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# Recent problems solved by 'nerdybill'

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 Linear-equations/538647: I am trying to help my son but I cant even understand, Does the system of equations have no solution, one solution, or infinitely many solutions? y = 5x – 4 y = 5x – 5 1 solutions Answer 353219 by nerdybill(7008)   on 2011-11-29 17:54:31 (Show Source): You can put this solution on YOUR website!Does the system of equations have no solution, one solution, or infinitely many solutions? y = 5x – 4 y = 5x – 5 . Since slope (5) is the same for both but the y-intercepts are diffferent we conclude that there is "no solution" . See the site below, it describes the three cases: http://www.mathwarehouse.com/algebra/linear_equation/systems-of-equation/index.php
 Linear-equations/538398: find the x and y intercepts of: y = -2x - 61 solutions Answer 353163 by nerdybill(7008)   on 2011-11-29 09:59:44 (Show Source): You can put this solution on YOUR website!find the x and y intercepts of: y = -2x - 6 . to find the x-intercepts, set y=0 solve for x: y = -2x - 6 0 = -2x - 6 6 = -2x -3 = x so, x-intercept is at (-3,0) . to find the y-intercepts, set x=0 solve for y: y = -2x - 6 y = -2(0) - 6 y = -6 so, y-intercept is at (0,-6)
 Percentage-and-ratio-word-problems/537209: From the top of the building in the illustration, a ball is thrown straight up with an initial velocity of 40 feet per second. The equation s = -16t2 + 40t + 48 gives the height s of the ball t seconds after it is thrown. Find the maximum height reached by the ball and the time it takes for the ball to hit the ground. (Round your answer to one decimal place.) Thank you in advance!1 solutions Answer 352762 by nerdybill(7008)   on 2011-11-27 14:59:05 (Show Source): You can put this solution on YOUR website!From the top of the building in the illustration, a ball is thrown straight up with an initial velocity of 40 feet per second. The equation s = -16t2 + 40t + 48 gives the height s of the ball t seconds after it is thrown. Find the maximum height reached by the ball and the time it takes for the ball to hit the ground. (Round your answer to one decimal place.) s = -16t2 + 40t + 48 The "vertex" defines the max height. It reaches this height when t = -b/(2a) t = -40/(2(-16)) t = -40/(-32) t = 1.25 seconds . Max height: s = -16(1.25)^2 + 40(1.25) + 48 s = 73.0 feet
 Percentage-and-ratio-word-problems/537211: The height (in feet) of the water level in a reservoir over a 1 year period is modeled by the function H(t) = 2.4(t - 10)2 + 15, where t = 1 represents January, t = 2 represents February, and so on. How low did the water level get that year, and when did it reach the low mark? Thank you in advance!1 solutions Answer 352761 by nerdybill(7008)   on 2011-11-27 14:54:26 (Show Source): You can put this solution on YOUR website!The height (in feet) of the water level in a reservoir over a 1 year period is modeled by the function H(t) = 2.4(t - 10)2 + 15, where t = 1 represents January, t = 2 represents February, and so on. How low did the water level get that year, and when did it reach the low mark? The vertex of H(t) = 2.4(t - 10)2 + 15 gives you the low point: equation given is in the "vertex" form: y= a(x-h)^2+k vertex is at (10,15) when did it reach the low mark? t = 10 (October) How low did the water level get: h(t) = 15 feet
