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# Recent problems solved by 'nerdybill'

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 Polynomials-and-rational-expressions/696718: hi i have a question about polynomial functions p(x)=x^3-x^2-9x+9 it says write p(x) as a product of linear factor so what should do? thank you1 solutions Answer 429257 by nerdybill(7003)   on 2012-12-24 07:33:34 (Show Source): You can put this solution on YOUR website!They basically are asking you to factor the polynomial. "Linear factors" mean they want the factors all with degree of 1. . p(x)=x^3-x^2-9x+9 group terms: p(x)=(x^3-x^2)-(9x-9) p(x)=x^2(x-1)-9(x-1) p(x)=(x-1)(x^2-9) p(x)=(x-1)(x^2-3^2) p(x)=(x-1)(x-3)(x+3)
 Travel_Word_Problems/696500: WHAT PERCENT IS 4 OF 9?1 solutions Answer 429061 by nerdybill(7003)   on 2012-12-22 00:26:03 (Show Source): You can put this solution on YOUR website! WHAT PERCENT IS 4 OF 9? 4/9 * 100 0.444 * 100 44.4%
 Miscellaneous_Word_Problems/696009: What am I supposed to do if a question is like this. A school bus with capacity for 42 passengers. How many school buses are needed to transport a total of 180 passengers on a trip to the state legislature?1 solutions Answer 428752 by nerdybill(7003)   on 2012-12-19 19:25:26 (Show Source): You can put this solution on YOUR website!What am I supposed to do if a question is like this. A school bus with capacity for 42 passengers. How many school buses are needed to transport a total of 180 passengers on a trip to the state legislature? . Just divide: 180/42 = 4.29 the math says you need 4.29 buses Since, you can't have a "partial" bus the answer is you will need 5 buses
 logarithm/696027: How do we solve a problem that looks like this: Log base 3 10= 2.1 Log base 3 11= 2.2 Log base 3 8= 1.9 Find Log base 3 330 Log base 3 330=?1 solutions Answer 428751 by nerdybill(7003)   on 2012-12-19 19:19:35 (Show Source): You can put this solution on YOUR website!How do we solve a problem that looks like this: Log base 3 10= 2.1 Log base 3 11= 2.2 Log base 3 8= 1.9 Find Log base 3 330 Log base 3 330=? . Log base 3 330 Log base 3 33*10 Log base 3 3*11*10 Log base 3(3) + Log base 3(11) + Log base 3(10) Log base 3(3^1) + Log base 3(11) + Log base 3(10) 1 + Log base 3(11) + Log base 3(10) 1 + 2.2 + Log base 3(10) 1 + 2.2 + 2.1 3.2 + 2.1 5.3
 Word_Problems_With_Coins/695858: A jar contains quarters and dimes whose value totals \$4.40. It has three times as many dimes as quarters. How many dimes is in the jar.1 solutions Answer 428675 by nerdybill(7003)   on 2012-12-19 09:06:55 (Show Source): You can put this solution on YOUR website! A jar contains quarters and dimes whose value totals \$4.40. It has three times as many dimes as quarters. How many dimes is in the jar. . Let d = number of dimes then d/3 = number of quarters . .10d + .25(d/3) = 4.40 .30d + .25d = 13.20 .55d = 13.20 d = 13.20/.55 d = 24 (number of dimes)
