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8.5 hr   x    12 lines  x   8 people/hr/line =       8.5  *  12 * 8  people = .......

this guy is posting some random stupid stuff that i dont even know what he means. here is the real answer, i have tested this on my aops and it works. 

the answer is basicly 141. want to see how i got it?

well, kinda cheated as well, i used fusion 360, i's a good way to cheat aops geometry problems, seriously. for some reason cant upload screenshots here. but just trust me on this

Is a class rank of 27 out of 136 college students considered good? 

It's in the lower 20% so the answer is No.   

_.

I'm sorry I don't have a proof for you, but I just looked at it and recognized that x = 4 will work. 

_.

For someone who is asking other to determine their judgement of themselves, then I can assume you are a very dependable person and you cannot make judgement by yourself.

As long as you are in the top 50%, then it is considered good. Otherwise, it depends on what you define as "good".

Something is missing from your problem.

hey guest!
 

latex is pretty hard, but once you get the hang of it, it becomes really easy!

here's a mini guide to latex!

first of all, always surround your latex with dollar signs! cause that's what makes it latex!

to make letters look fancy like this: \(x\), just surround the letter with $ signs. so, the latex for that is $x$.

to make fractions like this: \(\frac{1}{2}\), do $\frac{x}{y}$ where x is the numerator and y is the denominator!

to make square roots like this: \(\sqrt{2}\) , do $\sqrt{x}$ where x is the value inside of the square root

to make powers like this: \(2^3\), do $2^3$

i'd say those are the basics for latex and the most commonly used ones! 

i hope this helped u! :)

if u need help with any other latex stuff, i'd be glad to help!

Because Brennan has the lightest bars, and Maya has the heaviest bars, the average weight of Blair's bars must be between their amounts. We can then write an inequality and solve it. Set the total weight as w and the number of bars Blair received as x. 

Average weight = Total weight/Number of bars

So Brennan's average weight = 0.45W/24

And Maya's average weight = 0.26W/13

Since the rest of the bars are given to Blair, she must have (1-0.45-0.26)W as her total weight.

Blair's average weight = 0.29W/x

Now we write our inequality:

\(\frac{0.45W}{24} < \frac{0.29W}{x} < \frac{0.26W}{13}\)

We can divide everyone by W. 

\(\frac{0.45}{24} < \frac{0.29}{x} < \frac{0.26}{13}\)

Then split it into two equations.

\(\frac{0.45}{24} < \frac{0.29}{x}\) and \(\frac{0.29}{x} < \frac{0.26}{13}\)

Simplify by cross-multiplying to get:

\(0.45x<0.29*24\) and \(0.26x>0.29*13\)

Isolate x to get:

x < 15.47 and x > 14.5

14.5 < x < 15.47

The only integer value that satisfies this is 15, which is our final answer.

If a quadratic has no real roots, the discriminant \(b^2-4ac\), where a=1, h+2=b and h+5=c, is less than 0. 

So let's plug in our values.

\((h+2)^2-4(h+5)<0\).

Expand:

\(h^2+4h+4-4h-20<0\)

Simplify by combining like terms:

\(h^2-16<0\)

This can be factorized into:

\((h+4)(h-4)<0\)

This can only happen when one is positive, and one term is negative. h+4 is obviously greater than h-4, so h+4 must be the positive one.

\(h+4>0\)  and  \(h-4<0\)

\(h>-4\)  and  \(h<4\).

Combine to get \(-4 < h < 4\)

Since h is the greatest positive integer, the answer is 3. 

Nice answer Geno :)

105 = 5*7*3

14=2*7

common factors are 7 and -7 and 1 and -1

Find the product of those.

We write the equation in 3x-7y=21 first. 

3x-7y=21

7y=3x-21

y=3/7x-3

To find the x-intercept, we plug in the value 0 for y.

0=3/7x-3

3/7x=3

x=7

To find the y-intercept, we plug in the value 0 for x.

y=3/7(0)-3

y= -3

The x-intercept is (7,0) and the y-intercept (0, -3).

To find the distance, we plug the points into the distance formula.

