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# Recent problems solved by 'nerdybill'

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 Linear-equations/192880: A high school class wants to raise money by recycling newspapers. The class decided to rent a truck at a cost of \$150 for the week. The market price for recycled newspapers is \$15 per ton. Write an equation representing the amount of money the class will make based on the number of tons of newspapers collected.. Explain what you did to get your answer.1 solutions Answer 144763 by nerdybill(6951)   on 2009-04-23 23:51:20 (Show Source): You can put this solution on YOUR website!. "profit" = "amount paid for newspaper" - "cost of rental truck" . Let x = tons of newspaper collected for recycling then f(x) is the "profit" as a function of x . f(x) = 15x - 150
 Polynomials-and-rational-expressions/192877: please help factor out a^2-8a+16 thanks1 solutions Answer 144762 by nerdybill(6951)   on 2009-04-23 23:47:12 (Show Source): You can put this solution on YOUR website!a^2-8a+16 . = (a-4)(a-4) = (a-4)^2
 test/192774: sophia used an 8-foot rope to secure a 6-foot tent pole as shown. approimately how far from the base is the rope tied???1 solutions Answer 144688 by nerdybill(6951)   on 2009-04-23 14:32:45 (Show Source): You can put this solution on YOUR website!sophia used an 8-foot rope to secure a 6-foot tent pole as shown. . Let x = distance where rope is tied off . Because the rope, tent and ground forms a right-triangle, we can apply Pythagorean theorem: . 8^2 = 6^2 + x^2 64 = 36 + x^2 28 = x^2 5.29 feet = x
logarithm/192786: Log(x-3) + log(2x + 1) = 2logx
1 solutions

Answer 144686 by nerdybill(6951)   on 2009-04-23 14:26:54 (Show Source):
You can put this solution on YOUR website!
Log(x-3) + log(2x + 1) = 2logx
Log(x-3)(2x + 1) = logx^2
(x-3)(2x + 1) = x^2
2x^2 +x -6x - 3 = x^2
2x^2 - 5x - 3 = x^2
x^2 - 5x - 3 = 0
.
Using the quadratic equation to solve for x yields:
x = {5.541, -0.541}
We can toss out the negative solution leaving:
x = 5.541
.
 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=37 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 5.54138126514911, -0.54138126514911. Here's your graph:

 Square-cubic-other-roots/192722: A concrete driveway measures 16 yards by 6 yards. The driveway will be 0.25 yards thick. (a) How many cubic yards of concrete will be needed? (b) How much will it cost if concrete is \$5.25 per cubic yard? 1 solutions Answer 144645 by nerdybill(6951)   on 2009-04-23 08:34:23 (Show Source): You can put this solution on YOUR website!A concrete driveway measures 16 yards by 6 yards. The driveway will be 0.25 yards thick. (a) How many cubic yards of concrete will be needed? (b) How much will it cost if concrete is \$5.25 per cubic yard? . a) 16*6*0.25 = 24 cubic yards . b) 5.25*24 = \$126
 Exponential-and-logarithmic-functions/192643: This question is from textbook log2 161 solutions Answer 144641 by nerdybill(6951)   on 2009-04-23 04:59:59 (Show Source): You can put this solution on YOUR website!log2(16) = log2(2^4) = 4
 Quadratic_Equations/192693: This question is from textbook Intermediate Algebra Recall that total profit P is the difference between total revenue R and total cost C. Given R(x)=1000x-x^2 and C(x)=3000+20x, find the total profit, the maximum value of the total profit, and the value of x at which it occurs.1 solutions Answer 144640 by nerdybill(6951)   on 2009-04-23 04:57:53 (Show Source): You can put this solution on YOUR website!Recall that total profit P is the difference between total revenue R and total cost C. Given R(x)=1000x-x^2 and C(x)=3000+20x, find the total profit, the maximum value of the total profit, and the value of x at which it occurs. . Profit = Revenue - Cost f(x) = R(x) - C(x) f(x) = (1000x-x^2) - (3000+20x) f(x) = 1000x-x^2 - 3000 - 20x f(x) = -x^2 + 980x - 3000 . By looking at the coefficient associated with the x^2 term (-1), we know that it is a parabola that opens downward. Therefore, finding the vertex will provide the answer: . To do this, manipulate the equation into the "vertex form": y= a(x-h)^2+k . f(x) = -x^2 + 980x - 3000 f(x) = (-x^2 + 980x) - 3000 f(x) = -(x^2 - 980x + __ ) - 3000 f(x) = -(x^2 - 980x + 240100) - 3000 + 240100 f(x) = -(x+490) + 237100 . maximum value of the total profit: \$237100 value of x at which it occurs: -490
 logarithm/192699: log base 2(5^2 + 7)1 solutions Answer 144639 by nerdybill(6951)   on 2009-04-23 04:40:40 (Show Source): You can put this solution on YOUR website!log base 2(5^2 + 7) = log base 2(25 + 7) = log base 2(32) = log base 2(2^5) = 5
 Rational-functions/192644: Factor: (16X^4)-11 solutions Answer 144630 by nerdybill(6951)   on 2009-04-23 00:21:37 (Show Source): You can put this solution on YOUR website!If you saw: a^2 - b^2 This is a "difference of squares" -- which factors out to: (a-b)(a+b) . So, if you started with: (16X^4)-1 Notice we can rewrite it as: (4x^2)^2 - 1^2 Now, you have a difference of squares resulting in: (4x^2 - 1)(4x^2 + 1) . Oh wait, but (4x^2 - 1) is also a difference squares: (2x-1)(2x+1)(4x^2 + 1)
 Equations/192691: Write the equation of the line that passes through (-4,7) with a slope of a half. thanks1 solutions Answer 144628 by nerdybill(6951)   on 2009-04-23 00:15:52 (Show Source): You can put this solution on YOUR website!Write the equation of the line that passes through (-4,7) with a slope of a half. . Given: point (-4,7) slope, m, 1/2 . Plug it all into the "point slope" form: y-y1 = m(x-x1) y-7 = (1/2)(x-(-4)) y-7 = (1/2)(x+4) y-7 = (1/2)x + 2 y = (1/2)x + 9 (this is the slope-intercept form:what they're looking for)
 Miscellaneous_Word_Problems/192537: This question is from textbook Elementary and Intermediate Algebra 110. Sky diving. The formula in Exercise 109 accounts for the effect of gravity only on a falling object. According to that formula, how long would it take a sky diver to reach the earth when jumping from 17,000 feet? (A sky diver can actually get about twice as much falling time by spreading out and using the air to slow the fall.) t=sqrt(h/16) 1 solutions Answer 144554 by nerdybill(6951)   on 2009-04-22 12:17:54 (Show Source): You can put this solution on YOUR website!t=sqrt(h/16) Plug in the height and solve for t: t=sqrt(17000/16) t=sqrt(1062.5) t=32.6 seconds
 Geometric_formulas/192554: Given a circle with the radius of 2, which is the length of an arc measuring 75 degrees?1 solutions Answer 144539 by nerdybill(6951)   on 2009-04-22 11:47:12 (Show Source): You can put this solution on YOUR website! Given a circle with the radius of 2, which is the length of an arc measuring 75 degrees? . Circumference = 2(pi)r = 2(3.14)(2) = 12.56 . Since the entire circle is 360 degrees: the arc is then (75/360)(12.56)= 2.62
 Equations/192547: Could someone please help with the following question. Equations are very confusing for me. x squared + 6x + 8 = 0 Thanks for the help.1 solutions Answer 144536 by nerdybill(6951)   on 2009-04-22 11:40:10 (Show Source): You can put this solution on YOUR website!The equation: x^2 + 6x + 8 = 0 is a quadratic . To solve, you can either "factor" or apply the "quadratic equation". . Always factor if you can, it is easier. . x^2 + 6x + 8 = 0 (x+4)(x+2) = 0 . This would be true if either (x+4) or (x+2) was equal to zero. . To find the solutions, set each to zero and solve: x+4=0 x = -4 and x+2=0 x = -2 . Therefore, two solutions for x: x = {-4,-2}
 Percentage-and-ratio-word-problems/192549: "A student missed 9 problems on a chemistry test and received a grade of 44%. If all the problems were of equal value, how many problems were on the test? Round off your answer to the nearest integer."1 solutions Answer 144534 by nerdybill(6951)   on 2009-04-22 11:35:03 (Show Source): You can put this solution on YOUR website! "A student missed 9 problems on a chemistry test and received a grade of 44%. If all the problems were of equal value, how many problems were on the test? Round off your answer to the nearest integer." . Let x = number of problems on the test then (x-9)/x = .44 x-9 = .44x .56x = 9 x = 9/.56 x = 16.071 or, rounded to the nearest integer: x = 16 problems on the test
 Quadratic_Equations/192501: the square of an integer is 30 more than the integer. find the integer.1 solutions Answer 144524 by nerdybill(6951)   on 2009-04-22 07:33:22 (Show Source): You can put this solution on YOUR website! the square of an integer is 30 more than the integer. find the integer. . Let x = the integer then x^2 = x + 30 x^2 -x -30 = 0 (x-6)(x+5) = 0 x = {-5,6} . Therefore, the integer could either be -5 or 6
Exponential-and-logarithmic-functions/192244: I need help with this problem:
log3x+log(x+2)=1
1 solutions