 logarithm/695165: 2logx-3log(x+1)1 solutions Answer 428349 by nerdybill(7003)   on 2012-12-17 11:15:57 (Show Source): You can put this solution on YOUR website!I'm assuming they're asking you to simplify: 2logx-3log(x+1) logx^2-3log(x+1) logx^2-log(x+1)^3 log(x^2/(x+1)^3)
 Age_Word_Problems/694755: How can I translate this word problem into an equation? Jim is 5 years older than Joe. If the sum of their ages is 55, how old are they?1 solutions Answer 428176 by nerdybill(7003)   on 2012-12-16 11:13:48 (Show Source): You can put this solution on YOUR website!How can I translate this word problem into an equation? Jim is 5 years older than Joe. If the sum of their ages is 55, how old are they? . Let x = age of Joe then x+5 = age of Jim . x + x+5 = 55 2x + 5 = 55 2x = 50 x = 25 years old (Joe) . Jim: x+5 = 25+5 = 30 years old
 Functions/694714: Let f(x)=x^2 +3x+9 and g(x)=(2x+3)/(x-2) Find f(-1)-g(0)1 solutions Answer 428139 by nerdybill(7003)   on 2012-12-16 08:32:40 (Show Source): You can put this solution on YOUR website! Let f(x)=x^2 +3x+9 and g(x)=(2x+3)/(x-2) Find f(-1)-g(0) . first, find f(1): f(x)=x^2 +3x+9 f(1)=(1)^2 +3(1)+9 f(1)=1+3+9 f(1)=13 . then, find g(0): g(x)=(2x+3)/(x-2) g(x)=(2(0)+3)/(0-2) g(x)=(3)/(-2) g(x)= -3/2 . finally: f(-1)-g(0) 13-(-3/2) 13 + 3/2 26/2 + 3/2 (26+3)/2 29/2 (answer)
Quadratic_Equations/694657: Bob throws a ball vertically upward from the top of the cliff, the height of the ball above the base of the cliff is approximated by the model h = 65 + 10t- 5t ^2 where h is the height in metres and t is the time in seconds.
a) How high is the cliff?
b) How long does it take the ball to reach a height of 50 metres above the cliff?
c) After how many seconds does the ball hit the ground?
1 solutions

Answer 428123 by nerdybill(7003)   on 2012-12-15 23:15:00 (Show Source):
You can put this solution on YOUR website!
Bob throws a ball vertically upward from the top of the cliff, the height of the ball above the base of the cliff is approximated by the model h = 65 + 10t- 5t ^2 where h is the height in metres and t is the time in seconds.
a) How high is the cliff?
h = 65 + 10t- 5t ^2
set t to zero to find height of cliff:
h = 65 + 10(0)- 5(0)^2
h = 65 metres
.
b) How long does it take the ball to reach a height of 50 metres above the cliff?
set h to 50 and solve for t
h = 65 + 10t- 5t ^2
50 = 65 + 10t- 5t^2
0 = 15 + 10t- 5t^2
0 = -5t^2+10t+15
0 = 5t^2-10t-15
0 = t^2-2t-3
0 = (t+1)(t-3)
t = {-1, 3}
throw out the negative solution leaving:
t = 3 seconds
.
c) After how many seconds does the ball hit the ground?
set h to 0 and solve for t:
h = 65 + 10t- 5t ^2
0 = 65 + 10t- 5t^2
0 = -5t^2+10t+65
0 = 5t^2-10t-65
0 = t^2-2t-13
solve using the "quadratic equation" to get
t = {4.74, -2.74}
throw out the negative solution leaving:
t = 4.74 seconds
.
