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# Recent problems solved by 'nerdybill'

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 Finance/218165: Factor out greatest common factor: 18m^8 - 4m^6 + 6m^4 1 solutions Answer 164328 by nerdybill(7003)   on 2009-09-28 01:54:23 (Show Source): You can put this solution on YOUR website!18m^8 - 4m^6 + 6m^4 . The common factor is 2m^4 Thus, factoring out gives you: (2m^4)(9m^4 - 2m^2 + 3)
 Graphs/218162: y=200+15m y=100+20m at what point do they intersect?1 solutions Answer 164326 by nerdybill(7003)   on 2009-09-28 00:58:47 (Show Source): You can put this solution on YOUR website!y=200+15m y=100+20m . Set them equal to each other and solve for m: 200+15m=100+20m 200=100+5m 100=5m 20 = m . Plug the above into either equation to find y: y=200+15m y=200+15(20) y=200+300 y=100 . They intersect at (m,y)=(20,100)
 Linear-equations/217636: Find the order pair that is a solution. y=2x-1 ( ,7)1 solutions Answer 164049 by nerdybill(7003)   on 2009-09-26 21:44:35 (Show Source): You can put this solution on YOUR website!Find the order pair that is a solution. y=2x-1 ( ,7) . An "ordered pair" is (x,y) In your problem, you're given the y but not the x. Plug the given y into the equation and solve for x: y=2x-1 7=2x-1 8=2x 4=x . Therefore, the ordered pair is (4,7)
 Triangles/217615: on a triangle how do u find the hypotenouse i kno what it is i jsut dont kno how u get the number like if the other two sides where like 3m and 4m how would u find the other side1 solutions Answer 164041 by nerdybill(7003)   on 2009-09-26 21:19:16 (Show Source): You can put this solution on YOUR website!If the triangle has one "right angle" (90 degrees) then you can apply Pythagorean theorem: a^2 + b^2 = c^2 where c is the hypotenuse (side opposite the 90 deg angle) 'a' and 'b' are the two sides . 3^2 + 4^2 = c^2 9 + 16 = c^2 25 = c^2 sqrt(25) = c 5 m = c
 Geometric_formulas/217361: half of a 16 in diameter circle fits snugly inside a rectangular box, how many square inches larger is the area of the box than the area of the circle?1 solutions Answer 163924 by nerdybill(7003)   on 2009-09-26 09:35:06 (Show Source): You can put this solution on YOUR website!half of a 16 in diameter circle fits snugly inside a rectangular box, how many square inches larger is the area of the box than the area of the circle? . Draw a diagram of the problem -- label everything you know -- it'll help you see the solution. . Area of "half circle" (1/2)(pi)8^2 = (1/2)(pi)8^2 = 32(pi) = 100.53 sq inches . box: length is 16 width is 8 Area = width*length Area = 8*16 Area = 128 sq inches . It is larger by: 128 - 100.53 = 27.47 sq inches
 Numbers_Word_Problems/217115: Find three consecutive even integers such that three times the middle integers is 10 more than the greatest answer:x=2 the integers are 4,6,8 anyone tell me how my text book got this answer full break down thank you 1 solutions Answer 163745 by nerdybill(7003)   on 2009-09-25 11:21:24 (Show Source): You can put this solution on YOUR website!Find three consecutive even integers such that three times the middle integers is 10 more than the greatest . Let x = smallest consecutive even integer then x+2 = middle of three consecutive even integers x+4 = largest of three consecutive even integers . 3(x+2) = (x+4) + 10 3x+6 = x+4+10 3x+6 = x+14 2x+6 = 14 2x = 8 x = 4 (smallest) . Middle: x+2 = 4+2 = 6 . Largest: x+4 = 4+4 = 8 . The three integers: 4,6,8
 Graphs/217035: find the slope and the y-intercept f (x) = - 2x -91 solutions Answer 163729 by nerdybill(7003)   on 2009-09-25 09:29:54 (Show Source): You can put this solution on YOUR website!f(x) = - 2x -9 is already in the "slope-intercept" form of a line: y = mx + b where m is slope b is the y-intercept at (0,b) . From inspection then, we see that m is -2 b is -9 . Therefore: slope is -2 and the y-intercept is at (0,-9)
