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# Recent problems solved by 'nerdybill'

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 Polynomials-and-rational-expressions/340284: OK....need help been trying for the last hour.. still can't get it. Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. If an object is propelled upward from ground level with an initial velocity of 224 feet per second, its height h in feet t seconds later is given by the equation h = 224t - 16t2. After how many seconds does the object hit the ground? 1 solutions Answer 243807 by nerdybill(6951)   on 2010-09-08 00:36:32 (Show Source): You can put this solution on YOUR website!Given: h = 224t - 16t^2 where h is height in feet t is time in seconds . To determine when the object hit the ground, set h to zero (because zero is when the object is on the ground) and solve for t: h = 224t - 16t^2 0 = 224t - 16t^2 0 = 14t - t^2 factoring the right side: 0 = t(14 - t) setting each term on the right to zero we get: t = {0, 14} . t=0 is when the object just started its flight So, t = 14 seconds (solution)
 Equations/340022: the model M = -0.711+206.6 is used to determine the maximum heart rate of M of and individual who is age A solve for A according to this model what is the age of and individual whose maximum heart rate is 155 simpliy all answers1 solutions Answer 243680 by nerdybill(6951)   on 2010-09-07 18:03:21 (Show Source): You can put this solution on YOUR website!the model M = -0.711+206.6 is used to determine the maximum heart rate of M of and individual who is age A solve for A according to this model what is the age of and individual whose maximum heart rate is 155 . M = -0.711A + 206.6 Where M is "max heartrate" A is age . M - 206.6 = -0.711A (M - 206.6)/(-0.711) = A (206.6-M)/(0.711) = A . Plug in 155 for M: (206.6-155)/(0.711) = A (51.6)/(0.711) = A 72.6 years old = A
 Miscellaneous_Word_Problems/339928: A ball is thrown straight upward at an initial speed of 149 feet per second. h=-16⁢t2+149⁢t When does the ball reach the highest point?1 solutions Answer 243597 by nerdybill(6951)   on 2010-09-07 15:25:11 (Show Source): You can put this solution on YOUR website!Given: h = -16t^2 + 149t . The time (t) when it reaches the "ighest" point would be at the "axis of symmetry": t = -b/2a = -149/(2*(-16)) = -149/(-32) = 4.66 sec
 Triangles/339847: The area of triangle T is 625 square inches. If the length of the base b is half the length of the altitude drawn to that base, then what is the length of the altitude? 1 solutions Answer 243508 by nerdybill(6951)   on 2010-09-07 11:38:03 (Show Source): You can put this solution on YOUR website!The area of triangle T is 625 square inches. If the length of the base b is half the length of the altitude drawn to that base, then what is the length of the altitude? . Let x = altitude then x/2 = base . (1/2)base*height = area (1/2)(x/2)x = 625 (x/4)x = 625 x^2/4 = 626 x^2 = 2504 x = 50 inches
 Linear-systems/339851: Find three consecutive integers whose sum is -33.1 solutions Answer 243506 by nerdybill(6951)   on 2010-09-07 11:35:21 (Show Source): You can put this solution on YOUR website!Find three consecutive integers whose sum is -33. . Let x = 1st integer then x+1 = 2nd integer x+2 = 3rd integer . x + x+1 + x+2 = -33 3x + 3 = -33 3x = -36 x = -12 (first integer) x+1 = -11 (2nd integer) x+2 = -10 (3rd integer) . The three integers are: -12, -11 and -10
 Travel_Word_Problems/339834: an object is dropped from an initial height of x feet. the objects height at any time t. on seconds , is given by h=-16t^2+s. How long does it take for an object dropped from 300 feet to hit the ground ?1 solutions Answer 243500 by nerdybill(6951)   on 2010-09-07 11:09:41 (Show Source): You can put this solution on YOUR website!Given: h=-16t^2+s Set s to 300 and h to 0 . 0=-16t^2+300 16t^2 = 300 t^2 = 18.75 t = 4.33 seconds
