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nerdybill answered: 6956 problems
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logarithm/376007: Express as a single logarithm and, if possible, simplify. 1n (x^2-64) - 1n (x+8) 1 solutions Answer 267403 by nerdybill(6958)   on 2010-11-24 22:56:36 (Show Source): You can put this solution on YOUR website! 1n (x^2-64) - 1n (x+8) 1n (x^2-64)/(x+8) 1n [(x-8)(x+8)]/(x+8) 1n (x-8)

Exponential-and-logarithmic-functions/375414: Express as equivalent expression that a single logarithm and if possible, simplify. (not sure how to subscript the 'a') 1 solutions Answer 266971 by nerdybill(6958)   on 2010-11-23 12:00:04 (Show Source): You can put this solution on YOUR website!

Polynomials-and-rational-expressions/375398: s^2+4s+4 Factor please? 1 solutions Answer 266970 by nerdybill(6958)   on 2010-11-23 11:57:31 (Show Source): You can put this solution on YOUR website! s^2+4s+4 (s+2)(s+2) or (s+2)^2

Polynomials-and-rational-expressions/375411: w^3-2w^2-63w factor the trinomial? 1 solutions Answer 266969 by nerdybill(6958)   on 2010-11-23 11:56:28 (Show Source): You can put this solution on YOUR website! w^3-2w^2-63w first, factor out what is common among all terms: w(w^2-2w-63) then factor the stuff inside the parenthesis: w(w-9)(w+7)

Linear_Equations_And_Systems_Word_Problems/375282: a coat cost 204.66 which included an 8% tax. what was the original cost before the sales tax? 1 solutions Answer 266968 by nerdybill(6958)   on 2010-11-23 11:50:54 (Show Source): You can put this solution on YOUR website! a coat cost 204.66 which included an 8% tax. what was the original cost before the sales tax? . Let x = original cost then x + .08x = 204.66 x(1+.08) = 204.66 x(1.08) = 204.66 x = 204.66/1.08 x = $189.50

Inverses/375403: Inverse of B(t) = e^t 1 solutions Answer 266966 by nerdybill(6958)   on 2010-11-23 11:39:50 (Show Source): You can put this solution on YOUR website! B(t) = e^t . set B(t) to y: y = e^t flip variables t = e^y solve for y: ln(t) = y . therefore:

Exponential-and-logarithmic-functions/375399: write an exponential equation y=ab^x whose graph passes through these points (1,10), (2,25) 1 solutions Answer 266965 by nerdybill(6958)   on 2010-11-23 11:36:42 (Show Source): You can put this solution on YOUR website! write an exponential equation y=ab^x whose graph passes through these points (1,10), (2,25) . From:(1,10) 10 = ab^1 10 = ab (equation 1) and from:(2,25) 25 = ab^2 (equation 2) . solve equation 1 for b: 10 = ab 10/a = b . substitute it into eq 2 and solve for a: 25 = ab^2 25 = a(10/a)^2 25 = a(100/a^2) 25 = (100/a) a = 100/25 a = 4 . substitute it into eq 1 and solve for b: 10 = ab 10 = 4b 10/4 = b 2.5 = b

Angles/375294: find the measure of a supplement of a 70 degree angle....thank you 1 solutions Answer 266963 by nerdybill(6958)   on 2010-11-23 11:33:00 (Show Source): You can put this solution on YOUR website! find the measure of a supplement of a 70 degree angle: . Two angles are "supplement" if the sum is 180 degrees. . Therefore, the measure of the supplement of 70 is: 180-70 = 110 degrees

Quadratic-relations-and-conic-sections/375307: Please help me solve this question. A ball is thrown vertically upward. After t seconds, it's height h (in feet) is given by the function h(t)= 104t-16t^2. What is the maximum height that the ball will reach? Do not round your answer. Height: ___ ft 1 solutions Answer 266962 by nerdybill(6958)   on 2010-11-23 11:31:02 (Show Source): You can put this solution on YOUR website! h(t)= 104t-16t^2 max height is at the vertex. . Vertex is when: t = -b/(2a) = -104/(2*(-16)) = -104/(-32) = 3.25 . h(3.25)= 104(3.25)-16(3.25)^2 h(3.25)= 338-169 h(3.25)= 169 feet

logarithm/375373: let log2=a log3 =b and log 5= c, what is log 16 log 0.00003 log 8/3 in terms of a, b , c? please help 1 solutions Answer 266941 by nerdybill(6958)   on 2010-11-23 10:06:29 (Show Source): You can put this solution on YOUR website! let log2=a log3 =b and log 5= c, what is log 16 log 0.00003 log 8/3 in terms of a, b , c? . log(16) = log(2^4) = 4*log(2) = 4a . log(0.00003) = log(3/10^5) = log(3) - log(10^5) = log(3) - 5log(10) = log(3) - 5log(2*5) = log(3) - 5[log(2)+log(5)] = b-5[a+c] . log 8/3 = log(8)-log(3) = log(2^3)-log(3) = 3log(2)-log(3) = 3a-b