 Linear-equations/537074: How do you change 4x-2y=10 into slope-intercept form? I have no idea what to do. Thanks for your time.1 solutions Answer 352718 by nerdybill(7008)   on 2011-11-27 10:57:15 (Show Source): You can put this solution on YOUR website!How do you change 4x-2y=10 into slope-intercept form? . The "slope-intercept" form of a line is: y = mx + b all you need to do, is to rearrange the terms of the given equation to make it look like the form above... You started with: 4x-2y=10 begin by subtracting 4x from both sides: -4x+4x-2y = -4x+10 -2y = -4x+10 multiply both sides by -1: 2y = 4x-10 divide both sides by 2: y = 2x-5 (this is what they're looking for)
 Length-and-distance/537067: A 18-foot ladder leans against a wall at a 74 degree angle of elevation. Find the distance from the ladder's base to the wall.1 solutions Answer 352713 by nerdybill(7008)   on 2011-11-27 10:05:15 (Show Source): You can put this solution on YOUR website!A 18-foot ladder leans against a wall at a 74 degree angle of elevation. Find the distance from the ladder's base to the wall. . Let x = distance (base to wall) . Applying trigonometry: cos x = adjacent/hypotenuse cos(74) = x/18 18*cos(74) = x 4.96 feet = x or approximately: 5 feet = x
 Travel_Word_Problems/537068: Janet can shovel snow in her driveway in 65 minutes, Tom can do the same job in 45 mins. How long will it take if they work together?1 solutions Answer 352711 by nerdybill(7008)   on 2011-11-27 10:01:57 (Show Source): You can put this solution on YOUR website!Janet can shovel snow in her driveway in 65 minutes, Tom can do the same job in 45 mins. How long will it take if they work together? . Let x = time (mins) it takes for both then x(1/65 + 1/45) = 1 multiply both sides by (65)(45): x(45 + 65) = (65)(45) x(110) = 2925 x = 26.6 minutes
 Linear-equations/536741: Good Saturday morning Tutors. I need help to write the slope-intercept equation for the line that passes through (-5,10) and (-4,3). 1 solutions Answer 352566 by nerdybill(7008)   on 2011-11-26 11:04:01 (Show Source): You can put this solution on YOUR website!write the slope-intercept equation for the line that passes through (-5,10) and (-4,3) . Begin by finding the slope between (-5,10) and (-4,3) m = (y2-y1)/(x2-x1) m = (3-10)/(-4-(-5)) m = (-7)/(-4+5) m = (-7)/(1) m = -7 . Use the slope (-7) and either one of the provided points (-4,3), plug into the "point-slope" form: y - y1 = m(x - x1) y - 3 = -7(x - (-4)) y - 3 = -7(x + 4) y - 3 = -7x - 28 y = -7x - 25 (this is what they're looking for)
 Number-Line/536725: use all four integers -6, -4, 3, and 8, along with any operation signs to complete the equation. _ _ _ _ = -21 solutions Answer 352565 by nerdybill(7008)   on 2011-11-26 10:49:18 (Show Source): You can put this solution on YOUR website!use all four integers -6, -4, 3, and 8, along with any operation signs to complete the equation. _ _ _ _ = -2 . ((-4) - (-6)) * 3 - 8 = -2
 Geometry_Word_Problems/536709: please help me solve this, find the area of a rectangle whose side is 5 feet and whose diagonal is , thankyou1 solutions Answer 352546 by nerdybill(7008)   on 2011-11-26 08:33:55 (Show Source): You can put this solution on YOUR website!find the area of a rectangle whose side is 5 feet and whose diagonal is . Apply Pythagorean theorem to find the length of the other side: Let x = length of other side of rectangle then feet . Area then is: 5*7 = 35 square feet