 logarithm/339788: Express as a product. log9 y^41 solutions Answer 243478 by nerdybill(6951)   on 2010-09-07 10:10:40 (Show Source): You can put this solution on YOUR website!Express as a product. log9 y^4 . It would simply be: Express as a product. 4log9 y
 Miscellaneous_Word_Problems/339815: A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 546 pounds after processing, how many pounds did it weigh before processing? (A) 191 (B) 355 (C) 737 (D) 840 (E) 1560 Could pls kindly help me with the above problem. Thanks 1 solutions Answer 243461 by nerdybill(6951)   on 2010-09-07 09:46:59 (Show Source): You can put this solution on YOUR website!A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 546 pounds after processing, how many pounds did it weigh before processing? (A) 191 (B) 355 (C) 737 (D) 840 (E) 1560 . Let x = weight beofre processing then x - .35x = 546 x(1-.35) = 546 x(.65) = 546 x = 546/.65 x = 840 pounds
 Money_Word_Problems/339756: A businessman invested \$12000 in two ventures. In one he made a profit of 8% and in the other he lost 4%. His net profit for the year was \$120. How much did he invest in each venture. I KNOW THE ANSWER BY GUESSING, BUT I NEED AN EQUATION TO ACTUALLY SHOW HOW I DID IT. 1 solutions Answer 243389 by nerdybill(6951)   on 2010-09-07 00:25:37 (Show Source): You can put this solution on YOUR website!A businessman invested \$12000 in two ventures. In one he made a profit of 8% and in the other he lost 4%. His net profit for the year was \$120. How much did he invest in each venture. . Let x = amount invested at 8% then 12000-x = amount invested at 4% . .08x - .04(12000-x) = 120 .08x - 480+.04x = 120 .12x - 480 = 120 .12x = 600 x = \$5000 (amount invested at 8%) . amount invested at 4%: 12000-x = 12000-5000 = \$7000

Thank you very much.
1 solutions

Answer 243253 by nerdybill(6951)   on 2010-09-06 12:16:10 (Show Source):
You can put this solution on YOUR website!

x={4, -4.5}
The negative solution is extraneous, throw it out leaving:
x = 4
.
 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=289 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, -4.5. Here's your graph:

 Quadratic_Equations/339349: x^3+x^2-20x=0 (this will come under cubic equation)"thank you"1 solutions Answer 243208 by nerdybill(6951)   on 2010-09-06 08:35:55 (Show Source): You can put this solution on YOUR website!x^3+x^2-20x=0 Start by factoring out what is common among all three terms: x(x^2+x-20) = 0 Factor the expression inside the parenthesis: x(x+5)(x-4) = 0 . Set each term to zero, giving you: x = (-5, 0, 4}
 Length-and-distance/339363: A gardener marks out a new section of lawn that is supposed to be a rectangle with sides of length 15m and 10m. To check he has marked out a rectangle he measures the length of the diagonal. How long should this be?1 solutions Answer 243206 by nerdybill(6951)   on 2010-09-06 08:31:53 (Show Source): You can put this solution on YOUR website!Apply the Pythagorean theorem: . Let d = length of diagonal then d^2 = 15^2 + 10^2 d^2 = 225 + 100 d^2 = 325 d = 18.028 m
 Quadratic_Equations/339380: If 9x^2 - y^2 = 0 then what is the positive value of the x/y ?1 solutions Answer 243204 by nerdybill(6951)   on 2010-09-06 08:28:33 (Show Source): You can put this solution on YOUR website!If 9x^2 - y^2 = 0 then what is the positive value of the x/y ? . Notice, I can rewrite: 9x^2 - y^2 = 0 as (3x)^2 - y^2 = 0 . This is a "difference of squares", so I can factor as: (3x-y)(3x+y) = 0 . The positive value of x/y is then: 3x-y = 0 3x = y x = y/3 x/y = 1/3 (this is your answer)
