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# Recent problems solved by 'nerdybill'

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 Angles/507602: 1. The measure of the supplement of an angle is 60 less than three times the measure of the complement of the angle. Find the measure of the angle.1 solutions Answer 340605 by nerdybill(6958)   on 2011-10-01 16:45:15 (Show Source): You can put this solution on YOUR website!The measure of the supplement of an angle is 60 less than three times the measure of the complement of the angle. Find the measure of the angle. . Let x = measure of angle then 90-x = complement of angle 180-x = supplement of angle . 180-x = 3(90-x) - 60 180-x = 270-3x - 60 180-x = 210-3x 180+2x = 210 2x = 30 x = 15 degrees
 Exponential-and-logarithmic-functions/507547: SOLVE Logbase5(1/25)=x 1 solutions Answer 340528 by nerdybill(6958)   on 2011-10-01 13:31:29 (Show Source): You can put this solution on YOUR website!Logbase5(1/25)=x Logbase5(1/5^2)=x Logbase5(5^(-2)/1)=x Logbase5(5^(-2))=x -2 = x
 Exponential-and-logarithmic-functions/507520: solve log(3x+4)=2log(x) 1 solutions Answer 340512 by nerdybill(6958)   on 2011-10-01 11:26:59 (Show Source): You can put this solution on YOUR website!log(3x+4)=2log(x) log(3x+4)=log(x^2) 3x+4 = x^2 0 = x^2 - 3x - 4 0 = (x-4)(x+1) x = {4, -1} we can throw out the -1 solution (extraneous) leaving: x = 4
 Percentage-and-ratio-word-problems/507505: I am trying to help my nephew with a word problem and am having trouble coming up with the equation. Could you please help me? Thank you. If an entire job can be done in 5 hours and 20 minutes how much of the job can be done in one hour. The equation is supposed to be in fractions. Thank you.1 solutions Answer 340498 by nerdybill(6958)   on 2011-10-01 09:53:51 (Show Source): You can put this solution on YOUR website!If an entire job can be done in 5 hours and 20 minutes how much of the job can be done in one hour. The equation is supposed to be in fractions. . 5 hours and 20 minutes is the same as: 5 + 20/60 5 + 1/3 15/3 + 1/3 16/3 hours . your equation is: "time" * "rate" "time" is one hour "rate" is 1 job per 16/3 hours . 1(1/(16/3)) 1(3/16) 3/16 of the entire job can be done in an hour
 Miscellaneous_Word_Problems/507432: a baseball is hit so that its height in feet after t seconds is s(t)=-16tsquared +44t+4 find the maximum height of the baseball 1 solutions Answer 340497 by nerdybill(6958)   on 2011-10-01 09:49:05 (Show Source): You can put this solution on YOUR website!a baseball is hit so that its height in feet after t seconds is s(t)=-16tsquared +44t+4 find the maximum height of the baseball . s(t)=-16tsquared +44t+4 s(t)=-16t^2 +44t+4 . Because the coefficient associated with the t^2 term is negative, we know it is a parabola that opens downwards. . therefore, the vertex is the max. . height is max when: t = -b/(2a) t = -44/(2(-16)) t = -44/(-32) t = 1.375 secs . max height: s(t)=-16t^2 +44t+4 s(1.375)=-16(1.375)^2 +44(1.375)+4 s(1.375)=-16(1.890625) +60.5+4 s(1.375)=-30.25 +60.5+4 s(1.375)= 34.25 feet
 Numeric_Fractions/507502: how much is 2-(-2)^31 solutions Answer 340495 by nerdybill(6958)   on 2011-10-01 09:40:12 (Show Source): You can put this solution on YOUR website!2-(-2)^3 2-(-2)(-2)(-2) 2-(4)(-2) 2-(-8) 2+8 10