 Equations/536721: Remove parenthesis and collect like terms 45y-(12y+50)=1 solutions Answer 352545 by nerdybill(7008)   on 2011-11-26 08:29:26 (Show Source): You can put this solution on YOUR website!Starting with: 45y-(12y+50) Distribute the "minus" sign to each term inside the parenthesis: 45y+(-12y-50) remove parenthesis: 45y-12y-50 (45-12)y-50 (33)y-50 33y-50
 Quadratic_Equations/536074: How can i complete the square with : 2k^2 + 4k-10=0 my answer was 5, it's obviously wrong... help plz! thank you1 solutions Answer 352115 by nerdybill(7008)   on 2011-11-23 10:37:28 (Show Source): You can put this solution on YOUR website!2k^2 + 4k-10=0 divide through by 2: k^2 + 2k-5=0 k^2 + 2k = 5 take 1/2 'b', square it and add to both sides: k^2 + 2k + 1 = 5 + 1 k^2 + 2k + 1 = 6 (k+1)(k+1) = 6 (k+1)^2 = 6 k+1 = sqrt(6) k = +-sqrt(6) - 1 k = {-sqrt(6)-1, sqrt(6)-1}
 Quadratic_Equations/536073: how can i complete the square with: x^2-10x=11 my answer, (-10x/2)^2 =11 was wrong. 1 solutions Answer 352114 by nerdybill(7008)   on 2011-11-23 10:34:57 (Show Source): You can put this solution on YOUR website!x^2-10x=11 take 1/2 'b', square it and add to both sides: x^2-10x+25=11+25 x^2-10x+25=36 (x-5)(x-5) = 36 (x-5)^2 = 36 x-5 = +-6 x = +-6 + 5 x = {-1, 11}
 Linear-equations/536042: write equation of a perpendicular line in slope intercept form if y=2/5x-4 (-1,2)1 solutions Answer 352109 by nerdybill(7008)   on 2011-11-23 09:41:14 (Show Source): You can put this solution on YOUR website!write equation of a perpendicular line in slope intercept form if y=2/5x-4 (-1,2) . Slope of: y=2/5x-4 is 2/5 . A line perpendicular must have a slope that is the negative reciprocal: (2/5)m = -1 m = -5/2 (this is the slope of the new line) . Plug slope (-5/2) and (1,2) into "point-slope" form: y - y1 = m(x - x1) y - 2 = (-5/2)(x - 1) y - 2 = (-5/2)x + 5/2 y = (-5/2)x + 5/2 + 2 y = (-5/2)x + 5/2 + 4/2 y = (-5/2)x + 9/2 (this is what they're looking for)
 logarithm/536046: Solve: log(36,10x-11)+log(36,X)=1/2 i get to this point here: log(36,10x^2-11x)=1/2 but then im lost after thanks Angela1 solutions Answer 352107 by nerdybill(7008)   on 2011-11-23 09:26:22 (Show Source): You can put this solution on YOUR website!Solve: log(36,10x-11)+log(36,X)=1/2 . i get to this point here: log(36,10x^2-11x)=1/2 (so far, so good) . 36^log(36,10x^2-11x) = 36^(1/2) 10x^2-11x = 36^(1/2) 10x^2-11x = 6 . 10x^2-11x = 6 10x^2-11x - 6= 0 10x^2 -15x+4x - 6= 0 (10x^2-15x) + (4x-6) = 0 5x(2x-3) + 2(2x-3) = 0 (2x-3)(5x+2) = 0 x = {3/2, -2/5} throw out the negative solution (extraneous) leaving: x = 3/2
 Rate-of-work-word-problems/535304: an older machine can do a job in 104 minuets, it takes only 40 minuets when a newer machine works simultaneously. how long would it take the newer machine to do the job working alone?1 solutions Answer 351846 by nerdybill(7008)   on 2011-11-21 18:15:12 (Show Source): You can put this solution on YOUR website!an older machine can do a job in 104 minuets, it takes only 40 minuets when a newer machine works simultaneously. how long would it take the newer machine to do the job working alone? . Let x = time (minutes) it takes for newer machine alone then 40(1/104 + 1/x) = 1 multiplyb both sides 104x: 40(x + 104) = 104x 40x + 4160 = 104x 4160 = 64x 65 minutes = x
