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The longer side of a rectangle should be on the side BC.

Try comparing them in pairs from the top down.

A = 100^500 = (100^400) * (100^100)  

B = 200^400 = (100^400) * (2^400) = (100^400) * (16^100) < A

So B is less than A

B = (100^400) * (16^100) = (100^300) *(100^100) * (16^100) = (100^300) *(1600^100) 

C =  300^300 = (100^300) * (3^300) =  (100^300) * (27^100) < B

So C is less than B

And you can do the others.

It might be easier to compare them from the bottom up but it is still the same basic method.

(5*6*5 )/ 3!     divided by    13C3

The probability is 7/26.

My above answer is incorrect!!!  I'll give it a try again.

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Let triangle ABC be a right triangle such that B is a right angle. A circle with a diameter of BC meets side AC at D. If the area of ABC is 180 and AC = 35, then what is BD?

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AC = 35       [ABC] = 180 u²

BD = (180 * 2) / 35 

I edited it, so it should be right now!

If you decide to list all of them,

You would get 27(As Guest said)

But there is an easier way, 

The first digit has three possibilities; it can either be a 2 a 5 or an 8. 

The second digit has three possibilities; it can either be a 2 a 5 or an 8.

The third digit has three possibilities; it can either be a 2 an 8 or a 5.

So \(3*3*3=27 \) possible integers.

Total Permutations =3^3 = 27

{2, 2, 2} | {2, 2, 5} | {2, 2, 8} | {2, 5, 2} | {2, 5, 5} | {2, 5, 8} | {2, 8, 2} | {2, 8, 5} | {2, 8, 8} | {5, 2, 2} | {5, 2, 5} | {5, 2, 8} | {5, 5, 2} | {5, 5, 5} | {5, 5, 8} | {5, 8, 2} | {5, 8, 5} | {5, 8, 8} | {8, 2, 2} | {8, 2, 5} | {8, 2, 8} | {8, 5, 2} | {8, 5, 5} | {8, 5, 8} | {8, 8, 2} | {8, 8, 5} | {8, 8, 8} (total: 27)

3 * x = 4        x = 1.3333333334

A = 8x  = 10 ²/₃

Is there a general way to solve problems like  ?

Hello Guest!

Click the link. It is well explained there.

97 = 6 + 13 D, solve for D

D = 7 - this is the common difference

So, your sequence begins like this:

6, 13, 20, 27, 34, 41..........and so on. Just add 7 to each term after the first.

The rule is: a(n) =7n - 1 . The rule is very simple. Just sub 1, 2, 3, 4, 5.......etc. for n and you get the term that you want.

1/   Using the law of cosines find angle A.

2/   Using angle A and side AC, calculate sides AD and CD

3/   [ACD] = 1/2(AD * CD)

Given positive integers x and y such that x not equal to y and 1/x + 1/y = 1/20, what is the smallest possible value for x + y?    

We need to have a total that will reduce to 1/20.  2/40 won't work because that requires x and y to be the same. 

How about 60.  3/60 will break up into 2/60 + 1/60 which adds to 3/60 but that has both x and y being 60.

So reduce 2/60 to 1/30.  Now x and y are different. 

              1          1            3           1  

So        –––  +  –––   =   –––   =   –––  

             30        60          60          20          This arrangement makes x + y = 90  

_.

The center of the circle is (5/2,15/2), and the radius is 5/sqrt(2).  So by power of a point, the length of the tangent is 7*sqrt(3).

By Hamilton's Theorem, the solutions are z = 4^{1/4}*e^(pi*i/4), 4^{1/4}*e^(pi*i/4 + pi/4), 4^{1/4}*e^(pi*i/4 + 2*pi/4), and 4^{1/4}*e^(pi*i/4 + 3*pi/4).  Since 4^{1/4} = sqrt(2) and e^(pi*i/4) = (1 + i)/sqrt(2), the first solution is 1 + i.  Then the other roots work out as

4^{1/4}*e^(pi*i/4 + pi/4) = 1 - i,

4^{1/4}*e^(pi*i/4 + 2*pi/4) = -1 - i, and

4^{1/4}*e^(pi*i/4 + 3*pi/4) = -1 + i.

Powers of 2 =(-9, -8,  -7, -6, -5, -4, -3, -2,  -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)=19

Powers of 3=(-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6)=13

Power of 5=(-4, -3, -2, -1, 0, 1, 2, 3, 4)=9

Powers of [2, 3, 5]=19 + 13 + 9 =41 rational numbers can be written as powers of 2 or 3 or 5.

Suppose that we have a right triangle ABC with the right angle at B such that AC = sqrt(89) and AB = 5. A circle is drawn with its center on AB such that the circle is tangent to AC and BC. If P is the point where the circle and side AC meet, then what is CP?

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CP = BC

BC = sqrt(AC² - AB²) = 8

The question should be: What is the length of a radius OP?

The probability is 5/36.

I'm getting an answer of 11/5.

So there are 226 numbers because 250-25+1=226.

The squares 5-15 fit between 25 and 250.

Also the cubes 3-6 fit.

So we get 11+4=15.

But 64 is a square and a cube.

So we get 15-1=14.

We can subtract 226 by 14 to get an answer of 212.

Nice job catmg!

The ambulance has 20 miles to travel and goes at 40 mph so it would take 30 minutes to go to the hospital
A helicopter has to go 15 miles to get to the hospital and goes at 1 MPH so it'd take 15 minutes but it takes 3 minutes for takoff and landing which would be added to a sum of 6. The helicopter then would take 15+6 minutes which is 21, 30-21 you get 9 
So 9 minutes is the answer
Hope this helps!