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 logarithm/549639: the half-life of a particular element is 4 days. after 20 days a sample has been reduced to a mass of 0.375g. what was the initial mass of the sample?1 solutions Answer 357926 by ankor@dixie-net.com(15656)   on 2011-12-21 19:35:15 (Show Source): You can put this solution on YOUR website!the half-life of a particular element is 4 days. after 20 days a sample has been reduced to a mass of 0.375g. what was the initial mass of the sample? : the radioactive decay formula: A = Ao*2^(-t/h), where A = resulting amt after t time Ao = initial amt t = time h = half-life of substance : Ao*2^(-20/4) = .375 Ao*2^(-5) = .375 Ao*.03125 = .375 Ao = Ao = 12 grams, the initial mass of the sample : : Check this on your calc: enter 12*2^(-20/4) result .375
 Inequalities/549601: I cannot find an example even similar to this one. Please help... 1/x+2/x^2 is less than or equal too 1/x-11 solutions Answer 357919 by ankor@dixie-net.com(15656)   on 2011-12-21 17:44:50 (Show Source): You can put this solution on YOUR website!1/x+2/x^2 is less than or equal too 1/x-1 Assume the problem is: + <= we can put the left side over a single denominator <= Cross multiply (x+2)(x-1) <= x^2 FOIL x^2 + x - 2 >= x^2 x^2 - x^2 + x - 2 <= 0 x - 2 <= 0 x <= +2, however x cannot = 1, (division by 0)
 Age_Word_Problems/549503: Susi is 25 years younger then her mother. In 7 years the mother will be 5 times older then Susi. cant figure this one out How old is the mother when she's 5times older and how old is susi??????????? 1 solutions Answer 357815 by ankor@dixie-net.com(15656)   on 2011-12-21 07:55:50 (Show Source): You can put this solution on YOUR website!Susi is 25 years younger then her mother. In 7 years the mother will be 5 times older then Susi. : There is a reason why you can't figure this out, it is impossible We will do the problem and see that ; s = Susi's present age, m = Mother's age : Write an equation for each statement: : "Susi is 25 years younger then her mother." s = m - 25 or we can say m = s + 25 : In 7 years the mother will be 5 times older then Susi. m + 7 = 5(s + 7) Simplify m + 7 = 5s + 35 m = 5s + 35 - 7 m = 5s + 28 now, replace m with (s+25), from the 1st statement s + 25 = 5s + 28 25 - 28 = 5s - s -3 = 4s s = , a nonsensical solution, perhaps they meant 7 year ago!! or they meant "In 7 years the mother will be 5 times older then Susi is now!" : Let me know what you think. C
 Numbers_Word_Problems/549427: the sum of two numbers is one-hundred seventy-eight. The difference between the number is six. what is the product of the two numbers.1 solutions Answer 357769 by ankor@dixie-net.com(15656)   on 2011-12-20 21:44:28 (Show Source): You can put this solution on YOUR website!the sum of two numbers is one-hundred seventy-eight. a + b = 178 : The difference between the number is six. a - b = 6 : Use elimination here, a + b = 178 a - b = 6 -----------adding eliminates b, find a 2a = 184 a = 184/2 a = 92 then 92 + b = 178 b = 178 - 92 b = 86 : what is the product of the two number, I'll let you find the product
 Rational-functions/549121: A SQUARE AND A RECTANGLE HAVE THE SAME AREA. THE LENGTH OF THE RECTANGLE IS 8 MORE THAN A SIDE OF THE SQUARE, AND THE WIDTH OF THE RECTANGLEIS 4 LESS THAN A SIDE OF THE SQUARE. FIND A SIDE OF THE SQUARE. NOTE: THIS IS A QUADRATIC EQUATION.1 solutions Answer 357766 by ankor@dixie-net.com(15656)   on 2011-12-20 21:33:56 (Show Source): You can put this solution on YOUR website!A SQUARE AND A RECTANGLE HAVE THE SAME AREA. THE LENGTH OF THE RECTANGLE IS 8 MORE THAN A SIDE OF THE SQUARE, AND THE WIDTH OF THE RECTANGLEIS 4 LESS THAN A SIDE OF THE SQUARE. FIND A SIDE OF THE SQUARE. : Let x = the side of the square then x^2 = the area of the square : (x+8) = the length of the rectangle (x-4) = the width of the rectangle then FOIL (x+8)(x-4) = x^2 - 4x + 8x - 32 x^2 + 4x - 32 = the area of the rectangle : Given the areas areas are equal x^2 + 4x - 32 = x^2 Combine the x^2's on the left x^2 - x^2 + 4x - 32 = 0 4x = 32 x = 32/4 x = 8 units is the side of the square : : See if this is right (8+8) * (8-4) = 8^2 16 * 4 = 64; confirms our solution of x=8