 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=56 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.74165738677394, -2.74165738677394. Here's your graph:

 percentage/694507: A man salary is 1850 dollars per month.Out of this 20 percent goes to his rent,690 dollars goes to foodand 940 dollars on other expenses.What percentage has he over spent?1 solutions Answer 427979 by nerdybill(7003)   on 2012-12-15 10:05:04 (Show Source): You can put this solution on YOUR website! A man salary is 1850 dollars per month.Out of this 20 percent goes to his rent,690 dollars goes to foodand 940 dollars on other expenses.What percentage has he over spent? . Total expenditure: .20(1850) + 690 + 940 370 + 690 + 940 1060 + 940 2000 . amount overspent: 2000-1850 = 150 . percentage over spent: 150/1850 * 100 0.08 * 100 8%
 logarithm/694297: Solve this application using logarithms. Refer to the examples above. How much principal, to the nearest dollar, should you invest at 4% in order to have \$3,000 for a vacation to Europe in 3 years?1 solutions Answer 427823 by nerdybill(7003)   on 2012-12-14 09:40:36 (Show Source): You can put this solution on YOUR website!Solve this application using logarithms. Refer to the examples above. How much principal, to the nearest dollar, should you invest at 4% in order to have \$3,000 for a vacation to Europe in 3 years? . Assuming simple interest then: a = pe^(rt) 3000 = pe^(.04*3) 3000 = pe^(.12) 3000/e^(.12) = p 2660.76 = p nearest dollar: \$2661 = p
 Rate-of-work-word-problems/694276: My son can clean the attic in 4 hours and I can do it in 2 hours. How long would it take if we worked together.1 solutions Answer 427810 by nerdybill(7003)   on 2012-12-14 08:14:33 (Show Source): You can put this solution on YOUR website! My son can clean the attic in 4 hours and I can do it in 2 hours. How long would it take if we worked together. . Let x = time (hours) for both then x(1/4 + 1/2) = 1 x(1/4 + 2/4) = 1 x(3/4) = 1 x(3) = 4 x = 4/3 hours or x = 1 hour and 20 minutes
 Angles/693887: The difference between the measure of an angle and it's suplementary is 36 find the measure of the two angles1 solutions Answer 427614 by nerdybill(7003)   on 2012-12-13 11:44:52 (Show Source): You can put this solution on YOUR website! The difference between the measure of an angle and it's suplementary is 36 find the measure of the two angles . Let x = measure of angle then 180-x = supplement of angle . x - (180-x) = 36 x - 180+x = 36 2x - 180 = 36 2x = 216 x = 108 degrees . supplement: 180-x = 180-108 = 72 degrees . measure of the two angles: 108 and 72 degrees
 Numbers_Word_Problems/693885: if 8 is added to twice a number and this sum is multiplied by 4 the result is the same as if the number is multiplied by 4 and 8 is added to the product1 solutions Answer 427611 by nerdybill(7003)   on 2012-12-13 11:21:45 (Show Source): You can put this solution on YOUR website! if 8 is added to twice a number and this sum is multiplied by 4 the result is the same as if the number is multiplied by 4 and 8 is added to the product . Let n = the number then 4(2n+8) = 4n+8 8n+32 = 4n+8 4n+32 = 8 4n = 24 n = 6 . The number is 6
 test/692675: Completing the square 2x^2+7x-41 solutions Answer 427066 by nerdybill(7003)   on 2012-12-10 23:26:19 (Show Source): You can put this solution on YOUR website!Completing the square 2x^2+7x-4 group x terms: (2x^2+7x)-4 factor out the 2: 2(x^2+7/2x) - 4 2(x^2+7/2x+49/4) - 4 - (2)(49/4) 2(x^2+7/2x+49/4) - 4 - (49/2) 2(x^2+7/2x+49/4) - 8/2- (49/2) 2(x^2+7/2x+49/4) - 57/2 2(x+7/2)^2 - 57/2
 Polynomials-and-rational-expressions/692160: Solve algebraically. 10^(x-3)+11=12101 solutions Answer 426936 by nerdybill(7003)   on 2012-12-10 01:41:14 (Show Source): You can put this solution on YOUR website!10^(x-3)+11=1210 10^(x-3) = 1199 (x-3) = log(1199) x = log(1199) + 3 x = 6.08
