on YOUR website!log(2x+5)=3 2x+5=10^3 2x+5=1000 2x=995 x = 995/2 x = 497.5
 Square-cubic-other-roots/604351: How do you simplify a radical of 451 solutions Answer 381111 by nerdybill(7003)   on 2012-04-27 12:59:17 (Show Source): You can put this solution on YOUR website! factor (using prime numbers): then, for pull out "pairs":
 Percentage-and-ratio-word-problems/604345: how do you convert 40.8% to a fraction in lowest terms?1 solutions Answer 381110 by nerdybill(7003)   on 2012-04-27 12:53:51 (Show Source): You can put this solution on YOUR website!how do you convert 40.8% to a fraction in lowest terms? since % is "per one hundred" we have: 40.8/100 multiply both numerator and denominator by 10: 408/1000 then, we reduce the fraction: 204/500 102/250 51/125
 Probability-and-statistics/604272: IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15 The z-score for an IQ score of 112 is -0.8 true or false1 solutions Answer 381074 by nerdybill(7003)   on 2012-04-27 09:02:48 (Show Source): You can put this solution on YOUR website!IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15 The z-score for an IQ score of 112 is -0.8 . z = (dataPoint - mean)/stdDev z = (112-100)/15 z = 12/15 z = .8 . Answer: false
 Probability-and-statistics/604273: IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15 If the z-score on your IQ score was 1.3, then you had a score of 119.5 true or false1 solutions Answer 381073 by nerdybill(7003)   on 2012-04-27 09:00:35 (Show Source): You can put this solution on YOUR website!IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15 If the z-score on your IQ score was 1.3, then you had a score of 119.5 . z = (dataPoint - mean)/stdDeviation z = (119.5 - 100)/15 z = (19.5)/15 z = 1.3 . Answer: true
 logarithm/604266: Solve for x: log base 5 (x^2+4x+4)=21 solutions Answer 381068 by nerdybill(7003)   on 2012-04-27 08:44:43 (Show Source): You can put this solution on YOUR website!Solve for x: log base 5 (x^2+4x+4)=2 x^2+4x+4 = 5^2 x^2+4x+4 = 25 x^2+4x-21 = 0 (x+7)(x-3) = 0 x = {-7, 3}
 Exponential-and-logarithmic-functions/604159: log base 1/3 27 what do you raise 1/3 to to get 27(I think this is how to read the problem) Can anyone explain how to get the answer please. Thank you 1 solutions Answer 380993 by nerdybill(7003)   on 2012-04-26 23:01:36 (Show Source):
 Polynomials-and-rational-expressions/604166: r^2+6r-271 solutions Answer 380987 by nerdybill(7003)   on 2012-04-26 22:48:36 (Show Source): You can put this solution on YOUR website!r^2+6r-27 (r+9)(r-3)