 Finance/549276: A DVD costs 7 times what you get when if you add the number of \$ in it's price to the number of cents. This gives it's price in cent . What is it ? Thanks.1 solutions Answer 357763 by ankor@dixie-net.com(15656)   on 2011-12-20 21:22:18 (Show Source): You can put this solution on YOUR website!A DVD costs 7 times what you get when if you add the number of \$ in it's price to the number of cents. This gives it's price in cent. What is it? : Let d = no. of dollars Let c = no. of cents : 100(d+.01c) = 7(d+c) 100d + c = 7d + 7c 100d - 7d = 7c -c 93d = 6c c = d reduce the fraction c = d we can see that an integer solution is possible when d = 2, then c = 31 Actually we have 3 integer solutions from this equation (c has to be less than 100) DVd cost: d . c \$2.31, 7(2+31) = 231 cents \$4.62, 7(4+62) = 462 cents \$6.93, 7(6+93) = 693 cents
 Rectangles/549412: if one side of a square is increased by 3 inches and the adjacent side is decreased by 2 inches, a rectangle is formed whose are is equal to the area of the square. Find a side of the square1 solutions Answer 357749 by ankor@dixie-net.com(15656)   on 2011-12-20 20:16:13 (Show Source): You can put this solution on YOUR website!if one side of a square is increased by 3 inches and the adjacent side is decreased by 2 inches, a rectangle is formed whose are is equal to the area of the square. Find a side of the square : Let x = the side of the square then x^2 = the area of the square : (x+3) = length of the rectangle and (x-2) = width of the rectangle then (x+3)*(x-2) = x^2 + x - 6, the area of the rectangle : Rect area = square area x^2 + x - 6 = x^2 x^2 - x^2 + x = 6 x = 6 inches is the side of the square : : See if this flies: (6+3)*(6-2) = 6^2 9 * 4 = 36
 test/549274: simon ordered 200 boxes of Fuji apples from china.he paid \$28 per box for the apples. there were 60 fruits in each box and he expected 15% of them yo spoil. if he wants to make a profit of 80% on cost what should be the selling price per fruit? 1 solutions Answer 357747 by ankor@dixie-net.com(15656)   on 2011-12-20 20:06:39 (Show Source): You can put this solution on YOUR website!simon ordered 200 boxes of Fuji apples from china.he paid \$28 per box for the apples. there were 60 fruits in each box and he expected 15% of them yo spoil. if he wants to make a profit of 80% on cost what should be the selling price per fruit? : Find the total cost of the apples: 28 * 200 = \$5,600 Find how much he should receive to realize an 80% profit: 1.80*5600 = \$10,080 : Find how many boxes he has after 15% of them spoil: .85(200) = 170 boxes Find how many apples he has: 170*60 = 10200 apples : Let x = amt he should charge to make the required amt 10200x = \$10080 x = x = \$.99 per apple to make at least the required amt of \$10,080
 Systems-of-equations/549413: Solve the given system of linear equations for X: 4X + y= -11 and X + 2y= 6 Please show how you get the answer Thank you, Natasha1 solutions Answer 357743 by ankor@dixie-net.com(15656)   on 2011-12-20 19:44:22 (Show Source): You can put this solution on YOUR website!Solve the given system of linear equations for X: 4X + y = -11 X + 2y = 6 ; We can use elimination here, multiply the 1st equation by 2, subtract the 2nd equation 8X +2y = -22 X + 2y = 6 -------------subtraction eliminates y, find x 7x = -28 x = -28/7 x = -4 : Find y using the 2nd equation, replace x with -4 -4 + 2y = 6 2y = 6 + 4 2y = 10 y = 10/2 y = 5 : : Check our solution of x=-4, y=5, using the 1st equation 4X + y = -11 4(-4) + 5 = -11 -16 + 5 = -11; confirms our solutions