 Surface-area/691752: A rectangular room is 20 feet long and 10 feet wide. If you paint a red rectangle on the floor that is 8 feet long and 3 feet wide, what is the area of the floor in the room that will NOT be red? please help! 1 solutions Answer 426839 by nerdybill(7003)   on 2012-12-09 12:32:59 (Show Source): You can put this solution on YOUR website!A rectangular room is 20 feet long and 10 feet wide. If you paint a red rectangle on the floor that is 8 feet long and 3 feet wide, what is the area of the floor in the room that will NOT be red? please help! "area of room" - "red area" (20*10) - (8*3) (200) - (24) 176 square feet
 Functions/691763: What is the slope-intercept form of y-2=1/2(x-4)1 solutions Answer 426838 by nerdybill(7003)   on 2012-12-09 12:31:02 (Show Source): You can put this solution on YOUR website!y-2=1/2(x-4) y-2= (1/2)x-2 y = (1/2)x-2+2 y = (1/2)x+0 y = (1/2)x (this is what they're looking for) where slope is 1/2 y-intercept is at 0
 Pythagorean-theorem/691737: The legs of a right triangle are 15 meters and 9 meters. Find the length of the hypotenuse?1 solutions Answer 426827 by nerdybill(7003)   on 2012-12-09 11:12:17 (Show Source): You can put this solution on YOUR website! The legs of a right triangle are 15 meters and 9 meters. Find the length of the hypotenuse? applying the Pythagorean theorem: h^2 = 15^2 + 9^2 h^2 = 225 + 81 h^2 = 306 h = 17.49 meters
 Money_Word_Problems/691679: how long would it take to double an investment of 1000 at 9 percent compounded quarterly?1 solutions Answer 426815 by nerdybill(7003)   on 2012-12-09 09:22:39 (Show Source): You can put this solution on YOUR website! how long would it take to double an investment of 1000 at 9 percent compounded quarterly? . Use: A = P(1+i/n)^(nt) where A is amount after time t (2P) P is the principal (P) i is the interest per year (.09) n is the times compounded during the year (4) t is number of years (what we're looking for) . A = P(1+i/n)^(t/n) 2P = P(1+.09/4)^(4t) 2 = (1+.09/4)^(4t) 2 = (1.0225)^(4t) = 4t = t 7.79 years = t
 Functions/691708: if h(r)= 2/3r-6, what is the value of h(-9)? 1 solutions Answer 426811 by nerdybill(7003)   on 2012-12-09 09:12:08 (Show Source): You can put this solution on YOUR website! if h(r)= 2/3r-6, what is the value of h(-9)? . substitute -9 for r and solve: h(r)= 2/3r-6 h(-9)= 2/3(-9)-6 h(-9)= 2(-3)-6 h(-9)= (-6)-6 h(-9)= -12
 logarithm/691704: log(x+3)=2+log(x) Can this problem be solved? I do not know what to do with 2+log(x) Thank you!1 solutions Answer 426810 by nerdybill(7003)   on 2012-12-09 09:09:07 (Show Source): You can put this solution on YOUR website!log(x+3)=2+log(x) log(x+3) - log(x) = 2 log[(x+3)/(x)] = 2 (x+3)/(x) = 10^2 (x+3)/(x) = 100 (x+3) = 100x 3 = 99x 3/99 = x 1/33 = x
 Miscellaneous_Word_Problems/691642: The measure of an angle is 5 times the measure of its supplement. Find the measures of the two angles1 solutions Answer 426793 by nerdybill(7003)   on 2012-12-09 01:54:17 (Show Source): You can put this solution on YOUR website! The measure of an angle is 5 times the measure of its supplement. Find the measures of the two angles . Let x = measure of angle then 180-x = supplement of angle . x = 5(180-x) x = 900-5x 6x = 900 x = 150 degrees (measure of angle) . supplement: 180-x = 180-150 = 30 degrees
 Miscellaneous_Word_Problems/691646: the Fahrenheit temperature, F, is found using formula F = 9/5C+32, where C the temperature in Celsius, determine the formula for C and justify each step.1 solutions Answer 426792 by nerdybill(7003)   on 2012-12-09 01:50:43 (Show Source): You can put this solution on YOUR website! Start with: F = 9/5C+32 subtract 32 from both sides: F - 32 = 9/5C multiply both sides by 5: 5F - 160 = 9C divide both sides by 9: (5F - 160)/9 = C
 Linear_Algebra/691652: where can i find the video explanation of college algebra without any log in or payment rules?1 solutions Answer 426790 by nerdybill(7003)   on 2012-12-09 01:44:14 (Show Source): You can put this solution on YOUR website!Try this site -- it was featured on 60 Minutes: http://www.khanacademy.org/ Use the "Watch" pull-down menu...