\(\sqrt{(7-0)^2+0-(-3)^2}\\ \sqrt{49+7}\\ \sqrt{58}\\ \)

Therefore the distance between the x and y intercept is \(\boxed{\sqrt{58}}\).

This could help: https://artofproblemsolving.com/wiki/index.php/LaTeX.

I picked up LaTeX because it was much more helpful to learn it for a math class I had to take. I learned it as classes went on, and picked up more symbols, etc. I would just say time is the main factor for learning.

This is what I did:

1)  I looked at triangle(BAP) and used the Law of Cosines to find angle(BAP).

     I set the length of AB = x.

     BP²  =  AP² + AB² - 2·AP·AB·cos( BAP )

        3²  =  1² + x² - 2·1·x·cos( BAP )

          9  =  1 + x² - 2x·cos( BAP )

         ( 8 - x² ) / ( -2x )  =  cos( BAP )

          cos( BAP ) =  ( x² - 8 ) / (2x )

2)  Then, I looked at triangle(DAP) and used the Law of Cosines to find angle(DAP).

     Since it's a square, AD = x.

     DP²  =  AP² + AD² - 2·AP·AD·cos( DAP )

        7²  =  1² + x² - 2·1·x·cos( DAP )

         49  =  1 + x² - 2x·cos( DAP )

         ( 48 - x² ) / ( -2x )  =  cos( DAP )

          cos( DAP ) =  ( x² - 48 ) / (2x )

3)  Since angle(DAP) = 90^o - angle(BAP)   --->   cos( DAP )  =  sin( BAP )

                      --->   sin( BAP )  =  ( x² - 48 ) / (2x )

4)  Since  sin²( BAP ) + cos²( BAP )  =  1

                [ ( x² - 48 ) / (2x ) ]²  +  [ ( x² - 8 ) / (2x ) ]²  =  1

           [ ( x⁴ - 96x² + 2304 ) / ( 4x² ) ]  +  [ ( x⁴ - 16x² + 64 ) / ( 4x² ) ]  =  1

multiplying both sides by 4x²:

            ( x⁴ - 96x² + 2304 )  +  ( x⁴ - 16x² + 64 )  =  4x²

                 2x⁴ - 116x²  + 2368  =  0

But this doesn't have any real solutions?

Where did I mess up?

Thanks very much guest.  

It is not as easy as the other one that I did.

(this is 228 not 288)

So I am still at a loss.

It does equal   (10/15 * 0.01) base  12     ....    to me that looks recurring.  I really do not know.

oh nooo

When your spacebar is broken, use periods or virgules or something to separate the words. 

_.

1)  Find BC (use the Law of Cosines)

2)  Find angle(DCB) (use either Law of Sines or Law of Cosines)

3)  Find angle(ACE)

4)  Find angle(CAE)

5)  Find AE.

It is: 1/4  NOT  1/14.

Using the midpoint formula, we find that the midpoint of the first segment is

\((\frac{2+0}{2}, \frac{4-2}{2})\)=\((\frac{2}{2}, \frac{2}{2})\)=\((1, 1)\)

The midpoint of the second segment is 

\((\frac{5+1}{2}, \frac{1+5}{2})\)=\((\frac{6}{2}, \frac{6}{2})\)=\((3, 3)\).

Using the slope formula, we find that the slope of the line with points \((1, 1)\) and \((3, 3)\) is:

\(\frac{3-1}{3-1}=\frac{2}{2}=1\)

Let's say there are x teams. 

Each team captain shakes hands x-1 times (everyone except themselves). There are x team captains so there are x(x-1) handshakes. However, we have to divide by two because for one handshake, we counted twice- once for each person shaking hands. So in all, there are x(x-1)/2 handshakes.

This equals 595 so x(x-1)/2=595

x(x-1)=595*2

\(x^2-x-595*2=0\)

Prime factorizing 595*2 = 2*5*7*17*= 34*35

So we can factorize as (x-35)(x+34)=0

We get two solutions, 35 & -34. Since the number must be positive, the answer is 35. 

Set our number as x and turn the words into math:

\(\frac{1}{4}x=3*19\)

\(x=3*19*4\)

\(\frac{1}{6}x=\frac{3*19*4}{6}\)

\(\frac{1}{6}x=38\)