 Money_Word_Problems/549420: A total of \$15,000 is invested in two accounts. One of the two accounts pays 8% per year, and the other account pays 12% per year. If the total interest paid in the first year is \$1,600, how much was invested in each account? Two answers are needed amount for 8% account and money made for 12% account. Please help!1 solutions Answer 357742 by ankor@dixie-net.com(15656)   on 2011-12-20 19:36:40 (Show Source): You can put this solution on YOUR website!Let x = amt invested at 8% Let y = amt invested at 12% : Write an equation for each statement: : A total of \$15,000 is invested in two accounts. x + y = 15000 or x = (15000-y), we can use this form for substitution : One of the two accounts pays 8% per year, and the other account pays 12% per year. If the total interest paid in the first year is \$1,600, .08x + .12y = 1600 substitute (15000-y) for x, find y .08(15000-y) + .12y = 1600 1200 - .08y + .12y = 1600 -.08y + .12y = 1600 - 1200 .04y = 400 y = 400/.04 y = \$10,000 invested at 12% then 15000 - 10000 = \$5,000 invested at 8% : : You can check this out .08(5000) + .12(1000) =
 Geometry_Word_Problems/549355: I am building a shed. I can use 400 square feet. I need to know height, width &I length it can be.1 solutions Answer 357741 by ankor@dixie-net.com(15656)   on 2011-12-20 19:26:32 (Show Source): You can put this solution on YOUR website!How about 20 by 20 by 8 ft high?
 Rational-functions/549119: If one side of a square is increased by 4 feet and an adjacent side is decreased by two feet,a rectangle is formed whose area is 12 square feet more than the area of the original square.Find the length of a side of the square.1 solutions Answer 357682 by ankor@dixie-net.com(15656)   on 2011-12-20 14:32:53 (Show Source): You can put this solution on YOUR website!If one side of a square is increased by 4 feet and an adjacent side is decreased by two feet, a rectangle is formed whose area is 12 square feet more than the area of the original square.Find the length of a side of the square. : Let x = the side of the original square and x^2 = area of the square then (x+4) = new length of the rectangle and (x-2) = new width then the area of the rectangle (x+4)*(x-2) = x^2 - 2x + 4x - 8 = x^2+2x-8 ; "a rectangle is formed whose area is 12 square feet more than the area of the original square." x^2 + x - 8 - x^2 = 12 2x = 12 + 8 2x = 20 x = 10 ft is the side of the original square : : : See if this checks out (14*8) - (10*10) = 112 - 100 = 12
 Travel_Word_Problems/549294: A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement?.1 solutions Answer 357595 by ankor@dixie-net.com(15656)   on 2011-12-20 08:35:50 (Show Source): You can put this solution on YOUR website!A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement?. : Let x = the value of the multiplier then the dimensions of the picture will be: 4x by 3x : the area 4x * 3x = 192 12x^2 = 192 x^2 = x^2 = 16 x = 4 is the multiplier : 4*4 = 16 is the length 4*3 = 12 is the width
 Triangles/549011: An airplane is flying at an elevation of 12,000 feet before diving at an angle of depression of 45 degrees for 25 seconds. The plane is traveling at an average rate of 260 miles per hour during the dive. At what elevation does the plane end the dive? 1 solutions Answer 357593 by ankor@dixie-net.com(15656)   on 2011-12-20 08:29:50 (Show Source): You can put this solution on YOUR website!An airplane is flying at an elevation of 12,000 feet before diving at an angle of depression of 45 degrees for 25 seconds. The plane is traveling at an average rate of 260 miles per hour during the dive. At what elevation does the plane end the dive? : This can be solved as a right triangle using the sine of 45 degrees, where: the change altitude (a) is the side opposite and the distance traveled in the dive is the hypotenuse (h) : We want the elevation change in feet. Change distance of the dive to feet traveled in 25 seconds: (3600 sec in 1 hr) h = * 25 = 9533.33 ft : sin(45) = a = sin(45)*9533.33 a = 6741.1 ft change in elevation therefore 12000 - 6741.1 = 5,258.9 ft altitude at the end of the dive
