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# Recent problems solved by 'nerdybill'

nerdybill answered: 6956 problems
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 Exponential-and-logarithmic-functions/192260: log(base3)(2x-1)=31 solutions Answer 144330 by nerdybill(6958)   on 2009-04-20 23:05:25 (Show Source): You can put this solution on YOUR website! log(base3)(2x-1)=3 2x-1=3^3 2x-1=27 2x=28 x=14
 Polynomials-and-rational-expressions/192290: please factor out y^2+y-12 thanks 1 solutions Answer 144328 by nerdybill(6958)   on 2009-04-20 23:03:44 (Show Source): You can put this solution on YOUR website!y^2+y-12 = (y+4)(y-3)
 Polynomials-and-rational-expressions/192291: please factor out y^2+12y-13 thank you 1 solutions Answer 144326 by nerdybill(6958)   on 2009-04-20 23:02:07 (Show Source): You can put this solution on YOUR website!y^2+12y-13 = (y+13)(y-1)
Exponential-and-logarithmic-functions/192261: log3x+log(x+2)=1
1 solutions

Answer 144318 by nerdybill(6958)   on 2009-04-20 22:23:38 (Show Source):
You can put this solution on YOUR website!
log3x+log(x+2)=1
log3x(x+2)=1
3x(x+2)=10^1
3x^2+6x=10
3x^2+6x-10=0
Solving the above using the quadratic equation yields two solutions:
x = {1.082, -3.082}
.
Details of quadratic follows:
.
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=156 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.08166599946613, -3.08166599946613. Here's your graph:

 logarithm/192210: log(x+9)-logx=31 solutions Answer 144256 by nerdybill(6958)   on 2009-04-20 17:16:19 (Show Source): You can put this solution on YOUR website!log(x+9)-logx=3 log(x+9)/x=3 (x+9)/x=10^3 (x+9)/x=1000 (x+9)=1000x 9=999x 1/111 = x
 logarithm/192211: 3log2x=41 solutions Answer 144255 by nerdybill(6958)   on 2009-04-20 17:10:24 (Show Source): You can put this solution on YOUR website! 3log2x=4 log(2x)^3=4 (2x)^3 = 10^4 8x^3 = 10000 x^3 = 1250 x = 10.772
 logarithm/192212: log(3x+7)=11 solutions Answer 144253 by nerdybill(6958)   on 2009-04-20 17:07:20 (Show Source): You can put this solution on YOUR website!log(3x+7)=1 (3x+7)= 10^1 3x+7 = 10 3x = 3 x = 1
 logarithm/192209: 2log4-log3+logx-4=01 solutions Answer 144252 by nerdybill(6958)   on 2009-04-20 17:06:10 (Show Source): You can put this solution on YOUR website!2log4-log3+logx-4=0 log4^2-log3+logx-4=0 log(4^2/3)+logx-4=0 log(16/3)+logx-4=0 log(16(x-4)/3)=0 16(x-4)/3 = 10^0 16(x-4)/3 = 1 16(x-4) = 3 x-4 = 3/16 x = 3/16 + 4 x = 3/16 + 64/16 x = 67/16
 logarithm/192193: Find the solution of the equation: 5Ln(1-x)= 81 solutions Answer 144235 by nerdybill(6958)   on 2009-04-20 16:13:00 (Show Source): You can put this solution on YOUR website!5Ln(1-x)= 8 Ln(1-x)^5= 8 (1-x)^5= e^8 1-x = fifthRoot(e^8) 1 = fifthRoot(e^8)+x 1 - fifthRoot(e^8) = x 1 - fifthRoot(2980.958) = x 1 - 4.953 = x -3.953 = x
 Polynomials-and-rational-expressions/192117: REDUCE EXPRESSION TO LOWEST TERMS -2x-8/x^2+2x-81 solutions Answer 144163 by nerdybill(6958)   on 2009-04-20 11:06:26 (Show Source): You can put this solution on YOUR website! Factoring numerator and denominator: . Canceling terms, we get: . Or, we could rewrite it as:
 Sequences-and-series/192065: This question is from textbook Saxon Algebra 2 Find a8 of a geometric sequence given that a3 = 32 and a5 = 512.1 solutions Answer 144125 by nerdybill(6958)   on 2009-04-19 23:27:28 (Show Source): You can put this solution on YOUR website!You can review this site: http://www.regentsprep.org/Regents/math/algtrig/ATP2/GeoSeq.htm . An = A1(r^(n-1)) . The idea is that because they gave you: a3 = 32 and a5 = 512 you can now find A1(first term) and r (the common ratio). Now, you can find any term after that. . An = A1(r^(n-1)) 32 = A1(r^2) A1 = 32/r^2 . An = A1(r^(n-1)) An = A1(r^4) 512 = (32/r^2)(r^4) 512 = 32(r^2) 16 = r^2 4 = r (common ratio) . A1 = 32/r^2 = 32/4^2 = 32/16 = 2 (first term) . An = A1(r^(n-1)) a8 = (2)(4^(8-1)) a8 = (2)(4^7) a8 = 2*16384 a8 = 32768
 Surface-area/192071: A farmer has 336 running feet of fence and wishes to form a rectangular pasture. One side of the pasture will be bounded by a very long wall, and so no fencing material will be needed for that side of the pasture. What should the dimensions of the pasture be if the area of the pasture is to be largest possible? Could you please provide a detailed explanation of how you work the problem to find the solution. Thanks! 1 solutions Answer 144123 by nerdybill(6958)   on 2009-04-19 23:09:50 (Show Source): You can put this solution on YOUR website!A farmer has 336 running feet of fence and wishes to form a rectangular pasture. One side of the pasture will be bounded by a very long wall, and so no fencing material will be needed for that side of the pasture. What should the dimensions of the pasture be if the area of the pasture is to be largest possible? . Let x = width and y = length . From the provided length of fencing available: 2x+y = 336 Solving for y: y = 336-2x . Area = xy Plugging in our value of y: Area = x(336-2x) Area = 336x-2x^2 Area = -2x^2 + 336x (parabola that opens downwards) . If we find the vertex, we'll find the maximum value of the width: Area = -2x^2 + 336x Area = -2(x^2 - 168x) Area = -2(x^2 - 168x + 7056) + 14112 Area = -2(x - 84)^2 + 14112 Since the vertex is at (84, 14112) we know the width is 84 feet . Length: 2x+y = 336 2(84)+y = 336 168+y = 336 y = 168 feet (length) . Dimension: 84 feet by 168 feet
 Quadratic-relations-and-conic-sections/192073: Find the exact vertex of the parabola algebraically... f(x) = (x - 1)^2 + (x + 3) Could you please provide a detailed explantion of how you achieved the solution. Thanks! 1 solutions Answer 144121 by nerdybill(6958)   on 2009-04-19 22:57:21 (Show Source): You can put this solution on YOUR website!The "vertex form" is y= a(x-h)2+k where (h,k) is the vertex . The idea is to make your equation look like that: f(x) = (x - 1)^2 + (x + 3) f(x) = (x - 1)(x - 1) + (x + 3) f(x) = x^2 - 2x + 1 + x + 3 f(x) = x^2 - x + 4 Group x-terms: f(x) = (x^2 - x) + 4 Complete the square: f(x) = (x^2 - x + __ ) + 4 f(x) = (x^2 - x + 1/4 ) + 4 -1/4 f(x) = (x - 1/2)^2 + 16/4 -1/4 f(x) = (x - 1/2)^2 + 15/4 . vertex = (1/2, 15/4)
 Quadratic-relations-and-conic-sections/192074: Find the exact vertex of the parabola algebraically... f(x) = -3x^2 + 5x + 1 Could you please provide a detailed explanation of how you achieved the solution. Thanks!1 solutions Answer 144120 by nerdybill(6958)   on 2009-04-19 22:51:48 (Show Source): You can put this solution on YOUR website!The "vertex form" of a parabola is: y= a(x-h)^2+k where (h,k) is the vertex . So, the idea is to manipulate the original equation into the "vertex form": f(x) = -3x^2 + 5x + 1 First, group the x terms: f(x) = (-3x^2 + 5x) + 1 Factor out a -3: f(x) = -3(x^2 + (-5/3)x) + 1 Complete the square: f(x) = -3(x^2 + (-5/3)x + __ ) + 1 f(x) = -3(x^2 + (-5/3)x + (25/36) ) + 1 + 25/12 f(x) = -3(x - 5/6 )^2 + 12/12 + 25/12 f(x) = -3(x - 5/6 )^2 + 37/12 (this is the vertex form) . Vertex = (5/6, 37/12)