 Geometry_Word_Problems/339372: a glass factory has an order for 1000 glass paper weighs; each is to be form of a cube. if this order requires 8000 cubic inches of glass, what is the surface area of one of the paper weighs? 1 solutions Answer 243203 by nerdybill(6951)   on 2010-09-06 08:25:28 (Show Source): You can put this solution on YOUR website! a glass factory has an order for 1000 glass paper weighs; each is to be form of a cube. if this order requires 8000 cubic inches of glass, what is the surface area of one of the paper weighs? . Let x = length of one side of the cube then x^3 is the volume of one cube . 1000x^3 = 8000 x^3 = 8 x = 2 inches . Surface of one side of cube: 2^2 = 4 square inches . Since there are 6 sides to a cube, the surface area is: 6 * 4 = 24 square inches
 Systems-of-equations/339262: please solve using the principle of zero products. 2x^2+x=42+9x1 solutions Answer 243161 by nerdybill(6951)   on 2010-09-05 21:05:49 (Show Source): You can put this solution on YOUR website!2x^2+x=42+9x moving all the terms to the left: 2x^2-8x=42 2x^2-8x-42=0 dividing both sides by 2: x^2-4x-21=0 factoring: (x-7)(x+3) = 0 . x = {-3, 7}
 Rate-of-work-word-problems/339147: if anna can paint a house in 4 hours and joe can paint a house in 6 hours. how long will it take them to do it together?1 solutions Answer 243089 by nerdybill(6951)   on 2010-09-05 16:22:30 (Show Source): You can put this solution on YOUR website! if anna can paint a house in 4 hours and joe can paint a house in 6 hours. how long will it take them to do it together? . Let x = number of hours working together then x(1/4 + 1/6) = 1 multiplying both sides by 24: x(6 + 4) = 24 10x = 24 x = 2.4 hours or x = 2 hours and 24 minutes
 Percentage-and-ratio-word-problems/339157: It takes my brother 15 min to clean one window. It takes me 20 minutes to clean one window. How long will it take us to clean 12 windows.1 solutions Answer 243088 by nerdybill(6951)   on 2010-09-05 16:19:38 (Show Source): You can put this solution on YOUR website! It takes my brother 15 min to clean one window. It takes me 20 minutes to clean one window. How long will it take us to clean 12 windows. . Let x = minutes to clean 12 windows together the x(1/15 + 1/20) = 12 multiplying both sides by 300: x(20 + 15) = 3600 35x = 3600 x = 3600/35 x = 102.86 minutes
 Polynomials-and-rational-expressions/339137: Lisa can shovel snow from her driveway in 35 minutes. Tom can do the same job in 55 minutes. How long would it take Lisa and Tom to shovel the driveway if they worked together? 1 solutions Answer 243077 by nerdybill(6951)   on 2010-09-05 15:20:54 (Show Source): You can put this solution on YOUR website!Lisa can shovel snow from her driveway in 35 minutes. Tom can do the same job in 55 minutes. How long would it take Lisa and Tom to shovel the driveway if they worked together? . Let x = minutes if they worked together then x(1/35 + 1/55) = 1 Multiplying both sides by 35*55: x(55 + 35) = 35*55 x(90) = 35*55 x = 1925/90 x = 21.39 minutes
Quadratic_Equations/338999: I've heard that tossing a coin into a fountain will bring me good luck, so I throw a silver dollar up with a velocity of 5m/sec. and it falls into the fountain 1.3 meters below my hand. How long is the coin in the air?
In this question i just really dont understand how to do quadratic equations when you dont have the acceleration unless its -9.8m/s squared, but really not sure.
1 solutions

Answer 243041 by nerdybill(6951)   on 2010-09-05 09:51:04 (Show Source):
You can put this solution on YOUR website!
I've heard that tossing a coin into a fountain will bring me good luck, so I throw a silver dollar up with a velocity of 5m/sec. and it falls into the fountain 1.3 meters below my hand. How long is the coin in the air?
In this question i just really dont understand how to do quadratic equations when you dont have the acceleration unless its -9.8m/s squared, but really not sure.
.
.