 Travel_Word_Problems/549209: A tire of a moving bicycle is 18 inches in radius. If the tire is making 3 rotations per second, find the bicycle's speed in miles per hour. What I have tried: Distance = 2 pi r 2 pi 18 = 2 pi in. 1 solutions Answer 357541 by ankor@dixie-net.com(15656)   on 2011-12-19 22:02:10 (Show Source): You can put this solution on YOUR website!A tire of a moving bicycle is 18 inches in radius. If the tire is making 3 rotations per second, find the bicycle's speed in miles per hour. : Find no. of inches traveled in 1 hr, divide by no. of inches in a mile. = 19.27 mph
 Triangles/549015: You are stationed at a radar base and you observe an unidentified airplane at an alititude of 6000 meters. The plane is flying towards the radar base at an angle of elevation of 30 degrees. After exactly one minute, the radar sweep reveals that the plane is now at an angle of elevation of 60 degrees and it is maintaining the same altitude. What is the speed of the plane in meters per second?1 solutions Answer 357465 by ankor@dixie-net.com(15656)   on 2011-12-19 16:52:40 (Show Source): You can put this solution on YOUR website! an unidentified airplane at an alititude of 6000 meters. The plane is flying towards the radar base at an angle of elevation of 30 degrees. After exactly one minute, the radar sweep reveals that the plane is now at an angle of elevation of 60 degrees and it is maintaining the same altitude. What is the speed of the plane in meters per second? : Use the tangent of the angle to find the distance (d) to a point directly below plane: when the angle is 30 degrees tan(30) = d1 = d1 = 10392.3 meters when the angle is 60 degrees tan(60) = d2 = d2 = 3464.1 meters : d1 - d2 = distance traveled by aircraft in 1 min 10392.3 - 3464.1 = 6928.2 m/min convert to m/sec = 115.47 m/sec :
 Miscellaneous_Word_Problems/548435: Doppler radar shows an electrical storm 2.5 miles away. If you see te lightning from this storm, how long will it be before you hear the thunder?1 solutions Answer 357093 by ankor@dixie-net.com(15656)   on 2011-12-18 07:32:49 (Show Source): You can put this solution on YOUR website!Doppler radar shows an electrical storm 2.5 miles away. If you see the lightning from this storm, how long will it be before you hear the thunder? : Using the speed of sound as 1100 ft/sec : = 12 sec
 Average/548538: I have a 92 on a quiz that is worth 5 percent of my grade what is the actual points I have for this quiz and how would I solve this type of problem to figure out my other points/grades? Thanks!1 solutions Answer 357050 by ankor@dixie-net.com(15656)   on 2011-12-17 21:54:38 (Show Source): You can put this solution on YOUR website!I have a 92 on a quiz that is worth 5 percent of my grade what is the actual points I have for this quiz and how would I solve this type of problem to figure out my other points/grades? : 5% really means it is only 1/20 of the grade, and example, say up to this quiz you have an 86 average, which is 95% of the grade; you want to know what affect this quiz of 92 will effect the overall average grade : Av = Av = Av = Av = 86.3, it will only raise the average .3 %