 Linear-equations/534869: Parallel, perpendicular pr neither? Y=-4x-91 Y=-121-5x 1 solutions Answer 351666 by nerdybill(7008)   on 2011-11-20 22:04:57 (Show Source): You can put this solution on YOUR website!Parallel, perpendicular pr neither? Y=-4x-91 Y=-121-5x . Examine the slope of each line: -4 and -5 since they're not the same, they're not parallel since they don't multiply to give you -1 they're not perpendicular therefore answer: Neither
 Triangles/534861: One leg of right triangle is 9 inches shorter than the other leg. The hypotenuse is 45 inches. What is the length of all sides?1 solutions Answer 351664 by nerdybill(7008)   on 2011-11-20 22:02:22 (Show Source): You can put this solution on YOUR website!One leg of right triangle is 9 inches shorter than the other leg. The hypotenuse is 45 inches. What is the length of all sides? . Let x = length of "other leg" then x-9 = 2nd leg . applying Pythagorean theorem: x^2 + (x-9)^2 = 45^2 x^2 + (x-9)(x-9) = 45^2 x^2 + x^2-18x+81 = 2025 2x^2-18x+81 = 2025 2x^2-18x-1944 = 0 x^2-9x-972 = 0 (X+27)(x-36) = 0 x = {-27, 36} throw out the negative answer leaving: x = 36 inches . Answer: the three sides are: 36, 27, and 45 inches
 Quadratic_Equations/534558: twice the price of a bike increased by 26 is 57. what is the price of the bike?1 solutions Answer 351584 by nerdybill(7008)   on 2011-11-20 11:33:09 (Show Source): You can put this solution on YOUR website!twice the price of a bike increased by 26 is 57. what is the price of the bike? . Let x = price of bike then 2p + 26 = 57 2p = 31 p = \$15.50
 Percentage-and-ratio-word-problems/534200: The cost to produce one DVD player is \$85 plus a one-time fixed cost of \$150,000. The revenue received from selling one DVD player is \$225. (a) Write a formula that gives the cost C of producing x DVD players 1 solutions Answer 351385 by nerdybill(7008)   on 2011-11-19 11:09:44 (Show Source): You can put this solution on YOUR website!The cost to produce one DVD player is \$85 plus a one-time fixed cost of \$150,000. The revenue received from selling one DVD player is \$225. (a) Write a formula that gives the cost C of producing x DVD players . Let x = number of DVD players then C = 85x + 150000 where "C" is cost
 Evaluation_Word_Problems/534070: Billy drops an egg off the roof of a buliding 80 ft above ground. Using the model . How long did it take for the egg to hit the ground? using the equation h=-16t^2+h 1 solutions Answer 351265 by nerdybill(7008)   on 2011-11-18 21:58:11 (Show Source): You can put this solution on YOUR website!Billy drops an egg off the roof of a buliding 80 ft above ground. Using the model . How long did it take for the egg to hit the ground? using the equation h(t)=-16t^2+h . Set h to 80 (represents initial height) and set h(t) to zero (represents ground level) solve for t: h(t)=-16t^2+h 0=-16t^2+80 16t^2 = 80 t^2 = 5 t = sqrt(5) t = 2.24 seconds
 Square-cubic-other-roots/533898: what is root 90 over root 10 simplified? 1 solutions Answer 351193 by nerdybill(7008)   on 2011-11-18 11:46:51 (Show Source): You can put this solution on YOUR website!what is root 90 over root 10 simplified? .