Graphs/375321: An investor of a new product believes that the cost of producing the product is given by the function: C(x) = 1.75x + 7000 How much does it cost to produce 2000 units of her invention? 1 solutions Answer 266940 by nerdybill(6958)   on 2010-11-23 10:00:38 (Show Source): You can put this solution on YOUR website! An investor of a new product believes that the cost of producing the product is given by the function: C(x) = 1.75x + 7000 How much does it cost to produce 2000 units of her invention? . In this case, x is 2000 So, plug it in and solve: C(x) = 1.75x + 7000 C(2000) = 1.75(2000) + 7000 C(2000) = 3500 + 7000 C(2000) = $10,500

Quadratic_Equations/375243: how do solve: h(t) = -16t^2 + 90t + 15 1 solutions Answer 266853 by nerdybill(6958)   on 2010-11-22 23:11:15 (Show Source): You can put this solution on YOUR website! how do solve: h(t) = -16t^2 + 90t + 15 . this is an equation of motion for a projectile of some sort. . You really can't "solve" this -- you can however answer some questions such as: -max height (vertex) -time it hits the max height (vertex) -time it hits the ground (set h(t) to zero solve for t) . What was the question?

logarithm/375242: log6 18 - log6 3 1 solutions Answer 266852 by nerdybill(6958)   on 2010-11-22 23:07:10 (Show Source): You can put this solution on YOUR website!

Polynomials-and-rational-expressions/374963: Can someone help me with this? It is asking me to simplify. (-8b^2+9b+4)-(9b^2+4) 1 solutions Answer 266684 by nerdybill(6958)   on 2010-11-22 15:34:04 (Show Source): You can put this solution on YOUR website! (-8b^2+9b+4)-(9b^2+4) distribute the "negative sign": (-8b^2+9b+4)-9b^2-4 removing the parenthesis -8b^2+9b+4-9b^2-4 grouping like-terms: -8b^2-9b^2+9b+4-4 (-8b^2-9b^2)+9b+(4-4) -17b^2+9b+0 -17b^2+9b

Expressions-with-variables/374996: Machine A can complete a task in 24 seconds. Together with machine B, the task can be completed in 18 s. How long would it take machine B working alone to complete the task? 1 solutions Answer 266683 by nerdybill(6958)   on 2010-11-22 15:31:38 (Show Source): You can put this solution on YOUR website! Machine A can complete a task in 24 seconds. Together with machine B, the task can be completed in 18 s. How long would it take machine B working alone to complete the task? . Let x = seconds it takes machine B (working alone) then 18(1/24 + 1/x) = 1 multiplying both sides by 24x: 18(x + 24) = 24x 18x + 432 = 24x 432 = 6x 72 secs = x

logarithm/374907: i need help solving this equation 1 solutions Answer 266609 by nerdybill(6958)   on 2010-11-22 12:14:05 (Show Source): You can put this solution on YOUR website! x = {-2, 8} . But, x=-2 turns out to be an "extraneous" solution so throw it out leaving: x = 8

logarithm/374866: what is the value of log 3 34 round to the nearest hundreth ? 1 solutions Answer 266586 by nerdybill(6958)   on 2010-11-22 10:22:26 (Show Source): You can put this solution on YOUR website! I suppose when you wrote: log 3 34 You meant: = =

Miscellaneous_Word_Problems/374292: When a projectile is fired, the vertical component of its initial velocity is such that its height h metres t seconds after firing is given by . Determine if the projectile will reach each height. a)2.75km b)4.0km 1 solutions Answer 266370 by nerdybill(6958)   on 2010-11-21 09:04:15 (Show Source): You can put this solution on YOUR website! Is a quadratic (parabola) that opens downwards. We can tell because the coefficient associated with the t^2 term is negative. If so, then the vertex defines the hight point. . Highest point is reached when the time is: t = -b/(2a) = -250/(2*(-4.9)) = -250/(-10.8) = 25.51 Highest point projectile will reach: meters kilometers . So, now we can answer the question: a)2.75km (yes) b)4.0km (no)