 Mixture_Word_Problems/217064: A lab has a 20% acid solution and a 50% acid solution. How many liters of each are required to obtain 600 liters of a 30% acid solution?1 solutions Answer 163725 by nerdybill(7003)   on 2009-09-25 09:24:06 (Show Source): You can put this solution on YOUR website! A lab has a 20% acid solution and a 50% acid solution. How many liters of each are required to obtain 600 liters of a 30% acid solution? . Let x = liters of 20% acid solution then 600-x = liters of 50% acid solution . .20x + .50(600-x) = .30(600) .20x + 300 - .50x = 180 300 - .30x = 180 300 = .30x + 180 120 = .30x 400 liters = x (amount of 20% acid solution) . Amount of 50% acid solution: 600-x = 600-400 = 200 liters
 logarithm/217065: Is there any way to evaluate e^1.9? My calculator on the computer does not have the e^x button. I have a TI-84 but it is too complex, I can't figure it out!1 solutions Answer 163724 by nerdybill(7003)   on 2009-09-25 09:18:10 (Show Source): You can put this solution on YOUR website!Your calculator does have an e^x key -- it's a "2nd" (yellow) function. . Hit the yellow "2nd" key (near top left) Hit the yellow "e^x" key (near bottom left -- 3rd row up) Hit "1.9" Hit "ENTER" (your solution will appear)
 Inequalities/217062: What is the y-intercept of the line in the equation y=-2/3x-12.1 solutions Answer 163722 by nerdybill(7003)   on 2009-09-25 09:14:05 (Show Source): You can put this solution on YOUR website!Because y=-2/3x-12 is already in the "slope-intercept" form of y = mx + b where m is slope b is the y-intercept at (0,b) . From inspection then b = -12 therefore the y-intercept is (0, -12)
 Graphs/217013: I need to know the slope of a line perpendicular to the line 7x-2y=-2 And, I need to know the slope of a line parallel to the line 7x-2y=-21 solutions Answer 163708 by nerdybill(7003)   on 2009-09-25 02:23:48 (Show Source): You can put this solution on YOUR website!I need to know the slope of a line perpendicular to the line 7x-2y=-2 Convert to "slope-intercept" form: y = mx + b 7x-2y=-2 -2y = -7x-2 y = (7/2)x + 1 Since the slope of the line is 7/2, a line perpendicular to this will have a "negative reciprocal" slope. Let m = slope of perpendicular line then m(7/2) = -1 m = -2/7 . And, I need to know the slope of a line parallel to the line 7x-2y=-2 Since we found the slope of: 7x-2y=-2 to be 7/2 a line parallel to this will have the SAME slope therefore, slope of a parallel line is 7/2
 absolute-value/216781: my 4th grade grandson is learning pre-algebra??? I only had algebra in 9th grade way back in the 60's and can't remember how to do any of it. How do I explain "Find the value of a x 3 for each value of a? Examples are a=2, a=5, a = 1 and a =4. I need help understanding so I can explain it to him. Thanks, Becky1 solutions Answer 163643 by nerdybill(7003)   on 2009-09-24 18:21:17 (Show Source): You can put this solution on YOUR website!The problem gives you an "equation": a x 3 . Then, they want to know the result if: a=2, a=5, a = 1 and a =4 Basically, replace 'a' with the value and multiply. . Set up a table. 1st column: a 2nd column: a stuffed into the equation 3rd column: resultant value . a | a x 3 | result ======================= 2 | 2 x 3 | 6 5 | 5 x 3 | 15 1 | 1 x 3 | 3 4 | 4 x 3 | 12