Applying the equation of motion:
h(t) = (1/2)gt + vt + vo
where
h(t) is height
g is gravity
v is initial velocity
t is time
vo is the initial height
.
h(t) = (1/2)(-9.8)t + 5t + 1.3
h(t) = -4.6t + 5t + 1.3
.
set h(t) to zero and solve for t:
0 = -4.6t + 5t + 1.3
t = {-0.217, 1.304}
we can throw out the negative solution leaving:
t = 1.3 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=48.92 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.216769932610683, 1.30372645434981. Here's your graph:

 Polynomials-and-rational-expressions/338984: (6x^2-31x+5)/(x-5)1 solutions Answer 242993 by nerdybill(6951)   on 2010-09-04 21:40:55 (Show Source): You can put this solution on YOUR website!(6x^2-31x+5)/(x-5) rewrite numerator as: (6x^2-30x-x+5)/(x-5) group terms: [(6x^2-30x)-(x-5)]/(x-5) factor: [6x(x-5)-(x-5)]/(x-5) factor: [(x-5)(6x-1)]/(x-5) canceling like-terms: 6x-11
 Angles/338882: Find the degree measure of an angle of 4.23 radians. A. 62º B. 242º C. 118º D. 28º1 solutions Answer 242908 by nerdybill(6951)   on 2010-09-04 15:10:58 (Show Source): You can put this solution on YOUR website!Find the degree measure of an angle of 4.23 radians. A. 62º B. 242º C. 118º D. 28º . since (pi) radians = 180 degrees . 180/(pi) * 4.23 180/3.14 * 4.23 242.48 degrees . Closest answer B
 Surface-area/338865: what is the area of a triangle if the base is 16 m and the height is 3m? 1 solutions Answer 242906 by nerdybill(6951)   on 2010-09-04 15:04:56 (Show Source): You can put this solution on YOUR website! what is the area of a triangle if the base is 16 m and the height is 3m? . area of any triangle is (1/2)bh where b is base h is height . area = (1/2)bh area = (1/2)(16)(3) area = (8)(3) area = 24 square meters
 Rate-of-work-word-problems/338897: An oil tanker can be emptied by the main pump in 5hours. An auxillary pump can empty the tanker in 9 hours. If the main pump is started at 5PM, when should the auxillary pump be started so the tanker is emptied by 9PM? How do I determine the "time"? I get to 1/9t=1/5 and not sure what to do. Thank you.1 solutions Answer 242905 by nerdybill(6951)   on 2010-09-04 15:02:33 (Show Source): You can put this solution on YOUR website!An oil tanker can be emptied by the main pump in 5hours. An auxillary pump can empty the tanker in 9 hours. If the main pump is started at 5PM, when should the auxillary pump be started so the tanker is emptied by 9PM? . From 5pm to 9pm is 4 hours... . Let x = number of hours to run aux pump then 4(1/5) + x(1/9) = 1 4/5 + x/9 = 1 multiplying both sides by 45: 36 + 5x = 45 5x = 9 x = 9/5 hours . 9/5 hour is the same as 9/5 * 60 = 108 minutes 1 hour and 48 minutes (time needed to run aux pump) . Time to start aux pump: 9 pm minus 1 hour and 48 minutes: 7:12 PM
 Rectangles/338823: The length of rectangle is 7 m less than twice the width. If the length is decreased by 1m and the width by 4 m, the perimeter will be 66. Find the dimensions of the original rectangle. Thank you so much for helping Alena1 solutions Answer 242883 by nerdybill(6951)   on 2010-09-04 11:31:05 (Show Source): You can put this solution on YOUR website!The length of rectangle is 7 m less than twice the width. If the length is decreased by 1m and the width by 4 m, the perimeter will be 66. Find the dimensions of the original rectangle. . Let w = width then from: "length of rectangle is 7 m less than twice the width" 2w-7 = length . Length decreased by 1 m: 2w-7-1 = 2w-8 . Width decreased by 4 m: w-4 . 2(width + length) = perimeter 2(w-4 + 2w-8) = 66 dividing both sides by 2: w-4 + 2w-8 = 33 3w-12 = 33 3w = 45 w = 15 meters (width) . length: 2w-7 = 2(15)-7 = 30-7 = 23 meters (length) . dimensions: 15 by 23 meters
 Exponents-negative-and-fractional/338848: how do you solve for (-2/3) raised to the power of -21 solutions Answer 242881 by nerdybill(6951)   on 2010-09-04 11:21:35 (Show Source): You can put this solution on YOUR website!how do you solve for (-2/3) raised to the power of -2 .