Linear-equations/373983: Please can someone help!! Find the slope-intercept equation of the line that has the given characteristics Slope 4 and y-intercept (0,7) The slope - intercept equation is ___? 1 solutions Answer 266169 by nerdybill(6958)   on 2010-11-20 10:58:10 (Show Source): You can put this solution on YOUR website! Plug the given information: Slope 4 and y-intercept (0,7) into the "point-slope" form of: y - y1 = m(x - x1) y - 7 = 4(x - 0) y - 7 = 4x y = 4x + 7 (this is what they're looking for)

Quadratic_Equations/373971: help me solve this, please. 7x+x(x-5)=0. I'm not sure what to put in place of the x 1 solutions Answer 266156 by nerdybill(6958)   on 2010-11-20 10:06:28 (Show Source): You can put this solution on YOUR website! 7x+x(x-5)=0 7x+x^2-5x=0 x^2 + 2x = 0 x(x+2) = 0 Setting each term on the left to zero we get: x = {0, -2}

Quadratic_Equations/373974: Write a quadratic equation for -7,5 1 solutions Answer 266155 by nerdybill(6958)   on 2010-11-20 10:04:00 (Show Source): You can put this solution on YOUR website! I'm assuming you want a quadratic that crosses at a point (x,y) where (x,y) = (-7,5) . If so, consider: y = x^2 + x + C Plug in your values, solve for C: 5 = (-7)^2 + (-7) + C 5 = 49 - 7 + C 5 = 42 + C -37 = C So, your equation would be: y = x^2 + x - 37

Linear-equations/373807: My niece is in 8th grade and is having trouble with Slope intercept form, Point intercept form and Standard form. I told her I would help her but in order to do that I must learn what these are. Can you help Me? 1 solutions Answer 266027 by nerdybill(6958)   on 2010-11-19 19:41:56 (Show Source): You can put this solution on YOUR website! www.purplemath.com is a good place to start. All three are used to describe a straight line. . Slope-intercept form: http://www.purplemath.com/modules/strtlneq.htm y = mx + b where m is the slope b is the y-intercept (point at which it crosses the y-axis) . Point-slope form: http://www.purplemath.com/modules/strtlneq2.htm y - y1 = m(x - x1) is basically used when you are given one point (x1, y1) and a slope and you want to determine the equation of the line. . Standard form is in the form: (not used too often) Ax + By = C

test/373616: Factor out the greatest common factor from the following. 6x^5 - 10x^4 1 solutions Answer 265890 by nerdybill(6958)   on 2010-11-19 08:59:12 (Show Source): You can put this solution on YOUR website! 6x^5 - 10x^4 Your greatest common factor is 2x^4: (2x^4)(3x - 5)

Numbers_Word_Problems/373599: The product of two integers is 24. How many values are possible for their sum? 1 solutions Answer 265888 by nerdybill(6958)   on 2010-11-19 08:41:35 (Show Source): You can put this solution on YOUR website! The product of two integers is 24. How many values are possible for their sum? . Four: 1*24 2*12 3*8 4*6

Exponential-and-logarithmic-functions/373233: Express each expression as a simplified single logarithm log6+log5-log2 1 solutions Answer 265669 by nerdybill(6958)   on 2010-11-18 15:06:05 (Show Source): You can put this solution on YOUR website! log6+log5-log2 log(6*5)-log2 log(30)-log2 log(30/2) log(15)

Miscellaneous_Word_Problems/373121: I am not sure how to go about this word problem so can you please help me solve this problem. I am getting overwhelmed! John wants to fence a 150 square meters rectangular field. He wants the length and width to be natural numbers {1,2,3,...}. What field dimensions will require the least amount of fencing? Show work. Thank you so much! Jessica 1 solutions Answer 265651 by nerdybill(6958)   on 2010-11-18 10:32:10 (Show Source): You can put this solution on YOUR website! John wants to fence a 150 square meters rectangular field. He wants the length and width to be natural numbers {1,2,3,...}. What field dimensions will require the least amount of fencing? . You could create a "table": width length area perimeter 1 150 150 302 2 75 150 154 3 50 150 106 5 30 150 70 6 25 150 62 10 15 150 50 15 10 150 50 25 6 150 62 30 5 150 70 . From the above, we see that the answer is a field that is: 10 feet by 15 feet

Exponential-and-logarithmic-functions/373122: I don't even know where to start. The problem is log2^x = 1/3log2^27. Can you please show me step by step. 1 solutions Answer 265648 by nerdybill(6958)   on 2010-11-18 10:14:56 (Show Source): You can put this solution on YOUR website! Apply "log rules"... . Starting with:

Equations/373108: Hi tutors.. :) Im having a problem with Algebra Number Problems. For example an equation like this : There are two numbers whose sum is 72. One number is twice the other. What are the numbers? Also. There are three consecutive integers. the sum of the smallest and largest is 36. I just dont get it:( Help please 1 solutions Answer 265647 by nerdybill(6958)   on 2010-11-18 10:11:15 (Show Source): You can put this solution on YOUR website! There are two numbers whose sum is 72. One number is twice the other. What are the numbers? . Let x = first number then from "One number is twice the other." we have 2x = second number . From: "There are two numbers whose sum is 72" we derive our equation: x + 2x = 72 3x = 72 x = 24 (first number) Second number: 2x = 2(24) = 48 . . . Also. There are three consecutive integers. the sum of the smallest and largest is 36. . Let x = first consecutive integer then x+1 = second consecutive integer x+2 = third . From:"the sum of the smallest and largest is 36" we get: x + x+2 = 36 2x+2 = 36 2x = 34 x = 17 (first) . Second: x+1 = 17+1 = 18 . Third: x+2 = 17+2 = 19

Quadratic_Equations/372797: Jack wanted to throw an apple to Lauren, who was on a balcony 40 feet above him, so he tossed it upward with an initial speed of 56 ft/s. Lauren missed it on the way up, but then caught it on the way down. How long was the apple in the air? Would I use the equation h(t) = -16t^2 + 56t +40? (where h = height and t = time) I'm not very good at solving quadratic word problems :( 1 solutions Answer 265524 by nerdybill(6958)   on 2010-11-17 18:32:32 (Show Source): You can put this solution on YOUR website! Well, you're close The general equation is h(t) = -(1/2)gt^2 + Vot + h(0) where g is gravity 32 ft/sec^2 Vo is initial velocity h(0) is initial height of Jack (not Lauren) . So, plugging in what we know h(t) = -(1/2)(32)t^2 + 56t + 0 which reduces to h(t) = -16t^2 + 56t . So, since Lauren is 40 feet up -- set h(t) to 40 and solve for t: h(t) = -16t^2 + 56t 40 = -16t^2 + 56t 0 = -16t^2 + 56t - 40 multiply both sides by -1: 0 = 16t^2 - 56t + 40 divide both sides by 8: 0 = 2t^2 - 7t + 5 0 = (2t-5)(t-1) So, t = {1, 5/2} 1 sec represents the time the apple reaches 40 ft (going up) So 5/2 secs or 2 and 1/2 secs (is your solution)

logarithm/372785: 3logx- log11- 4logz+2logy in condensed form 1 solutions Answer 265516 by nerdybill(6958)   on 2010-11-17 18:23:41 (Show Source): You can put this solution on YOUR website! 3logx- log11- 4logz+2logy logx^3 - log11- logz^4 + logy^2 log(x^3/11) - logz^4 + logy^2 log(x^3/11)/z^4 + logy^2 log(x^3/11z^4) + logy^2 log(x^3/11z^4)y^2 log(x^3y^2/11z^4)

Linear-systems/372684: If an object is projected vertically upward from an altitude of s(o) feet with an intial velocity of v(o) ft/sec, then its distance above the ground after t seconds is: s(t)=-16t^2+ v(o)t+ s(o). If s(1)= 64 and s(2)=66, what are s(o) and v(o)? I honestly do not know how to set the problem up! Please help, it would be greatly appreciated!Thanks :) 1 solutions Answer 265418 by nerdybill(6958)   on 2010-11-17 14:26:23 (Show Source): You can put this solution on YOUR website! Given: s(t)=-16t^2+ v(o)t+ s(o). If s(1)= 64 and s(2)=66, what are s(o) and v(o)? . So, when x=1 then s(1)=64 and when x=2 then s(2)=66 . From here, you now have two unknowns and two equations: when x=1 then s(1)=64 s(t)=-16t^2+ v(o)t+ s(o) s(1)=-16(1)^2+ v(o)(1)+ s(o) 64=-16+ v(o)+ s(o) 89=v(o)+ s(o) equation 1 . when x=2 then s(2)=66 s(t)=-16t^2+ v(o)t+ s(o) s(2)=-16(2)^2+ v(o)(2)+ s(o) 66=-16(4)+ 2v(o)+ s(o) 130=2v(o)+ s(o) equation 2 . Considering the "system of equations" then: 130=2v(o)+ s(o) 89=v(o)+ s(o) . Multiply both sides of the bottom equation by -1 and add: 130=2v(o)+ s(o) -89=-v(o)- s(o) --------------------- 41 ft/sec = v(0) . Substitute the above into: 89=v(o)+ s(o) 89=41+ s(o) 48 feet = s(o)