Answer 144523 by nerdybill(6951)   on 2009-04-22 07:30:09 (Show Source):
You can put this solution on YOUR website!
Apply "log rules":
log3x+log(x+2)=1
log(3x)(x+2)=1
(3x)(x+2)=10^1
3x^2+6x=10
3x^2+6x-10=0
x = {1.082, -3.082}
We can toss out the negative solution leaving:
x = 1.082
.
.
 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:

 Quadratic_Equations/192500: Tashin Baker is planning an expansion of a square flower garden in a city park. If each side of the original square is increased by 7 meters and the new total area of the garden will be 144 square meters. Find the lengh of the original garden.1 solutions Answer 144522 by nerdybill(6951)   on 2009-04-22 07:20:40 (Show Source): You can put this solution on YOUR website! Tashin Baker is planning an expansion of a square flower garden in a city park. If each side of the original square is increased by 7 meters and the new total area of the garden will be 144 square meters. Find the lengh of the original garden. . Let x = length of original garden then (x+7)(x+7) = 144 x^2 + 14x + 49 = 144 x^2 + 14x - 95 = 0 . Factoring the left side: (x+19)(x-5) = 0 x = {-19, 5} We can toss out the negative solution leaving: x = 5 meters (measure of one side of original garden)
 logarithm/192436: log(x+9)=log(2x-7)1 solutions Answer 144505 by nerdybill(6951)   on 2009-04-21 23:12:34 (Show Source): You can put this solution on YOUR website! log(x+9)=log(2x-7) (x+9)=(2x-7) 9 = x-7 16 = x
 Expressions-with-variables/192475: Translate the following phrase into an algebraic expression. Five, subtracted from three times a number. 1 solutions Answer 144504 by nerdybill(6951)   on 2009-04-21 22:49:30 (Show Source): You can put this solution on YOUR website!Five, subtracted from three times a number. . Let n = a number then 3n - 5 (this is what they're looking for)
 test/192336: Hello, I am having a little trouble with this algebra problem. if someone could be kind enough to tell me how to go about solving it. I would be very grateful Dustin is designing triangular pen for his angora rabbits named boo bop and flair hair. Now "Boo and Flair" will not settle for just any pen; it has to meet these specifications: The first side of the triangle must be 8 feet shorter than the second side. the third side must be 4 times as long as the first side. Find the length of each side of the triangle if the perimeter is 26.1 solutions Answer 144365 by nerdybill(6951)   on 2009-04-21 10:47:12 (Show Source): You can put this solution on YOUR website!The first side of the triangle must be 8 feet shorter than the second side. the third side must be 4 times as long as the first side. Find the length of each side of the triangle if the perimeter is 26. . Let x = length of second side then because "first side of the triangle must be 8 feet shorter than the second side" we get x-8 = length of first side and from "third side must be 4 times as long as the first side" we get 3(x-8) = length of third side . And, because the perimeter is 26: 26 = x + x-8 + 3(x-8) 26 = x + x-8 + 3x - 24 26 = 5x - 32 58 = 5x 11.6 feet = x (second side) . First side: x-8 = 11.6-8 = 3.6 feet (first side) . Third side: 3(x-8) = 3(11.6-8) = 3(3.6) = 10.8 feet (third side)
 Complex_Numbers/192338: how do you factor 125t cubed+8. our book gives this answer: (5t + 2)(25t squared- 10t+ 4) thank you!1 solutions Answer 144364 by nerdybill(6951)   on 2009-04-21 10:22:25 (Show Source): You can put this solution on YOUR website!125t^3 + 8 . What you're suppose to see is that this is the same as: (5t)^3 + 2^3 Which is a special case -- "sum of cubes". See this web site for additional info: http://www.purplemath.com/modules/specfact2.htm . a^3 + b^3 = (a + b)(a^2 – ab + b^2) In your case: a is 5t b is 2 . Therefore: 125t^3 + 8 = (5t)^3 + 2^3 = (5t + 2)((5t)^2 - (5t)(2) + 2^2) = (5t + 2)(25t^2 - 10t + 4)
 Triangles/192306: The height of a triangle is 4in greater than twice its base. The area of the trianlge is 168 square in. What is the base of the triangle?1 solutions Answer 144339 by nerdybill(6951)   on 2009-04-21 00:12:42 (Show Source): You can put this solution on YOUR website! The height of a triangle is 4in greater than twice its base. The area of the trianlge is 168 square in. What is the base of the triangle? . We know that for any triangle: area = (1/2)bh where b is base h is height . Let b = length of the base then 2b+4 = length of the height . 168 = (1/2)b(2b+4) 336 = b(2b+4) 336 = 2b^2 + 4b 0 = 2b^2 + 4b - 336 0 = b^2 + 2b - 168 0 = (b+14)(b-12) b = 12 inches (base)
 Exponential-and-logarithmic-functions/192260: log(base3)(2x-1)=31 solutions Answer 144330 by nerdybill(6951)   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(6951)   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(6951)   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(6951)   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}
.