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# Recent problems solved by 'nerdybill'

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 test/446897: What is your distance if you travel at 65 mph for three hours?1 solutions Answer 307757 by nerdybill(7003)   on 2011-05-09 09:46:36 (Show Source): You can put this solution on YOUR website!What is your distance if you travel at 65 mph for three hours? since: d = rt (distance formula) where d is distance r is rate or speed t is time . d = 65*3 d = 195 miles
 Polynomials-and-rational-expressions/446907: The length of a rectangle flower garden is three feet more than its width. The area is 70 square feet. Using an algbriac equation find the length and the width of the flower garden. Would I use width = x and length = x+3 = to 70? Is that how I would set this equation up? 1 solutions Answer 307756 by nerdybill(7003)   on 2011-05-09 09:44:57 (Show Source): You can put this solution on YOUR website!The length of a rectangle flower garden is three feet more than its width. The area is 70 square feet. Using an algbriac equation find the length and the width of the flower garden. . Let x = width then because "length of a rectangle flower garden is three feet more than its width" we get x+3 = length (basically, what you had) . Now, you have to apply your knowledge of the area of any rectangle: area = width * length giving you your equation: 70 = x(x+3) now we solve for x: 70 = x(x+3) 70 = x^2+3x 0 = x^2+3x-70 0 = (x+10)(x-7) x = {-10, 7} we can throw out the negative solution (extraneous) since it doesn't make sense leaving: x = 7 feet (width) . Length: x+3 = 7+3 = 10 feet
 Polynomials-and-rational-expressions/446839: So I'm dealing with trinomials and I think it's along the line of polynomials. In order to solve this question I have to factor this trinomial -->32Nsquared-80N+50. Thank you for the help!1 solutions Answer 307751 by nerdybill(7003)   on 2011-05-09 09:18:13 (Show Source): You can put this solution on YOUR website! begin by factoring out common factor:
 real-numbers/446879: 280% of what is 241 solutions Answer 307750 by nerdybill(7003)   on 2011-05-09 09:15:03 (Show Source): You can put this solution on YOUR website!280% of what is 24 280/100 * 24 2.8 * 24 67.2
 Trigonometry-basics/446884: How would I solve e^5x=7?1 solutions Answer 307749 by nerdybill(7003)   on 2011-05-09 09:14:08 (Show Source): You can put this solution on YOUR website!I presume the x is part of the exponent: take the natural log of both sides to give you:
 Exponential-and-logarithmic-functions/446788: I need help solving this problem: log 4 (x ^2 -3) + log 4 10=11 solutions Answer 307672 by nerdybill(7003)   on 2011-05-08 23:09:56 (Show Source): You can put this solution on YOUR website!log 4 (x ^2 -3) + log 4 10=1 log 4 10(x ^2 -3) =1 10(x ^2 -3) = 4^1 10x^2 -30 = 4 10x^2 = 34 x^2 = 3.4 x = sqrt(3.4) x = {-1.84, 1.84} throw out the negative solution (extraneous) leaving: x = 1.84
Rate-of-work-word-problems/446552: One machine works 8 hours faster then a second machine. If the two machines take twelve hours to finish the job working together, how long will it take them individually.
I just need to figure out how to get to aquadratic equasion.
1 solutions

Answer 307535 by nerdybill(7003)   on 2011-05-08 13:38:07 (Show Source):
You can put this solution on YOUR website!
One machine works 8 hours faster then a second machine. If the two machines take twelve hours to finish the job working together, how long will it take them individually.
.
Let x = time (hrs) it takes for slower machine
then
x-8 = time of faster machine
.
12(1/x + 1/(x-8)) = 1
multiplying both sides by x(x-8):
12(x-8 + x) = x(x-8)
12(2x-8) = x(x-8)
24x-96 = x^2-8x
-96 = x^2-32x
0 = x^2-32x+96
applying the quadratic equation we get:
x = {28.65, 3.35}
we can throw out the 3.35 leaving:
x = 28.65 hrs (slower machine)
.
faster machine:
x-8 = 28.65-8 = 20.65 hrs
.
 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=640 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 28.6491106406735, 3.35088935932648. Here's your graph:

 Inequalities/446528: Car payments. As a rule of thumb, debt payments (other than mortgages) should be less than 8% of a consumer’s monthly gross income. Oliver makes \$54,000 a year and has a \$100 student-loan payment every month. What size car payment can he afford?1 solutions Answer 307519 by nerdybill(7003)   on 2011-05-08 12:00:51 (Show Source): You can put this solution on YOUR website!Car payments. As a rule of thumb, debt payments (other than mortgages) should be less than 8% of a consumer’s monthly gross income. Oliver makes \$54,000 a year and has a \$100 student-loan payment every month. What size car payment can he afford? gross monthly = 54000/12 = \$4500 per month 8% of that is: .08*4500 = \$360 subtracting the student-loan: 360-100=\$260 . Ans: he can afford \$260 per month
 Rate-of-work-word-problems/446518: If Hose A can fill up a tank in 20 minutes and Hose B can fill up the tank in 15 minutes , how long will it take for the hose together to fill up the tank ? 1 solutions Answer 307514 by nerdybill(7003)   on 2011-05-08 11:47:23 (Show Source): You can put this solution on YOUR website!If Hose A can fill up a tank in 20 minutes and Hose B can fill up the tank in 15 minutes , how long will it take for the hose together to fill up the tank ? . Let x = time (minutes) it takes for both then x(1/20 + 1/15) = 1 multiplying both sides by 60: x(3 + 4) = 60 7x = 60 x = 60/7 x = 8.57 minutes
 test/446519: If 8- (8 - m) = 8, Then m = ?1 solutions Answer 307513 by nerdybill(7003)   on 2011-05-08 11:44:31 (Show Source): You can put this solution on YOUR website! 8- (8 - m) = 8 8- 8 + m = 8 0 + m = 8 m = 8
 Evaluation_Word_Problems/446520: differentiate, with respect to x: -2/x1 solutions Answer 307512 by nerdybill(7003)   on 2011-05-08 11:42:50 (Show Source):
logarithm/446447: Solve the logarithmic equation for x. (Round your answer to four decimal places.)
ln(x − 6) + ln(x + 7) = 1
1 solutions

Answer 307505 by nerdybill(7003)   on 2011-05-08 10:56:44 (Show Source):
You can put this solution on YOUR website!
ln(x − 6) + ln(x + 7) = 1
ln(x − 6)(x + 7) = 1
(x − 6)(x + 7) = e^1
x^2+x-42 = e^1
x^2+x-42-e^1 = 0
x^2+x-42-2.718282 = 0
x^2+x-44.718282 = 0
apply the quadratic formula to get:
x = {6.2058, -7.2058}
the negative solution is extraneous -- throw it out leaving:
x = 6.2058
.
 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=179.87312732 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6.20583938295572, -7.20583938295572. Here's your graph:

 logarithm/446463: Have A couple questions about logs I'm supposed to solve e^2x=0.4 i got 2 i have to simplify ln e^x+6 i got x+6 and given that log base a 5=0.8271 and log base a 20=1.5395 find log base a 4?1 solutions Answer 307492 by nerdybill(7003)   on 2011-05-08 10:23:10 (Show Source): You can put this solution on YOUR website!e^2x=0.4 i got 2 2x=ln(0.4) x=ln(0.4)/2 x = -0.45815 . i have to simplify ln e^x+6 i got x+6 you would be correct. . and given that log base a 5=0.8271 and log base a 20=1.5395 find log base a 4? can be rewritten as:
 Polynomials-and-rational-expressions/446368: factor the expression completely: x^4-9x^2 please help me as as u cannnnnnnnnnnnnnnnn waiting for replyyy1 solutions Answer 307386 by nerdybill(7003)   on 2011-05-07 20:27:35 (Show Source): You can put this solution on YOUR website!Think "difference of squares"... . x^4-9x^2 x^2(x^2-9) can be rewritten as: x^2(x^2-3^2) x^2(x-3)(x+3)
 expressions/446288: how do i simplify this (((-2[37-(-46-68)]1 solutions Answer 307332 by nerdybill(7003)   on 2011-05-07 14:40:34 (Show Source): You can put this solution on YOUR website!-2[37-(-46-68)] -2[37-(-114)] -2[37+114] -2[151] -302
 Square-cubic-other-roots/446291: f(x) = 2x² + x - 5 replace x with 3 Can someone tell me do we multiply 2 by 3 first or after square root? Thank you1 solutions Answer 307331 by nerdybill(7003)   on 2011-05-07 14:38:45 (Show Source): You can put this solution on YOUR website!f(x) = 2x² + x - 5 replace x with 3 Can someone tell me do we multiply 2 by 3 first or after square root? you really mean "square" as opposed to square root. but, to answer your question, you apply the "order of operations" (PEMDAS) exponents first... . f(x) = 2x² + x - 5 f(3) = 2*3² + 3 - 5 f(3) = 2*9 + 3 - 5 f(3) = 18 + 3 - 5 f(3) = 21 - 5 f(3) = 16
 Evaluation_Word_Problems/446204: how do you simplify (2^(-2) + 5^(-1))^(-2)1 solutions Answer 307329 by nerdybill(7003)   on 2011-05-07 14:35:48 (Show Source):
 Numeric_Fractions/446230: What is 441% of 612?1 solutions Answer 307300 by nerdybill(7003)   on 2011-05-07 11:13:56 (Show Source): You can put this solution on YOUR website!441% of 612 441/100 * 612 4.41 * 612 2698.92
 logarithm/445852: log x – log 4 = 11 solutions Answer 307038 by nerdybill(7003)   on 2011-05-06 01:28:15 (Show Source): You can put this solution on YOUR website!log x – log 4 = 1 log x/4 = 1 x/4 = 10^1 x/4 = 10 x = 40
 logarithm/445849: log x+ log 5=21 solutions Answer 307037 by nerdybill(7003)   on 2011-05-06 01:27:08 (Show Source): You can put this solution on YOUR website!log x+ log 5=2 log 5x =2 5x = 10^2 5x = 100 x = 20
 logarithm/445854: log (2x + 2) – log (x + 5) =01 solutions Answer 307036 by nerdybill(7003)   on 2011-05-06 01:26:03 (Show Source): You can put this solution on YOUR website!log (2x + 2) – log (x + 5) =0 log (2x + 2)/(x + 5) =0 (2x + 2)/(x + 5) =10^0 (2x + 2)/(x + 5) =1 (2x + 2)=(x + 5) x + 2 = 5 x = 3
 logarithm/445853: log x + log 5 = 51 solutions Answer 307035 by nerdybill(7003)   on 2011-05-06 01:24:01 (Show Source): You can put this solution on YOUR website!log x + log 5 = 5 log 5x = 5 5x = 10^5 x = 10^5/5 x = 20000
 Linear-equations/445782: Given two points through which a line passes, write the equation of each line in slope-intercept form. (4,0) and (2,-5)1 solutions Answer 306987 by nerdybill(7003)   on 2011-05-05 20:43:41 (Show Source): You can put this solution on YOUR website!first, find the slope between: (4,0) and (2,-5) m = (y2-y1)/(x2-x1) m = (-5-0)/(2-4) m = -5/(-2) m= 5/2 . use the slope and one point (4,0) plug it into "point-slope" form: y - y1 = m(x - x1) y - 0 = (5/2)(x - 4) y = (5/2)x - 10 (this is what they're looking for)
 Quadratic_Equations/445732: Pleas help me solve this equation: (((2x^2+5x+3=0)))1 solutions Answer 306984 by nerdybill(7003)   on 2011-05-05 20:40:18 (Show Source): You can put this solution on YOUR website!2x^2+5x+3=0 solve by factoring the left: (2x+3)(x+1) = 0 x = {-3/2,-1}
 Angles/445555: Find the complementary angle to 49 degrees1 solutions Answer 306920 by nerdybill(7003)   on 2011-05-05 14:48:16 (Show Source): You can put this solution on YOUR website!Find the complementary angle to 49 degrees: 90 - 49 = 41 degrees
 Probability-and-statistics/445562: Write a proportion to solve: A student types 120 words in 3 min and x words in 5 min. Find x. 1 solutions Answer 306918 by nerdybill(7003)   on 2011-05-05 14:47:17 (Show Source): You can put this solution on YOUR website!120 words in 3 min and x words in 5 mins: 120/3 = x/5 cross multiplying: 5(120) = 3x 5(120)/3 = x 5(40) = x 200 = x that's 200 words in 5 minutes
 Complex_Numbers/445518: i^7851 solutions Answer 306886 by nerdybill(7003)   on 2011-05-05 12:43:20 (Show Source): You can put this solution on YOUR website!It cycles withing these four possibilities: i^1 = i i^2 = -1 i^3 = -i i^4 = 1 . divide 785 by 4 to get: 784 with a remaider of 1 therefore: i^785 = i
 Probability-and-statistics/445502: The formula for the area of circle is A= pi.r^2 .(page 395# 28) Find the inverse of the funtion 1 solutions Answer 306868 by nerdybill(7003)   on 2011-05-05 12:04:28 (Show Source): You can put this solution on YOUR website!A= pi.r^2 this is equivalent to: f(r) = pi*r^2 y = pi*r^2 switch y's and r's: r = pi*y^2 solve for y: r = pi*y^2 r/pi = y^2 sqrt(r/pi) = y . therefore, the inverse is: sqrt(A/pi) so, if you knew the area (A), you can find the radius (r)
 Mixture_Word_Problems/445483: The function H described by H(x)=2.75x + 71.48 can be used to predict the height, in centimeters of a woman whose humerus(the bone from the elbow to the shoulder) is x cm long. Predict the height of a woman whose humerous is 33 cm long.1 solutions Answer 306864 by nerdybill(7003)   on 2011-05-05 11:58:55 (Show Source): You can put this solution on YOUR website!Given: H(x)=2.75x + 71.48 set x=33 and solve: H(33)=2.75(33) + 71.48 H(33)=90.75 + 71.48 H(33)= 162.23 cm
 Numeric_Fractions/444899: 6 - 3/6=? Thanks 1 solutions Answer 306602 by nerdybill(7003)   on 2011-05-04 11:34:52 (Show Source): You can put this solution on YOUR website!6 - 3/6 = 36/6 - 3/6 = (36 - 3)/6 = 33/6 = 11/2
 Miscellaneous_Word_Problems/444904: Please help me solve this equation: the measure of the supplement of an angle is 60 degrees less than twice the measure of the angle. Find the measures of both angles. (algebraic solution)1 solutions Answer 306601 by nerdybill(7003)   on 2011-05-04 11:33:39 (Show Source): You can put this solution on YOUR website!the sum of an integer squared and 4 times the integer is 77. Find the integers . Let x = the integers then x^2 + 4x = 77 x^2 + 4x - 77 = 0 (x+11)(x-7) = 0 x = {-11, 7}