 Percentage-and-ratio-word-problems/507450: How many gallons of a 60% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 50% difference?1 solutions Answer 340491 by nerdybill(6958)   on 2011-10-01 09:35:33 (Show Source): You can put this solution on YOUR website!How many gallons of a 60% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 50% difference? . Let x = amount (gallons) of 60% antifreeze then .60x + .10(90) = .50(x+90) .60x + 9 = .50x+45 .10x + 9 = 45 .10x = 36 x = 360 gallons
 Linear-equations/507452: the given conditions to write an equation for the line in point-slope form. {{slope=6/7, passing through (8,7)}} is the answer y+7=6/7 (x+8)1 solutions Answer 340490 by nerdybill(6958)   on 2011-10-01 09:31:47 (Show Source): You can put this solution on YOUR website!the given conditions to write an equation for the line in point-slope form. {{slope=6/7, passing through (8,7)}} is the answer y+7=6/7 (x+8) . "point-slope" form is: y - y1 = m(x - x1) plugging in given values: y - 7 = 6/7(x - 8)
 Polynomials-and-rational-expressions/507465: Bob's Barber Shop estimates their gross revenue for the second quarter to be given by the polynomial 7x^3 - 9x^2 - 2x + 4. The shop estimated their cost for that quarter to be given by x^2 + 7x - 5. For the second quarter find and simplify a polynomial that will represnt their profit.1 solutions Answer 340489 by nerdybill(6958)   on 2011-10-01 09:28:00 (Show Source): You can put this solution on YOUR website!Bob's Barber Shop estimates their gross revenue for the second quarter to be given by the polynomial 7x^3 - 9x^2 - 2x + 4. The shop estimated their cost for that quarter to be given by x^2 + 7x - 5. For the second quarter find and simplify a polynomial that will represnt their profit. . Profit is "revenue" - "cost" (7x^3 - 9x^2 - 2x + 4) - (x^2 + 7x - 5) 7x^3 - 9x^2 - 2x + 4 - x^2 - 7x + 5 7x^3 - 10x^2 - 2x + 4 - 7x + 5 7x^3 - 10x^2 - 9x + 4 + 5 7x^3 - 10x^2 - 9x + 9
 Money_Word_Problems/507473: A delivery truck arrives at the Robert's store with 8 small boxes and 5 large boxes. The total charge for the boxes, without the tax and delivery charges, is 184 pesos. A large box cost 3 pesos more than a small box. What is the cost of each box? 1 solutions Answer 340487 by nerdybill(6958)   on 2011-10-01 09:22:43 (Show Source): You can put this solution on YOUR website!A delivery truck arrives at the Robert's store with 8 small boxes and 5 large boxes. The total charge for the boxes, without the tax and delivery charges, is 184 pesos. A large box cost 3 pesos more than a small box. What is the cost of each box? . Let x = cost (pesos) of small box then x+3 = cost (pesos) of large box . 8x + 5(x+3) = 184 8x + 5x+15 = 184 13x+15 = 184 13x = 169 x = 13 pesos (small box) . Large box: x+3 = 13+3 = 16 pesos
 Linear-equations/507177: What is 8x - 5y = 15 in slope intercept form1 solutions Answer 340362 by nerdybill(6958)   on 2011-09-30 08:59:06 (Show Source): You can put this solution on YOUR website!What is 8x - 5y = 15 in slope intercept form . "Slope-intercept" form is: y = mx + b where m is the slope b is the y-intercept at (0,b) . 8x - 5y = 15 -5y = -8x + 15 5y = 8x - 15 y = (8/5)x - 3 (this is what they're looking for)
 Money_Word_Problems/507180: a man invest twice as much as 8% as he invests at 5%.his total annual income from the two investments is 840.how much is invested at each rate? 1 solutions Answer 340361 by nerdybill(6958)   on 2011-09-30 08:57:24 (Show Source): You can put this solution on YOUR website!a man invest twice as much as 8% as he invests at 5%.his total annual income from the two investments is 840.how much is invested at each rate? . Let x = amount (\$) invested at 5% then 2x = amount (\$) invested at 8% . .05x + .08(2x) = 840 .05x + .16x = 840 .21x = 840 x = 840/.21 x = \$4000 (amount invested at 5%) . amount invested at 8%: 2x = 2(4000) = \$8000