 Miscellaneous_Word_Problems/216771: It takes you 50 seconds to walk from the 1st floor to the 3rd floor. How long will it take to walk from the 1st floor to the 6th floor, if you are walking at the same speed and all floors are equivalent? When trying to solve this, I divided the 50 seconds by the 3 floors and got 50/3. I then multiplied 50/3 by the 6 floors and got 100 seconds. This answer was incorrect, though.1 solutions Answer 163640 by nerdybill(7003)   on 2009-09-24 18:16:41 (Show Source): You can put this solution on YOUR website!It takes you 50 seconds to walk from the 1st floor to the 3rd floor. How long will it take to walk from the 1st floor to the 6th floor, if you are walking at the same speed and all floors are equivalent? . Your mistake is that there are only TWO flights of stairs between the 1st and 3rd floors. You start at 1st floor. You walk up one flight (2nd floor). You walk up second flight (3rd floor). . 50/2 = 25 seconds per flight of stairs . 5 flights to 6th floor: 5 * 25 = 125 seconds
 Mixture_Word_Problems/216452: How many liters of a 60% acid solution must be mixed with a 75% acid solution to get 20L of a 72% solution?1 solutions Answer 163438 by nerdybill(7003)   on 2009-09-24 00:21:46 (Show Source): You can put this solution on YOUR website! How many liters of a 60% acid solution must be mixed with a 75% acid solution to get 20L of a 72% solution? . Let x = liters of 60% acid solution to be added then 20-x = liters of 75% acid solution to be added . Our equation: .60x + .75(20-x) = .72(20) .60x + 15 - .75x = 14.4 15 - .15x = 14.4 - .15x = -.6 x = 4 L (60% solution) . 75% solution: 20-x = 20-4 = 16 L
 Graphs/216461: p/3 - 3p/8 = 4 I have no idea where to start :P1 solutions Answer 163431 by nerdybill(7003)   on 2009-09-23 23:56:40 (Show Source): You can put this solution on YOUR website!p/3 - 3p/8 = 4 Multiply both sides by 24 to get rid of denominators: 8p - 9p = 96 -p = 96 p = -96 . To check, plug back into original equation: p/3 - 3p/8 = 4 -96/3 - 3(-96)/8 = 4 -32 - 3(-12) = 4 -32 + 36 = 4 4 = 4
 Travel_Word_Problems/216188: A car travels from A to B. First half of the distance it moves with a speed 60 mph, and the second half - with a speed 40 mph. Find the average speed of a car for the whole trip.1 solutions Answer 163266 by nerdybill(7003)   on 2009-09-23 17:55:14 (Show Source): You can put this solution on YOUR website!A car travels from A to B. First half of the distance it moves with a speed 60 mph, and the second half - with a speed 40 mph. Find the average speed of a car for the whole trip. . Applying the "distance formula" (d=rt): . Let x = total distance from A to B then "time traveled 1st half" = (x/2)/60 = x/120 "time traveled 2nd half" = (x/2)/40 = x/80 . Total time: x/120 + x/80 . Average speed is "total distance"/"total time" = x/(x/120 + x/80) Dividing numerator and denominator by 'x': = 1/(1/120 + 1/80) = 10/(1/12 + 1/8) = 10/(2/24 + 3/24) = 10/(5/24) = 240/5 = 48 mph
 Quadratic_Equations/215941: An object is thrown downward from the top of a tower. The distance in feet that it falls in t seconds is given by the following. s(t) = 16t2 + 14t (c) Find the average velocity from t = 3 seconds to t = 5 seconds. 3 ft/sec 1 solutions Answer 163123 by nerdybill(7003)   on 2009-09-23 08:26:44 (Show Source): You can put this solution on YOUR website!s(t) = 16t2 + 14t average velocity from t = 3 seconds to t = 5 seconds . s(3) = 16*3^3 + 14(3) s(3) = 16*27 + 14(3) s(3) = 474 . s(5) = 16*5^3 + 14(5) s(5) = 16*125 + 14(5) s(5) = 2070 . Avg vel = (s(5)-s(3))/(5-2) Avg vel = (2070-474)/(3) Avg vel = (1596)/(3) Avg vel = 532 feet/sec
 Matrices-and-determiminant/215965: x-3y=6 3x+y=-22 its using cramer's rule i've tried to work the problem but i jus keep getting 46 and 401 solutions Answer 163120 by nerdybill(7003)   on 2009-09-23 08:16:27 (Show Source): You can put this solution on YOUR website!x-3y=6 3x+y=-22 . coefficient matrix: 1 -3 3 1 Det of coefficients: (1-(-9)) = 10 . x-matrix 6 -3 -22 1 Detx: 6 - 66 = -60 . y-matrix 1 6 3 -22 Dety: -22 - 18 = -40 . x = Detx/Detcoef = -60/10 = -6 y = Dety/Detcoef = -40/10 = -4 .