 Angles/191952: Two angles atre complementary. The sum of the measure of the first angle and one-fourth the second angle is 69 degrees. Find the measure of the angles.1 solutions Answer 144017 by nerdybill(6958)   on 2009-04-19 12:24:32 (Show Source): You can put this solution on YOUR website! Two angles atre complementary. The sum of the measure of the first angle and one-fourth the second angle is 69 degrees. Find the measure of the angles. . Two angles are complementary if their sum equals 180 degrees. . Let x = measure of second angle then 180-x = measure of first angle . (180-x) + (1/4)x = 69 720 - 4x + x = 276 720 - 3x = 276 -3x = -444 x = 148 degrees (second angle) . First angle: 180-x = 180-148 = 32 degrees (first angle)
 Word_Problems_With_Coins/191932: I always save my change week to week. This week I found all nickels and dimes. There were twice as many dimes as nickles and the value of the dimes was \$.90 more than the value of the nickles. How many nickles and dimes do I have? I THINK I KNOW THE ANSWERS BUT I AM HAVING TROUBLE COMING UP WITH THE CORRECT WAY TO WRITE IT. PLEASE HELP!!1 solutions Answer 144013 by nerdybill(6958)   on 2009-04-19 11:05:45 (Show Source): You can put this solution on YOUR website!There were twice as many dimes as nickles and the value of the dimes was \$.90 more than the value of the nickles. . Let n = number of nickels then 2n = number of dimes . .10(2n) = .05n + .90 .20n = .05n + .90 .15n = .90 n = .90/.15 n = 6 (nickels) . Dimes: 2n = 2(6) = 12 (dimes)
 Polynomials-and-rational-expressions/191938: This question is from textbook College Algebra A Graphing Approach #8. x^4 + 5x^2 -36 = 0 I started working this problem and then got confused. If you could help with this. Thanks1 solutions Answer 144011 by nerdybill(6958)   on 2009-04-19 11:02:37 (Show Source): You can put this solution on YOUR website!x^4 + 5x^2 -36 = 0 Factoring: (x^2+9)(x^2-4) = 0 . Setting each term to zero: (x^2+9) = 0 x^2 = -9 x = sqrt(-9) x = +- 3i . (x^2-4) = 0 x^2 = 4 x = sqrt(4) x = +- 2
 Linear_Algebra/191935: This question is from textbook How are addition and multiplication used to solve a linear equation? Demonstrate by solving "12x + 6 = 31 – 2x" Thank You!1 solutions Answer 144009 by nerdybill(6958)   on 2009-04-19 10:58:54 (Show Source): You can put this solution on YOUR website!To solve a linear equation, isolate the unknown to one side of the equat ion. . 12x + 6 = 31 – 2x . Start by moving all the x terms to the left. Do this by ADDING 2x to both sides: 12x + 6 + 2x = 31 – 2x + 2x 14x + 6 = 31 . Next, subtract 6 from both sides: 14x + 6 - 6 = 31 - 6 14x = 25 . Finally, MULTIPLY both sides by (1/14): (1/14)14x = 25(1/14) x = 25/14 (solution for x)
 Linear-systems/191921: Find the slope and y-intercept 0f 3x-5y+5=0. Show answers in fractions.1 solutions Answer 143999 by nerdybill(6958)   on 2009-04-19 10:04:19 (Show Source): You can put this solution on YOUR website!Manipulate the equation into the "slope-intercept" form: y = mx + b where m is slope b is the y-intercept . 3x-5y+5=0 3x-5y= -5 -5y= -3x -5 5y= 3x + 5 y = (3/5)x + (5/5) y = (3/5)x + 1 . By inspection, based on the "slope-intercept" form we have: slope is 3/5 y-intercept is at (0,1)
