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Question:These are really hard word problems for extra credit for my Algebra 2 class. A lot are about geometry. I'm usually really good at math I just can't figure these out. Answers to any of them would be helpful.
1. If the number 86 in base ten is represented as 321 in base b, what is the baseten representation of the number 123 in base b?
2. A right triangle with integer side lengths a, b, and c satisfies a
Answers:Wow, what the heck kind of evil math class is this??? 3. Positive integer pairs that multiply to 72: 1*72 2*36 3*24 4*18 6*12 8*9 Solving c^2  a^2  b^2 = 101 for c, you get c = sqrt(a^2 + b^2 + 101) Thru trial & error (I actually used a spreadsheet), you find the a, b pair to be 4 & 18, and c = 21. So a + b + c = 4 + 18 + 21 = 43 4. x = number of boys that passed = number of girls that passed Total number of boys = b, so 2/3*b = x, therefore b = 3/2*x Total number of girls = g, so 3/4*g = x, therefore g = 4/3*x Total number of kids who passed = x + x = 2x (that is boys that passed plus girls that passed) Total number of kids = b + g = 3/2*x + 4/3*x = 9/6*x + 8/6*x = 17/6*x Fraction of kids who passed = number of kids who passed/total number of kids = 2x/(17/6*x) [the x's cancel out] = 2/(17/6) = 12/17. Twelve seventeenths of the kids passed. ************************** EDIT: Okay, I'm going to do another, these questions are just bugging me. 6. The answer is 3, there are 3 distinct real numbers that have this property. They are 0, 5 & 10. Before I prove this, here are a few definitions. Median is the middle number of a set. So if I have 12, 2, 16, 4, 9, then 9 would be the median because half the numbers are higher & half the numbers are lower. If two numbers are the same, one can still be the median. So if I have 1, 3, 3, 7, 8, then 3 is the median. Mean is your typical average, add up the numbers & divide by the number of numbers. There were 5 numbers in my first example, so mean = (12 + 2 + 16 + 4 + 9)/5 = 8.6. In your question, the equation you will always have is median = mean, or median = (x + 1 + 4 + 6 + 9)/5 or median = (x + 20)/5. So you will get a distinct x every time you have a different median. If x is equal to or less than 4, your median is 4 because your 1 & x will be less than or equal to 4 & 6 & 9 will be greater. That gives you one distinct x [4 = (x+ 20)/5 so x = 0]. If x is equal to or greater than 6, your median is 6, this gives you a second distinct x [6 = (x+20)/5, so x = 10]. The third case is if x is between 4 & 6, or 4
Answers:Wow, what the heck kind of evil math class is this??? 3. Positive integer pairs that multiply to 72: 1*72 2*36 3*24 4*18 6*12 8*9 Solving c^2  a^2  b^2 = 101 for c, you get c = sqrt(a^2 + b^2 + 101) Thru trial & error (I actually used a spreadsheet), you find the a, b pair to be 4 & 18, and c = 21. So a + b + c = 4 + 18 + 21 = 43 4. x = number of boys that passed = number of girls that passed Total number of boys = b, so 2/3*b = x, therefore b = 3/2*x Total number of girls = g, so 3/4*g = x, therefore g = 4/3*x Total number of kids who passed = x + x = 2x (that is boys that passed plus girls that passed) Total number of kids = b + g = 3/2*x + 4/3*x = 9/6*x + 8/6*x = 17/6*x Fraction of kids who passed = number of kids who passed/total number of kids = 2x/(17/6*x) [the x's cancel out] = 2/(17/6) = 12/17. Twelve seventeenths of the kids passed. ************************** EDIT: Okay, I'm going to do another, these questions are just bugging me. 6. The answer is 3, there are 3 distinct real numbers that have this property. They are 0, 5 & 10. Before I prove this, here are a few definitions. Median is the middle number of a set. So if I have 12, 2, 16, 4, 9, then 9 would be the median because half the numbers are higher & half the numbers are lower. If two numbers are the same, one can still be the median. So if I have 1, 3, 3, 7, 8, then 3 is the median. Mean is your typical average, add up the numbers & divide by the number of numbers. There were 5 numbers in my first example, so mean = (12 + 2 + 16 + 4 + 9)/5 = 8.6. In your question, the equation you will always have is median = mean, or median = (x + 1 + 4 + 6 + 9)/5 or median = (x + 20)/5. So you will get a distinct x every time you have a different median. If x is equal to or less than 4, your median is 4 because your 1 & x will be less than or equal to 4 & 6 & 9 will be greater. That gives you one distinct x [4 = (x+ 20)/5 so x = 0]. If x is equal to or greater than 6, your median is 6, this gives you a second distinct x [6 = (x+20)/5, so x = 10]. The third case is if x is between 4 & 6, or 4
Question:I have two really hard math problems. Well, not hard but confusing.. They gave me the answers and I had to show the processes, so please just put the process that you did to get to the answer... Thanks:)
1. Chariot races reached their peak in popularity in ancient Rome around the 1st and 2nd centuries A.D. A chariot wheel had a radius of about one foot. One lap around the track in the Circus Maximus was approximately 2,300 feet. How many chariotwheel revolutions did it take to complete one lap? the answer is 366 feet, but i dont know how to get to it...