 Angles/338825: Two angles are supplementary. One angle has a measure that is five less than four times the other . What is the measure of the larger angle? 1 solutions Answer 242880 by nerdybill(6951)   on 2010-09-04 11:16:58 (Show Source): You can put this solution on YOUR website! Two angles are supplementary. One angle has a measure that is five less than four times the other . What is the measure of the larger angle? . When two angles are supplementary, the sum of the two angles is 180 degrees. . Let x = one angle then from: "One angle has a measure that is five less than four times the other" 4x-5 = second angle . x + 4x-5 = 180 5x-5 = 180 x-1 = 36 x = 37 deg . second angle: 4x-5 = 4(37)-5 = 148-5= 143 degrees (larger angle)
 Equations/338840: Hi, Im Beckah. Im having issues with my math homework. Im in geometry, but we have an algebra problem in our homework. The question is " Which equation represents the following problem? Fifteen minus three times a number(n) equels negitive twenty-two. Find the number." So, I found the equation - it's 15-3n=-22 , right? So, now Im trying to find the number, but everytime I solve for it I get the wrong number, I know this becuase I go back and check, but I don't get -22. Do you think you could help me out? Thank you. :)1 solutions Answer 242879 by nerdybill(6951)   on 2010-09-04 11:05:47 (Show Source): You can put this solution on YOUR website!Starting with: 15-3n=-22 we subtract 15 from both sides: 15-3n-15 = -22-15 -3n = -37 divide both sides by -3: n = 37/3 (this is your answer) . To check, we substitute back in: 15-3n=-22 15-3(37/3)=-22 15-37=-22 -22 = -22
 Graphs/338626: Write the equation of the line that passes through (1, 3) and (4, 4) in standard form. Please and thank you Sincerely Alisha1 solutions Answer 242758 by nerdybill(6951)   on 2010-09-03 16:22:23 (Show Source): You can put this solution on YOUR website!Write the equation of the line that passes through (1, 3) and (4, 4) in standard form. . Standard form of a line: Ax + By = C where A is a positive integer, and B, and C are integers . First, determine slope between the two points using: m = (y2-y1)/(x2-x1) m = (4-3)/(4-1) m = 1/3 (slope) . Next, use one of the two points (1,3) and the slope (1/3) and plug it into the "point-slope" form: y-y1 = m(x-x1) y-3 = (1/3)(x-1) multiplying both sides by 3: 3y-9 = x-1 subtracting x from both sides: -x + 3y-9 = -1 adding 9 to both sides: -x + 3y = 8 (this is what they're looking for)
 Sequences-and-series/338686: What is the 30th term in the sequence 14,19,24,29? What is the 69th term in the sequence 13,19,25,31?1 solutions Answer 242755 by nerdybill(6951)   on 2010-09-03 16:15:03 (Show Source): You can put this solution on YOUR website!an = a1 + (n – 1)d additional info on arithmetic sequence: http://www.mathwords.com/a/arithmetic_sequence.htm . What is the 30th term in the sequence 14,19,24,29? arithmetic sequence: a1 is 14 n is 30 d is 5 . 30th term is: a1 + (n – 1)d 14 + (30 - 1)(5) 14 + (29)(5) 14 + (145) 159 . What is the 69th term in the sequence 13,19,25,31? a1 is 13 n is 69 d is 6 . 69th term is: a1 + (n – 1)d 13 + (69 – 1)(6) 13 + (68)(6) 13 + 408 421
 Numbers_Word_Problems/338654: A barrel contains 30 gallons of 40% antifreeze. How many gallons of an 80% antifreeze solution should be added to make the barrel contain 50% antifreeze?1 solutions Answer 242753 by nerdybill(6951)   on 2010-09-03 16:07:13 (Show Source): You can put this solution on YOUR website!A barrel contains 30 gallons of 40% antifreeze. How many gallons of an 80% antifreeze solution should be added to make the barrel contain 50% antifreeze? . Let x = gallons of 80% antifreeze added then .40(30) + .80x = .50(30+x) 12 + .80x = 15 + .50x 12 + .30x = 15 .30x = 3 x = 10 gallons