 Polynomials-and-rational-expressions/191928: I need some help with subtracting this polynomial: (-8c^2+4c+2)-(6c^2+2) Thank you again! 1 solutions Answer 143998 by nerdybill(6958)   on 2009-04-19 09:59:39 (Show Source): You can put this solution on YOUR website!(-8c^2+4c+2)-(6c^2+2) . Distribute the negative to terms inside the right parenthesis: -8c^2+4c+2-6c^2-2 . Group like-terms: (-8c^2-6c^2)+4c+(2-2) . Combine: (-14c^2)+4c+(0) . -14c^2+4c Or, factoring out 2c: 2c(-7c + 2)
 Geometry_Word_Problems/191931: The area of a rectangle is 64cm^2. Its length is 4times the width. What is its length and width? THANK YOU TO WHO EVER HELPS ME WITH THIS. THANK YOU THANK YOU THANK YOU.1 solutions Answer 143996 by nerdybill(6958)   on 2009-04-19 09:55:43 (Show Source): You can put this solution on YOUR website!The area of a rectangle is 64cm^2. Its length is 4times the width. What is its length and width . Let w = width then 4w = length . w(4w) = 64 4w^2 =64 w^2 = 16 w = 4 cm (width) . Length: 4w = 4(4) = 16 cm (length)
 Polynomials-and-rational-expressions/191880: I need help again, please help me add: (2x^2-3xy+y^2)+(-8x^2-8xy-y^2)+(x^2+xy-4Y^2) Thank you soooooooo much!!!1 solutions Answer 143979 by nerdybill(6958)   on 2009-04-19 00:39:46 (Show Source): You can put this solution on YOUR website!(2x^2-3xy+y^2)+(-8x^2-8xy-y^2)+(x^2+xy-4Y^2) . Remove parentheses: 2x^2-3xy+y^2-8x^2-8xy-y^2+x^2+xy-4Y^2 . Group like-terms: (2x^2-8x^2+x^2)+(-3xy-8xy+xy)+(y^2-y^2-4Y^2) . Combine like-terms: (-5x^2)+(-10xy)+(-4Y^2) -5x^2-10xy-4Y^2 or -(5x^2+10xy+4Y^2)
 Expressions-with-variables/191891: 13+a=25+b b-a= ?1 solutions Answer 143978 by nerdybill(6958)   on 2009-04-19 00:31:08 (Show Source): You can put this solution on YOUR website!Isolate "b-a" to one side of the equation. . If you started with: 13+a=25+b Subtract 'a' from both sides: 13 = 25+b-a Now, subtract 25 from both sides: 13-25 = b-a -12 = b-a (this is what they're looking for)
 Percentage-and-ratio-word-problems/191866: If jan can paint a house in 4 hours and jim can paint a house in 6 hours, how long will it take for them to paint the house together.1 solutions Answer 143973 by nerdybill(6958)   on 2009-04-18 21:24:28 (Show Source): You can put this solution on YOUR website! If jan can paint a house in 4 hours and jim can paint a house in 6 hours, how long will it take for them to paint the house together. . Let x = hours for both to paint house then x(1/4 + 1/6) = 1 x/4 + x/6) = 1 6x + 4x = 24 10x = 24 x = 2.4 hours or 2 hours and 24 minutes
 Linear-equations/191860: Find the slope -intercept equation of the line that has the given characteristics slope 3 and y -intercept (0,9)1 solutions Answer 143962 by nerdybill(6958)   on 2009-04-18 19:07:49 (Show Source): You can put this solution on YOUR website!Find the slope -intercept equation of the line that has the given characteristics slope 3 and y -intercept (0,9) . The "slope-intercept" form of a line is y = mx + b where m is slope b is the y-intercept . Therefore, for: slope 3 and y -intercept (0,9) we have y = 3x + 9 (this is what they're looking for)
 Functions/191837: Which relation is also a function? A) (3,-3), (4,-3), (2,-3) B) (1,7), (8,4), (-3,-4), (1,4) C) (2,0), (2,3), (2,8), (2,-3) D) (1,-1), (0,0), (1,0), (0,-1)1 solutions Answer 143951 by nerdybill(6958)   on 2009-04-18 16:36:41 (Show Source): You can put this solution on YOUR website!For it to be a function, for any value of 'x', there should only be one value of 'y',. . The ONLY answer that fits would be: A.