2. One of the artistic traditions of Tantric Buddhism is dultsonkyilkhor, which is creation of intricately designed prayer circles (called mandalas) using colored sand. The sand is funneled through a hollow metal tube about 0.5 centimeter in diameter. If the prayer circle were a meter across, approximately how many funneltips of sand would be needed to cover its surface
Thank you so much!
Answers:1) 2(pi)r = circumference of wheel = 6.28 feet. which means the chariot travels 6.28 feet per revolution track = 2300 feet. 2300/6.28 = 366.24 revolutions. be sure to get the units right. it's not 366 feet but 366 revolutions. 2) 1 meter across = diameter. Therefore the radius is half that 0.5 m x 100 = 50 cm area of a circle is (pi)r^2 so (3.14...)(50)^2 = 7854 square centimeters is the area of the prayer circle. same process for the metal tube (pi)(.5)^2 = .7854 (That number is familiar) So now it's the area of the prayer cicle divided by area of funnel tips . 7854/.7854 = 10,000 funnel tips.
Answers:1) 2(pi)r = circumference of wheel = 6.28 feet. which means the chariot travels 6.28 feet per revolution track = 2300 feet. 2300/6.28 = 366.24 revolutions. be sure to get the units right. it's not 366 feet but 366 revolutions. 2) 1 meter across = diameter. Therefore the radius is half that 0.5 m x 100 = 50 cm area of a circle is (pi)r^2 so (3.14...)(50)^2 = 7854 square centimeters is the area of the prayer circle. same process for the metal tube (pi)(.5)^2 = .7854 (That number is familiar) So now it's the area of the prayer cicle divided by area of funnel tips . 7854/.7854 = 10,000 funnel tips.
Question:Amy paid $89.58 for a pair of running shoes during a 20% off sale, what was the regular price of the shoes___________?
Answers:First set up an equation. If you set up an equation where X is equal to the regular price of the shoes you will get something like this... x.20x=89.59 As you can see X is the original price and if you multiply the original price times 20%(.20) you will get the amount that was taken off the original price and if you subtract such values from X you will get 89.59. All you have to do now is solve for X and you will get the original price of the shoes. x.20x=.80x (remember that it is assume there is a 1 in front of x) Your equation turns into .80x=89.59 X=$111.99 Dollars, this is the original price of the shoes
Answers:First set up an equation. If you set up an equation where X is equal to the regular price of the shoes you will get something like this... x.20x=89.59 As you can see X is the original price and if you multiply the original price times 20%(.20) you will get the amount that was taken off the original price and if you subtract such values from X you will get 89.59. All you have to do now is solve for X and you will get the original price of the shoes. x.20x=.80x (remember that it is assume there is a 1 in front of x) Your equation turns into .80x=89.59 X=$111.99 Dollars, this is the original price of the shoes
Question:I have a math test today and Im trying to study but I cant figure out the set up for this math problem can anyone help out? I dont need you to solve it, I just need the set up, thanks ahead!
The sum of three numbers is 45. One number is ten more than a second number. It is also twice the third. Find the numbers.
Answers:The sum of three numbers is 45: x + y + z = 45 One number is ten more than a second number: x = y + 10 It is also twice the third: x = 2 * z
Answers:The sum of three numbers is 45: x + y + z = 45 One number is ten more than a second number: x = y + 10 It is also twice the third: x = 2 * z
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Really hard math problem :SOOOOOOO hard
Super hard math problem :When I ll think you re desperate I ll post the soloution.