 Rate-of-work-word-problems/507078: Joe and Moe can mow the lawn in 26 minutes if they work together. If Moe works twice as fast as Joe, how long does it take Joe to mow the lawn alone? 1 solutions Answer 340331 by nerdybill(6958)   on 2011-09-29 23:23:39 (Show Source): You can put this solution on YOUR website!Joe and Moe can mow the lawn in 26 minutes if they work together. If Moe works twice as fast as Joe, how long does it take Joe to mow the lawn alone? . Let J = time (minutes) Jo takes to mow alone then 2j = time Moe takes . 26(1/J + 1/(2J)) = 1 multiplying both sides by 2J: 26(2 + 1) = 2J 26(3) = 2J [26(3)]/2 = J [13(3)] = J 39 minutes = J (Jo's time)
 Rectangles/506570: What is the area of a circle of diameter 70 m? Use 22/7 as an approximation for π.1 solutions Answer 340197 by nerdybill(6958)   on 2011-09-29 09:41:43 (Show Source): You can put this solution on YOUR website!Since area of any circle is (pi)r^2 . (22/7)(70/2)^2 (22/7)(35)^2 (22/7)(1225) (22)(175) 3850 square meters
 Rate-of-work-word-problems/506533: One man can paint a garage in 28 hours. After working for 12 hours, he was given a new job, and a second man finished painting in 18 hours. How long would the second man take take to paint to whole garage?1 solutions Answer 340191 by nerdybill(6958)   on 2011-09-29 09:01:10 (Show Source): You can put this solution on YOUR website!One man can paint a garage in 28 hours. After working for 12 hours, he was given a new job, and a second man finished painting in 18 hours. How long would the second man take take to paint to whole garage? . Let x = time (hours) it takes second man to paint whole garage then 12(1/28) + 18(1/x) = 1 multiplying both sides by 28x: 12(x) + 18(28) = 28x 12x + 504 = 28x 504 = 16x 31.5 hours = x
 Signed-numbers/505995: i can't solve 4[-4(3-12)-17]and could you please explain the steps in getting the answer please thank you1 solutions Answer 340054 by nerdybill(6958)   on 2011-09-28 13:52:11 (Show Source): You can put this solution on YOUR website!You need to apply the "order of operations" (PEMDAS). . 4[-4(3-12)-17] 4[-4(-9)-17] 4[36-17] 4[19] 76
 Volume/505914: What is the volume of a box with a length of 14 cm, a width of 10 cm, and a height of 8 cm?1 solutions Answer 340008 by nerdybill(6958)   on 2011-09-28 10:50:58 (Show Source): You can put this solution on YOUR website!What is the volume of a box with a length of 14 cm, a width of 10 cm, and a height of 8 cm? volume = length*width*height volume = 14*10*8 = 1120 cubic cm
 Numbers_Word_Problems/505509: Four times a number decreased by 25 is the same as 9 times the number. Find the number1 solutions Answer 339904 by nerdybill(6958)   on 2011-09-27 18:11:16 (Show Source): You can put this solution on YOUR website!Four times a number decreased by 25 is the same as 9 times the number. Find the number Let n = the number the 4n - 25 = 9n -25 = 5n -25/5 = n -5 = n The number is -5
 absolute-value/505398: what is the value of x, if x/2+3/8=7?1 solutions Answer 339875 by nerdybill(6958)   on 2011-09-27 16:14:45 (Show Source): You can put this solution on YOUR website!x/2+3/8=7 multiply both sides by 8: 8(x/2+3/8) = 8(7) 4x+3 = 56 4x = 53 x = 53/4