 Quadratic_Equations/691625: Find the vertex of the parabola fx=x^2-6x-21 solutions Answer 426785 by nerdybill(7003)   on 2012-12-09 00:04:19 (Show Source): You can put this solution on YOUR website!fx=x^2-6x-2 you could "complete the square": fx=(x^2-6x)-2 fx=(x^2-6x+9)-2-9 fx=(x^2-6x+9)-11 fx=(x-3)^2+(-11) so, vertex is at (3, -11)
 Quadratic-relations-and-conic-sections/691391: Write an equation for the parabola with the vertex (1,3) that passes through (-2,-15). I have tried to figure out how to do y=A(x-h)^2, but cannot figure out how to apply it to the problem. Sorry if topic is wrong, I can't click on the right one.1 solutions Answer 426677 by nerdybill(7003)   on 2012-12-08 13:42:40 (Show Source): You can put this solution on YOUR website!Write an equation for the parabola with the vertex (1,3) that passes through (-2,-15) . Vertex form of a parabola is y = a(x-h)^2 + k where (h,k) is the vertex . Since the problem gives you the vertex we can plug it in: y = a(x-1)^2 + 3 Now, we plug in the given point and solve for a: -15 = a(-2-1)^2 + 3 -15 = a(-3)^2 + 3 -15 = a(9) + 3 -18 = a(9) -2 = a . So, our equation is now: y = -2(x-1)^2 + 3
 Volume/691412: Here is the question: The dimensions of a brick, in inches, are 2 by 4 by 8. How many such bricks are needed to have a total volume of exactly 1 cubic foot? I know that to find volume you multiply 2x4x8. So I did that and got 64, but I'm not sure what to do from there. Hope you can help!1 solutions Answer 426676 by nerdybill(7003)   on 2012-12-08 13:38:06 (Show Source): You can put this solution on YOUR website!The dimensions of a brick, in inches, are 2 by 4 by 8. How many such bricks are needed to have a total volume of exactly 1 cubic foot? Since they give you the dimensions of the brick in INCHES -- we begin by converting 1 cubic foot into cubic inches: 12*12*12 = 1728 cubic inches . You already found that the volume of a brick is 64 cubic inches . to find how many bricks are needed to make 1 cubic foot: 1728/64 = 27 bricks
 logarithm/691405: If log(base 3)(5) = x, find log(base 3) (25/27) in terms of x1 solutions Answer 426674 by nerdybill(7003)   on 2012-12-08 13:34:38 (Show Source): You can put this solution on YOUR website!If log(base 3)(5) = x, find log(base 3) (25/27) in terms of x . log(base 3)(25/27) log(base 3)(25) - log(base 3)(27) log(base 3)(25) - log(base 3)(3^3) log(base 3)(25) - 3 log(base 3)(5*5) - 3 log(base 3)(5)+log(base 3)(5) - 3 x+x - 3 2x-3
 logarithm/691403: solve 2log(base e)(x) + log(base e)(7) = 1 please...1 solutions Answer 426673 by nerdybill(7003)   on 2012-12-08 13:31:22 (Show Source): You can put this solution on YOUR website!2log(base e)(x) + log(base e)(7) = 1 log(base e)(x^2) + log(base e)(7) = 1 log(base e)(7x^2) = 1 (7x^2) = e^1 x^2 = e/7 x = .6232
logarithm/691401:
1 solutions

Answer 426672 by nerdybill(7003)   on 2012-12-08 13:28:10 (Show Source):
You can put this solution on YOUR website!
2log(base9)x = 1/2 + log(base9)(5x + 18)
log(base9)x^2 = 1/2 + log(base9)(5x + 18)
log(base9)x^2 - log(base9)(5x + 18) = 1/2
log(base9)x^2/(5x + 18) = 1/2
x^2/(5x + 18) = 9^(1/2)
x^2/(5x + 18) = 3
x^2 = 3(5x + 18)
x^2 = 15x + 46
x^2-15X = 46
x^2-15X-46 = 0