 Graphs/548482: Good afternoon, Hello i have homework on slope intercept equations and i needed help. Here's the problem it says 3x-2y=18 i have to put that in slope intercept form.1 solutions Answer 357048 by ankor@dixie-net.com(15656)   on 2011-12-17 21:09:53 (Show Source): You can put this solution on YOUR website!3x - 2y = 18 subtract 3x from both sides -2y = -3x + 18 Y has to be positive, multiply both sides by -1 2y = 3x - 18 y has to have a coefficient of 1, Divide both sides by 2 y = x - 9; the slope intercept form
 Radicals/548513: A picture frame measures 26 in. by 24 in.. There is 575 in. squared of picture showing. The frame is of uniform thickness. Find the thickness of the frame.1 solutions Answer 357042 by ankor@dixie-net.com(15656)   on 2011-12-17 19:55:05 (Show Source): You can put this solution on YOUR website!A picture frame measures 26 in. by 24 in.. There is 575 in. squared of picture showing. The frame is of uniform thickness. Find the thickness of the frame. : Let x = the width of the frame then (26-2x) by (24-2x) is the dimensions of the pictures, which is 575 sq/in therefore, the area equation: (26-2x)*(24-2x) = 575 FOIL 624 - 52x - 48x + 4x^2 = 575 Combine like terms to form a quadratic equation: 4x^2 - 100x + 624 - 575 = 0 4x^2 - 100x + 49 = 0 We can us the quadratic formula, but this will factor to (2x-49)(2x-1) = 0 two solutions, but only one will make sense 2x = 49 x = 49/2 x = 24.5", obviously this could not be the width of frame and 2x = 1 x = .5 inch is the reasonable width of the frame : : We can confirm this by finding the area using x=.1, then 2x = 1, so we have (26+1)(24+1) = 675 for the overall area, like was given
 Graphs/548484: Good afternoon, Hello i have homework on slope intercept equations and i needed help. Here's the problem it says line parallel to y= 3x=4 with the y- intercept of 10 i have to put that in slope intercept form.1 solutions Answer 357024 by ankor@dixie-net.com(15656)   on 2011-12-17 16:51:31 (Show Source): You can put this solution on YOUR website!Here's the problem it says line parallel to y= 3x+4 with the y- intercept of 10 i have to put that in slope intercept form. : Parallel lines have the same slope, therefore the equation for this equation is: y = 3x + 10 as you can see
 Rate-of-work-word-problems/548491: one pipe can fill a cooling tank in 3 hours less that a second pipecan.if the two pipes together can fill seven-ninths of the tank in 4 hours ,how many hours would it take each pipe alone to fill the tank1 solutions Answer 357023 by ankor@dixie-net.com(15656)   on 2011-12-17 16:39:34 (Show Source): You can put this solution on YOUR website!one pipe can fill a cooling tank in 3 hours less that a second pipe can. if the two pipes together can fill seven-ninths of the tank in 4 hours, how many hours would it take each pipe alone to fill the tank : Let p = one pipes filling time then (p+3) = another pipes filling time : Let a full tank = 1 : + = Multiply by 9p(p+3), results 9(p+3)(4) + 9p(4) = 7p(p+3) 36p + 108 + 36p = 7p^2 + 21p 72p + 108 = 7p^2 + 21p : combine like terms on the right 0 = 7p^2 + 21p - 72p - 108 7p^2 - 51p - 108 = 0; a quadratic equation You can use the quadratic equation here, but this will factor to: (7p + 12)(p - 9) = 0 the positive solution is all we want here p = 9 hrs time for one pipe alone and 12 hrs for the other pipe alone : : Let's check this out, using decimals + = .444 + .333 = .777 which is very close to 7/9
 Travel_Word_Problems/548415: after 30 minutes a car moving at a constant speed has traveled 25 miles. given that the distance varies directly as time, how far will the car travel in 140 minutes?1 solutions Answer 357019 by ankor@dixie-net.com(15656)   on 2011-12-17 16:22:05 (Show Source): You can put this solution on YOUR website!after 30 minutes a car moving at a constant speed has traveled 25 miles. given that the distance varies directly as time, how far will the car travel in 140 minutes? : = Cross multiply 140d = 30*25 30d = 140*25 30d = 3500 d = d = 116.67 miles : :