 Rate-of-work-word-problems/505268: A bath tub can be filled by the hot and cold water pipes in 4 minutes, and when full it can be emptied by the waste pipe in 5 minutes. If it is half full, and all three pipes are set running, when will the tub be filled?1 solutions Answer 339840 by nerdybill(6958)   on 2011-09-27 12:26:55 (Show Source): You can put this solution on YOUR website!A bath tub can be filled by the hot and cold water pipes in 4 minutes, and when full it can be emptied by the waste pipe in 5 minutes. If it is half full, and all three pipes are set running, when will the tub be filled? . Let t = time (mins) tub is filled then t(1/4 - 1/5)= 1/2 multiplying both sides by 20: t(5 - 4)= 10 t(1)= 10 t = 10 minutes
 Circles/505281: I am trying to determine if this equation is a circle and give center and radius. I know it is a circle because x and y have equal coefficients and I know the formula but I can't figure how to set it up. Equation is: x^2+y^2-12x+10y = -25. Thank you1 solutions Answer 339836 by nerdybill(6958)   on 2011-09-27 12:00:08 (Show Source): You can put this solution on YOUR website!equation of a circle: (x - h)^2 + (y - k)^2 = r^2 . For your problem: x^2+y^2-12x+10y = -25 group x's and y's: (x^2-12x)+(y^2+10y) = -25 complete the squares: (x^2-12x+36)+(y^2+10y+25) = -25+36+25 (x-6)^2+(y+5)^2 = 36 (x-6)^2+(y+5)^2 = 6^2 . Center: (6,5) Radius: 6
 Geometric_formulas/505260: if x is 80% of y, then y is what percent of x?1 solutions Answer 339832 by nerdybill(6958)   on 2011-09-27 11:16:11 (Show Source): You can put this solution on YOUR website!if x is 80% of y, then y is what percent of x? . "x is 80% of y": x = .80y . "y is what percent of x": x = .80y x/(.80) = y (1/.80)x = y 1.25x = y or "y is 125% of x"
 Rate-of-work-word-problems/505214: Together Sophie and Clarissa can paint a house in 6 days. It takes Clarissa 5 days less than Sophie to paint the house by herself. How many days does it take Sophie to paint the house by herself?1 solutions Answer 339817 by nerdybill(6958)   on 2011-09-27 08:55:43 (Show Source): You can put this solution on YOUR website!Together Sophie and Clarissa can paint a house in 6 days. It takes Clarissa 5 days less than Sophie to paint the house by herself. How many days does it take Sophie to paint the house by herself? . Let x = time (days) it takes for Sophie to do it alone then x-5 = time it takes for Clarissa . 6(1/x + 1/(x-5)) = 1 multiplying both sides by x(x-5): 6(x-5 + x) = x(x-5) 6(2x-5) = x(x-5) 12x-30 = x^2-5x -30 = x^2-17x 0 = x^2-17x+30 0 = (x-15)(x-2) x = {15, 2} the 2 won't make sense, throw it out leaving: x = 15 days (Sophie's time) . Clarissa: x-5 = 15-5 = 10 days
 Linear-equations/504708: Can you put this in standard form? slope= 5/6;(22,12)1 solutions Answer 339683 by nerdybill(6958)   on 2011-09-26 15:51:43 (Show Source): You can put this solution on YOUR website!Can you put this in standard form? slope= 5/6;(22,12) . plug given data into "point-slope" form: y - y1 = m(x - x1) y - 12 = (5/6)(x - 22) y - 12 = (5/6)x - (5/6)22 y - 12 = (5/6)x - (5/3)11 y - 12 = (5/6)x - 55/3 y = (5/6)x - 55/3 + 12 y = (5/6)x - 55/3 + 36/3 y = (5/6)x - 19/3 ("slope-intercept" form) -(5/6)x + y = - 19/3 -(5/6)x + y = -19/3 ("standard" form) OR -5x/6 + y = -19/3 ("standard" form)