 Rational-functions/533853: Find the x and y intercept for 5y-x=10 I need help1 solutions Answer 351180 by nerdybill(7008)   on 2011-11-18 10:14:50 (Show Source): You can put this solution on YOUR website!Find the x and y intercept for 5y-x=10 . Rearrange the given equation into the "point-slope" form: y = mx + b where m is the slope b is the y-intercept at (0,b) . 5y-x=10 5y=x+10 y = (1/5)x + 2 From inspection, then we have slope is 1/5 y-intercept is at (0,2)
 Linear-systems/533861: Solve the system of equations using substitution. y = 4x + 10 y = 3x + 7 Please Explain how you go the answer! Thank You!!1 solutions Answer 351178 by nerdybill(7008)   on 2011-11-18 10:12:42 (Show Source): You can put this solution on YOUR website!y = 4x + 10 (equation 1) y = 3x + 7 (equation 2) . Plug definition of y from equation 2 into equation 1 and solve for x: 3x + 7 = 4x + 10 7 = x + 10 -3 = x . Plug definition of x above into equation 2 to find y: y = 3x + 7 y = 3(-3) + 7 y = -9 + 7 y = -2 . Answer: x = -3 y = -2
 percentage/533856: Jane's weekly salary of \$320 increased to \$360. Find the percent increase1 solutions Answer 351177 by nerdybill(7008)   on 2011-11-18 10:09:20 (Show Source): You can put this solution on YOUR website!Jane's weekly salary of \$320 increased to \$360. Find the percent increase . (360-320)/320 * 100 (40)/320 * 100 .125 * 100 12.5%
 Linear-equations/532886: i forgot how to do slope intercept form because point slope confused me this week. My question is how do you write an equation in slope intercept with an equation like (3,1); slope=21 solutions Answer 350921 by nerdybill(7008)   on 2011-11-16 18:05:34 (Show Source): You can put this solution on YOUR website!Plug the given info: (3,1); slope=2 . into the "point-slope" form of y - y1 = m(x - x1) y - 1 = 2(x - 3) y - 1 = 2x - 6 y = 2x - 5 (this is what they're looking for)
 Travel_Word_Problems/531929: If my steps are 2 feet a part how many steps would I take to make a mile?1 solutions Answer 350636 by nerdybill(7008)   on 2011-11-15 10:36:14 (Show Source): You can put this solution on YOUR website!If my steps are 2 feet a part how many steps would I take to make a mile? since 5280 feet per mile 1 mile * 5280 feet/mile * 1/2 step/feet 5280/2 2640 steps
 Rate-of-work-word-problems/531348: A pipe can fill a tank in 30minutes and another pipe can make empty the tank in 45 minutes. How much time it takes to empty the tank if both are working together. 1 solutions Answer 350423 by nerdybill(7008)   on 2011-11-14 13:46:52 (Show Source): You can put this solution on YOUR website!A pipe can fill a tank in 30minutes and another pipe can make empty the tank in 45 minutes. How much time it takes to empty the tank if both are working together. assuming the tank was completely filled at the start then: Let x = time (minutes) to empty tank then x(1/30 - 1/45) = 1 multiplying both sides by 90: x(3 - 2) = 90 x(1) = 90 x = 90 minutes
 Inverses/530998: 1/x + 1/y = 5, can you solve for x without ending up with an xy 1 solutions Answer 350288 by nerdybill(7008)   on 2011-11-13 19:06:11 (Show Source): You can put this solution on YOUR website!Not sure what you mean but here's how to solve for x: 1/x + 1/y = 5 multiply both sides by xy: (xy)(1/x + 1/y) = 5xy distribute on the left: y + x = 5xy y = 5xy - x factor the right: y = x(5y - 1) y/(5y-1) = x
 Linear_Equations_And_Systems_Word_Problems/530973: the average american uses 100 gallons of water each day. a.write an equation that gives the gallons of water that a person uses the t days. b.graph the equation for t greater than or equal to 0. c.how many days does it take for the average american to uses 5000 gallons of water?1 solutions Answer 350284 by nerdybill(7008)   on 2011-11-13 18:58:06 (Show Source): You can put this solution on YOUR website!the average american uses 100 gallons of water each day. a.write an equation that gives the gallons of water that a person uses the t days. f(t) = 100t b.graph the equation for t greater than or equal to 0. you do this part c.how many days does it take for the average american to uses 5000 gallons of water? set f(t) to 5000 and solve for t: f(t) = 100t 5000 = 100t 50 days = t
 Angles/530983: The base angles of an isosceles triangle are congruent. If the measure of each of the base angles is twice the measure of the third angle, find the measure of all three angles.1 solutions Answer 350282 by nerdybill(7008)   on 2011-11-13 18:51:45 (Show Source): You can put this solution on YOUR website! The base angles of an isosceles triangle are congruent. If the measure of each of the base angles is twice the measure of the third angle, find the measure of all three angles. Let x = measure of third angle then 2x = measure of base angle . 2x + 2x + x = 180 5x = 180 x = 36 degrees (third angle) . base angle: 2x = 2(36) = 72 degrees . the three angles are: 72, 36 and 72 degrees