 Graphs/548384: Question: Write an equation for the points (-8,-2), (0,-2), (8,-2), which are plotted on the graph below. *I was provided a graph with the plotted points which I gave in my question above. Not sure how I would go about, even if possible, providing a graph for my question. Hope you understand my question and can help me. 1 solutions Answer 356971 by ankor@dixie-net.com(15656)   on 2011-12-17 08:55:57 (Show Source): You can put this solution on YOUR website!This is a horizontal line which is: y = 0x - 2, or just y = -2
 Miscellaneous_Word_Problems/548243: Suppose I can mow the lawn at the park by my house in 8 hours. It takes my neighbor 10 hours to mow he same lawn. If I started mowing at 8am, then he came and began helping me at 10am, what time would we finish mowing the lawn?1 solutions Answer 356928 by ankor@dixie-net.com(15656)   on 2011-12-16 21:00:16 (Show Source): You can put this solution on YOUR website!Suppose I can mow the lawn at the park by my house in 8 hours. It takes my neighbor 10 hours to mow he same lawn. If I started mowing at 8am, then he came and began helping me at 10am, what time would we finish mowing the lawn? : Let t = your mowing time then (t-2) = neighbor's mowing time : Let the completed job = 1 : + = 1 multiply by 40 to clear the denominators, results: 5t + 4(t-2) = 40 5t + 4t - 8 = 40 9t = 40 + 8 9t = 48 t = 48/9 t = 5 hrs or 5 hrs 20 min, working together You would finish at: 8:00 + 5:20 = 1:20 PM : : See if this checks out + = .67 + .33 = 1
 Percentage-and-ratio-word-problems/547925: My question: When five new girls joined a class, the percent of girls increased from 40% to 50%. What is the number of boys in the class? What I tried: 1.If there is 50% girls in the class, then there is 50% boys, so however many girls are in the class, is how many boys are in the class. 2.I said that the ORIGINAL total class accumulation, was 45 kids, because if there is 25 boys in the class, and 20 girls in the class, the boy population is 60%, and the girl's is 40%. However, I said that if I increase the girl population by 10%, I would need to add five girls, so now there is 25 girls, and 25 boys (50% boys and girls) What am I doing wrong? Can you help me solve it? 3. My teacher said this was incorrect, and I got a 5/10 on this problem; 3 for work, 1 for solution, and 1 for check. If you could help me, I would appreciate it! Thanks a lot!!!1 solutions Answer 356857 by ankor@dixie-net.com(15656)   on 2011-12-16 13:49:46 (Show Source): You can put this solution on YOUR website!When five new girls joined a class, the percent of girls increased from 40% to 50%. What is the number of boys in the class? : Use algebra to solve this: : Let g = original number of girls in the class Let b = no. of boys then (g+b) = original number in the class : Originally = .4, (40%) g = .4(g+b) g = .4g + .4b g - .4g = .4b .6g = .4b multiply 10 to get rid of the decimal 6g = 4b : Add 5 girls equation = .5 g + 5 = .5(g+b+5) g + 5 = .5g + .5b + 2.5 g = .5g + .5b + 2.5 - 5 g - .5g = .5b - 2.5 .5g = .5b - 2.5 get rid of the decimal, mult by 2 g = b - 5 replace g with (b-5) in the 1st equation (6g = 4b) 6(b-5) = 4b 6b - 30 = 4b 6b - 4b = 30 2b = 30 b = 15 boys in the class : : Check this: g = b - 5 g = 15 - 5 g = 10 girls originally then when 5 girls are added, it will be 15:15