 Number-Line/215893: One half of a number increased by 16 is four less than two thirds of the number. Find the number. Help please? I got 1/2x+16=4-2/3x as my equation but I don't know how to solve it.1 solutions Answer 163119 by nerdybill(7003)   on 2009-09-23 08:04:01 (Show Source): You can put this solution on YOUR website!One half of a number increased by 16 is four less than two thirds of the number. Find the number. Help please? . Let x = number then (1/2)x + 16 = (2/3)x - 4 Multiply both sides by 6: 3x + 96 = 4x - 24 96 = x - 24 120 = x
 Rate-of-work-word-problems/215962: This question is from textbook An old water pump can fill up a large trough in 10 minutes, but a second, newer pump takes only 3 minutes and 20 seconds to fill the trough. How long would it take to fill the trough using both pumps at the same time?1 solutions Answer 163118 by nerdybill(7003)   on 2009-09-23 07:59:04 (Show Source): You can put this solution on YOUR website! An old water pump can fill up a large trough in 10 minutes, but a second, newer pump takes only 3 minutes and 20 seconds to fill the trough. How long would it take to fill the trough using both pumps at the same time? . Convert rate to seconds: Old pump: fill trough per 10 minutes is equivalent fill trough per 600 seconds . New pump: fill trough per 3 minutes 20 seconds is equivalent fill trough per 200 seconds . Let x = seconds it takes for both pump then x(1/600 + 1/200) = 1 Multiplying both sides by 600: x(1 + 3) = 600 4x = 600 x = 150 seconds . So, for both pumps to fill the trough: 2 minutes 30 seconds
 Linear_Algebra/215949: f(x)=3x +7 then f(x+2)=1 solutions Answer 163116 by nerdybill(7003)   on 2009-09-23 07:53:37 (Show Source): You can put this solution on YOUR website! f(x)=3x +7 then f(x+2)= 3(x+2) + 7 f(x+2)= 3x+6 + 7 f(x+2)= 3x+13
 Functions/215905: A company has costs and revenue functions, in dollars given by C(q)=4000 + 10q and R(q)=30q What is the break-even point? I know what the answer is...its 200. But I cant figure out at all how they got that. Can you please help explain? Thanks, Mike1 solutions Answer 163115 by nerdybill(7003)   on 2009-09-23 07:51:40 (Show Source): You can put this solution on YOUR website!A company has costs and revenue functions, in dollars given by C(q)=4000 + 10q and R(q)=30q What is the break-even point? . The "break-even point" is when: "cost" = "revenue" or C(q) = R(q) 4000 + 10q = 30q 4000 = 20q 200 = q
 Inverses/215916: The quarterly profit of Cunningham Realty depends on the amount of money x spent on advertising/quarter according to the rule where P(x) and x are measured in thousands of dollars. What is Cunningham's profit when it's quarterly advertising budget is 28,000 ? 1 solutions Answer 163114 by nerdybill(7003)   on 2009-09-23 07:49:22 (Show Source): You can put this solution on YOUR website!The quarterly profit of Cunningham Realty depends on the amount of money x spent on advertising/quarter according to the rule (0 where P(x) and x are measured in thousands of dollars. What is Cunningham's profit when it's quarterly advertising budget is 28,000 ? . So, x = 28 Simply plug it the given value of x into the equation and solve: So, profit is \$128,000
 Exponential-and-logarithmic-functions/215919: Please do each step. Show your work. Solve each aequation for x. Part 1: log[3](x+5)=2 Step 1: Write the given logarithmic equation in exponential form. Step 2: Solve the exponential equation from step 1 for x. Step 3: Check for extraneous solutions. Step 4: State the solution for the given equation.1 solutions Answer 163098 by nerdybill(7003)   on 2009-09-23 00:17:45 (Show Source): You can put this solution on YOUR website!Solve each aequation for x. Part 1: log[3](x+5)=2 Step 1: Write the given logarithmic equation in exponential form. x+5 = 3^2 Step 2: Solve the exponential equation from step 1 for x. x+5 = 3^2 x+5 = 9 x = 4 Step 3: Check for extraneous solutions. None. Step 4: State the solution for the given equation. x = 4
 Exponents/215894: What is greater, or ?1 solutions Answer 163077 by nerdybill(7003)   on 2009-09-22 22:51:05 (Show Source): You can put this solution on YOUR website! = = . = = . So, is greater.