 Equations/504695: Hi I am in the 8th grade and I am not good at algebra at all but I know I have to learn it. Can you help me solve this equation: 3[8+(4+2)]= Can you tell me how to solve this is layman terms because I want to learn how to do it myself.1 solutions Answer 339682 by nerdybill(6958)   on 2011-09-26 15:36:42 (Show Source): You can put this solution on YOUR website!You would apply the "order of operations" A memory device is: PEMDAS(please excuse my dear aunt sally) . P: parentheses first E: exponents next MD: multiplication/division from left to right AS: addition/subtraction from left to right . 3[8+(4+2)] 3[8+6] 3[14] 42
 Linear-equations/504586: find the equation of the line passing through (-1, 2) and parallet to 2x-4y = 241 solutions Answer 339651 by nerdybill(6958)   on 2011-09-26 12:24:24 (Show Source): You can put this solution on YOUR website!find the equation of the line passing through (-1, 2) and parallel to 2x-4y = 24 . Two lines are parallel if they have the same slope. First, find slope of: 2x-4y = 24 -4y = -2x+24 4y = 2x-24 y = (1/2)x-6 slope is 1/2 . plug slope (1/2) and given point (-1, 2) into "point-slope" form: y - y1 = m(x -x1) y - 2 = (1/2)(x -(-1)) y - 2 = (1/2)(x + 1) y - 2 = (1/2)x + 1/2 y = (1/2)x + 1/2 + 2 y = (1/2)x + 1/2 + 4/4 y = (1/2)x + 5/2 (this is what they're looking for)
 Expressions-with-variables/503861: please help me solve [(5+3)^2/4]^2-31 solutions Answer 339439 by nerdybill(6958)   on 2011-09-25 11:34:43 (Show Source): You can put this solution on YOUR website!Apply the "order of operations" (PEMDAS): [(5+3)^2/4]^2-3 [(8)^2/4]^2-3 [64/4]^2-3 [16]^2-3 256-3 253
 Expressions-with-variables/503768: a number raised to the third power multiplied by 125 is equal to 1/8 . what is the number?1 solutions Answer 339426 by nerdybill(6958)   on 2011-09-25 09:28:42 (Show Source): You can put this solution on YOUR website! a number raised to the third power multiplied by 125 is equal to 1/8 . what is the number? . Let x = the number then (x^3)(125) = 1/8 x^3 = 1/(8*125) x^3 = 1/(1000) x^3 = 1/(10*10*10) take cube root of both sides: x = 1/10
 Trigonometry-basics/503770: what is the answer of 5\6 of 42 pounds1 solutions Answer 339425 by nerdybill(6958)   on 2011-09-25 09:25:05 (Show Source): You can put this solution on YOUR website!(5\6)(42) = (5)(8) = 40 pounds
 Linear_Equations_And_Systems_Word_Problems/503824: Two-thirds of a number increased by three-fourth is five-third, what is the number?1 solutions Answer 339424 by nerdybill(6958)   on 2011-09-25 09:23:25 (Show Source): You can put this solution on YOUR website!Two-thirds of a number increased by three-fourth is five-third, what is the number? . Let x = the number then (2/3)x + 3/4 = 5/3 multiplying both sides 12: 8x + 9 = 20 8x = 11 x = 11/8
 Expressions-with-variables/503767: katrina can design a 3 feet by 3 feet board using egg shells in 3 hours.her cousin,pia volunteered to help katrina.if they work together,it will take them 1 hour and 40 minutes to finish the job.how long does it take pia to do the job done?1 solutions Answer 339423 by nerdybill(6958)   on 2011-09-25 09:21:01 (Show Source): You can put this solution on YOUR website!katrina can design a 3 feet by 3 feet board using egg shells in 3 hours.her cousin,pia volunteered to help katrina.if they work together,it will take them 1 hour and 40 minutes to finish the job.how long does it take pia to do the job done? . Let x = time (minutes) it takes pia alone then time it takes for both: 1 hour and 40 minutes = 100 minutes . katrina's rate: 1/180 . 100(1/180 + 1/x) = 1 multiplying both sides by 180x: 100(x + 180) = 180x 100x + 18000 = 180x 18000 = 80x 225 minutes = x or 3 hours and 45 minutes = x (pia doing it alone)