 Miscellaneous_Word_Problems/548244: I have a tank that can be filled by a small pipe in 12 hours or by a large pipe in 8 hours. Suppose I start filling the tank with the large pipe for two hours. After that 2 hours is up, I use both pipes and continue filling the tank for a length of time, t. I then turn off the large pipe and it takes 2 more hours to fill the tank with just the small pipe. How long of a time is t?1 solutions Answer 356852 by ankor@dixie-net.com(15656)   on 2011-12-16 13:26:27 (Show Source): You can put this solution on YOUR website!I have a tank that can be filled by a small pipe in 12 hours or by a large pipe in 8 hours. Suppose I start filling the tank with the large pipe for two hours. After that 2 hours is up, I use both pipes and continue filling the tank for a length of time, t. I then turn off the large pipe and it takes 2 more hours to fill the tank with just the small pipe. How long of a time is t? : Let the completed task = 1 (a full tank) : from the given information: (t+2) = filling time of the large pipe and (t+2) = filling time of the smaller : + = 1 Multiply by 24, results: 2(t+2) + 3(t+2) = 24 2t + 4 + 3d + 6 = 24 2t + 3t = 24 - 10 5t = 14 t = t = 2.8 hrs ; : See if that checks out + = + = .4 + .6 = 1
 Triangles/548013: The figure below is an isosceles triangle. The altitude is 5 inches and the congruent sides are 8 inches. Find the length of the base to the nearest tenth of an inch. Show all work and explanations. I really dont understand this please help!1 solutions Answer 356818 by ankor@dixie-net.com(15656)   on 2011-12-16 11:25:17 (Show Source): You can put this solution on YOUR website!The figure below is an isosceles triangle. The altitude is 5 inches and the congruent sides are 8 inches. Find the length of the base to the nearest tenth of an inch. : we can use pythag, a^2 + b^2 = c^2 a = 5 b = the base c = 8 : 5^2 + b^2 = 8^2 25 + b^2 = 64 b^2 = 64 - 25 b^2 = 39 b = b = 6.245 * 12.5 inches is the base
 Geometry_Word_Problems/547933: Please help me solve this problem. The sum of the measures of the complement and supplement of an angle is 214 to the 0 power. Find the measure of the angle.1 solutions Answer 356712 by ankor@dixie-net.com(15656)   on 2011-12-15 21:55:16 (Show Source): You can put this solution on YOUR website!The sum of the measures of the complement and supplement of an angle is 214 to the 0 power. Find the measure of the angle. : I think you mean degree here, not 214^0, any no. ^0 is equal to 1 and that would not make sense : let a = the angle then (90-a) = the complement and (180-a) = the supplement ; These are given as = to 214, therefore we have: (90-a) + (180-a) = 214 Combine like terms 270 - 2a = 214 -2a = 214 - 270 -2a = -56 a = a = +28 degrees
 Mixture_Word_Problems/548035: Can you please help me solve this problem? "A chemist mixed a 20% alcohol solution with a 12% alcohol solution to obtain 200mL of a 15% alcohol solution. How many mL of the 20% solution did he use?"1 solutions Answer 356711 by ankor@dixie-net.com(15656)   on 2011-12-15 21:47:33 (Show Source): You can put this solution on YOUR website!A chemist mixed a 20% alcohol solution with a 12% alcohol solution to obtain 200mL of a 15% alcohol solution. How many mL of the 20% solution did he use?" : Let x = amt of 20% solutions required It states the results should be 200 ml, therefore (200-x) = amt of 12% required : Write a decimal equiv mixture equation : .20x + .12(200-x) = .15(200) .20x + 24 - .12x = 30 .20x - .12x = 30 - 24 .08x = 6 x = x = 75 ml of 20% solution : : Check this (200-75=125 ml of 12%) .20(75) + .12(125) = .15(200) 15 + 15 = 30; confirms our solution
 Age_Word_Problems/547982: If x units of a product costs C dollars to manufacture and earn revenue of R dollars, the value of x where the expressions for C and R are equal is called the break-even quantity, the number of units that produce zero profit. Find the break-even quantiry when C=14x + 28000 and R=16x1 solutions Answer 356710 by ankor@dixie-net.com(15656)   on 2011-12-15 21:39:11 (Show Source): You can put this solution on YOUR website!Find the break-even quantity when C=14x + 28000 and R=16x : This isn't hard, if R = C. we have: " 16x = 14x + 28000 16x - 14x = 28000 2x = 28000 x = 14000