 Equations/191845: how can the number 45 be divided into two parts so that 4 times one part is 9 less than 5 times the other?1 solutions Answer 143950 by nerdybill(6958)   on 2009-04-18 16:33:48 (Show Source): You can put this solution on YOUR website! how can the number 45 be divided into two parts so that 4 times one part is 9 less than 5 times the other? . Let x = first part then 45-x = second part . 4(45-x) = 5x-9 180 - 4x = 5x-9 180 = 9x-9 189 = 9x 21 = x (first part) . Second part: 45-x = 45-21 = 24 (second part)
 Triangles/191808: This question is from textbook Beginning Algebra The area of a triangle is 30 square inches. The base of the triangle measures 2 inches more than twice the height of a triangle. Find the measures of the base and the height. 1 solutions Answer 143929 by nerdybill(6958)   on 2009-04-18 08:35:14 (Show Source): You can put this solution on YOUR website! The area of a triangle is 30 square inches. The base of the triangle measures 2 inches more than twice the height of a triangle. Find the measures of the base and the height. . Area of any triangle = (1/2)bh where b is base h is height . Let h = height then 2h+2 = base . 30 = (1/2)(2h+2)h 30 = (h+1)h 30 = h^2+h 0 = h^2+h-30 0 = (h+6)(h-5) . h ={-6,5} We can toss out the negative solution leaving us with: h = 5 inches . base: 2h+2 = 2(5)+2 = 10+2 = 12 inches . Therfore, height is 5 inches base is 12 inches
x^2=6x-3
1 solutions

Answer 143823 by nerdybill(6958)   on 2009-04-17 16:44:56 (Show Source):
You can put this solution on YOUR website!
x^2=6x-3
Move all terms to the left:
x^2-6x+3 = 0
Since we can't factor, we must resort to the quadratic equation.
Doing so, yields two solutions:
x = {5.449, 0.551}
.
Details of quadratic equation follows:
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=24 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 5.44948974278318, 0.550510257216822. Here's your graph:

 Equations/191718: Can you please help me solve this equation? 5(-2x+1)= -9(x+1) Thank you so very much! 1 solutions Answer 143822 by nerdybill(6958)   on 2009-04-17 16:39:59 (Show Source): You can put this solution on YOUR website!5(-2x+1)= -9(x+1) Distributing on the left and right side: -10x+5= -9x-9 5= x-9 14 = x
 Linear-systems/191714: Hi there, I need some help again. Can someone help me solve this? I don't even understand the problem. Thanks! The perimeter of a rectangle is 108m. The length is 9m more then twice the width find the dimensions. What is the length.1 solutions Answer 143820 by nerdybill(6958)   on 2009-04-17 16:38:02 (Show Source): You can put this solution on YOUR website! Hi there, I need some help again. Can someone help me solve this? I don't even understand the problem. Thanks! The perimeter of a rectangle is 108m. The length is 9m more then twice the width find the dimensions. What is the length. . Let w = width of rectangle then 2w+9 = length of rectangle . 2(width + length) = perimeter . 2(w + 2w+9) = 108 2(3w+9) = 108 6w+18 = 108 6w = 90 w = 16 m . length: 2w+9 = 2(16)+9 = 32+9 = 41 m