 Graphs/215713: Ok, I'm going to try this one more time... I need help solving AND factoring the following equation (taken from Bittinger's College Algebra: Graphs and Models 4th Edition, page 76, problem number 39.) A point to remember: The x^2 is NEGATIVE, and the 2x and 3 are both POSITIVE. Thank you in advance!1 solutions Answer 162953 by nerdybill(7003)   on 2009-09-22 16:39:45 (Show Source):
 Mixture_Word_Problems/215529: How many gallons of 50% antifreeze solution must be mixed with 70 gallons of 25% antifreeze to get a mixture that is 40% antifreeze?1 solutions Answer 162849 by nerdybill(7003)   on 2009-09-22 01:15:20 (Show Source): You can put this solution on YOUR website! How many gallons of 50% antifreeze solution must be mixed with 70 gallons of 25% antifreeze to get a mixture that is 40% antifreeze? . Let x = amount of 50% antifreeze added then .50x + .25(70) = .40(70 + x) .50x + 17.5 = 28 + .40x .50x = 10.5 + .40x .10x = 10.5 x = 10.5/.10 x = 105 gallons
 Triangles/215350: the altitude of an equilateral triangle is 18 inches. find the length of a side and the perimeter.1 solutions Answer 162723 by nerdybill(7003)   on 2009-09-21 16:43:56 (Show Source): You can put this solution on YOUR website!the altitude of an equilateral triangle is 18 inches. find the length of a side and the perimeter. . Let x = measure of one side then from Pythagorean theorem: 18^2 +(x/2)^2 = x^2 18^2 +x^2/4 = x^2 18^2 = x^2 - x^2/4 18^2 = 3x^2/4 324 = 3x^2/4 108 = x^2/4 432 = x^2 20.785 inches = x . Perimeter is 3x = 3(20.785) = 62.354 inches
 Travel_Word_Problems/215231: jacinta can solve 20 multiplication questions in one minute. her friend can solve the same number in 3 minutes. how long will it take both of them together to solve 20 questions? 1 solutions Answer 162641 by nerdybill(7003)   on 2009-09-21 10:17:42 (Show Source): You can put this solution on YOUR website!jacinta can solve 20 multiplication questions in one minute. her friend can solve the same number in 3 minutes. how long will it take both of them together to solve 20 questions? . Really, in this case, the fact that there are 20 questions is not relevant. . Let x = time it takes for both to solve x(1/1 + 1/3) = 1 x(3/3 + 1/3) = 1 x(4/3) = 1 x(4) = 3 x = 3/4 of a minute Or (3/4) * 60 = 45 seconds
 Travel_Word_Problems/215229: a plane travels 2250 km in 3 hours. find its average speed? 1 solutions Answer 162638 by nerdybill(7003)   on 2009-09-21 10:12:17 (Show Source): You can put this solution on YOUR website!a plane travels 2250 km in 3 hours. find its average speed? . That's 2250 km per 3 hours . Or, 2250/3 = 750 km per hour
 Linear_Equations_And_Systems_Word_Problems/215241: This question is from textbook Applied Calculus A manufacturer sells a product at \$8.80 per unit, selling all produced. The fixed cost is \$2,160 and the variable cost is \$7.25 per unit. (a) At what level of production will there be a profit of \$4,100? (b) At what level of production will there be a loss of \$1,200? (c) At what level of production will the break-even point occur? 1 solutions Answer 162616 by nerdybill(7003)   on 2009-09-21 08:34:36 (Show Source): You can put this solution on YOUR website!A manufacturer sells a product at \$8.80 per unit, selling all produced. The fixed cost is \$2,160 and the variable cost is \$7.25 per unit. . Profit equation: P(x) = 8.80x - 7.25x - 2160 P(x) = 1.55x - 2160 where x is the number of units . (a) At what level of production will there be a profit of \$4,100? Set P(x) = 4100 and solve for x: 4100 = 1.55x - 2160 6260 = 1.55x 4038.71 units = x . (b) At what level of production will there be a loss of \$1,200? Set P(x) = -1200 and solve for x: -1200 = 1.55x - 2160 960 = 1.55x 619.35 units = x . (c) At what level of production will the break-even point occur? Set P(x) = 0 and solve for x: 0 = 1.55x - 2160 2160 = 1.55x 1393.55 units = x