tertre

Converting feet to inches, we have 2.5*12=30 inches. This is for the front wheel, while the back wheel's radius is 4 inches. Revolutions come hand in hand with the circumference, so we have 2*30*pi=60pi for the front wheel and 2*4*pi=8pi for the back wheel. Now, when 60pi=100 then by indirect proportion \(\frac{60*100}{8}=\boxed{750} \) revolutions. 

Add the first two equations: 3y-2z=-8

y+z=-1

Now, multiply the second equation by 2, so 2y+2z=-2. Then, subtract the first equation from the second: y=-8+2, y=-6.

-6+z=-1, z=-1+6=5

And, x equals 3x+3(-6)=3, 3x-18=3, 3x=21, x=7.

Thus, the answer is \((x,y,z)=(3,-2,1).\)

We have \(\frac{x+y}{xy}=\frac{1}{12}, 12(x+y)=xy\) . \(12x+12y=xy\) . Try to plug in numbers!

We have HCF * LCM= 6 * 60=360. So, the numbers 12 and 30 work! 

Also, the last questions was posted here: https://web2.0calc.com/questions/help_81210

Oh, I get what PM means. We have \(\frac{\pi*r^2}{4},\frac{9\pi}{4}.\)

No problem! 

Just a few combinations would work...I'll try to create a solution...

1 step: Rectangle has 2 vertical and 2 horizontal lines.

You want to pick 2 vertical lines from the figure and two horizontal lines from the figure. 

The side lengths are 2004 * 3(increased by 1), so we have 2004C2 * 3C2, the choose function means combinations. 

Now, we have to get the non-shaded area, so is it 2*1002C2*3C2? Idk, can someone confirm

This is just complementary counting, so it is 1-X, the result. Is the answer \(\boxed{\frac{1002}{2003}}?\)

I'll try to confirm this later.

We have \(xy-x+y=39\) . By inspection, that both are relatively prime, as stated in the problem.Thus, we have \(x=11, y=5\), so their sum is    \(11+5=\boxed{16}.\)

This sounds kind of hard, CPhill's answer seems perfectly fine to me.

Right off the bat, we see that 164 and 37 are relatively prime, We also see that 164 is 21 less than a multiple of 37. So, we can switch, 37y+164x=1, and 164 is 15 less than a multiple of 37, so 37y+185x-21x=1, 37y+185x=1+21x. Now, we can factor out 37, yielding us with 37(5x+y)=1+21x. So, 1+21x has to be a multiple of 37. So, x can be 21x+1=148, 21x=147 and x=7. Substituting it back, we see that \(y=\frac{-1147}{37}=-31.\) Thus, the answer is \(\boxed{(7,-31)}.\)