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Heron's: \(\sqrt{s(s-a)(s-b)(s-c)}\), where \(s\) is the semiperimeter and \(a,b,c\) are the sides. The semiperimeter can be found by \(\frac{A+B+C}{2}=\frac{4+6+8}{2}=\frac{18}{2}=9.\) Now, we have \(\sqrt{9(9-4)(9-6)(9-8)}=\sqrt{9*5*3*1}=\sqrt{135}=3\sqrt{15}.\)

Make f(x)=g(x), so -x^2+4x+1=x+1, s=0, x=3. Select 0 and 3.

This will result in an irrational number

10 + 1/10 =  11/10

10 + 10/11 = 120/11

10 + 11/120 = 1211/120

10 + 120/1211 = 12230/1211

5 + 1211/12230 ≈  5.099....   =  √26

thank so much

Last one, then I have to go.

We have \(y=x^2-6x+8\) and \(y=-2x+5\) . We know that both equations are the same, since we have found \(y\) in terms of \(x.\) Therefore, \(x^2-6x+8=-2x+5\) . This time, by factoring we get \(x=1, x=3,\) so when \(x=1\), \(y\) equals   \(y=-2(1)+5=-2+5=3\) and when \(x=3, \) \(y\) equals \(y=-2(3)+5, y=-6+5, y=-1.\) Thus, the ordered pair is \(\boxed{(1,3), (3,-1)}.\)

Here a very short computer code to calculate it for you:
c=1E100; listforeach(b,reverse(5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10), c=b + 1/c);printc
c=5.0990195135 9278483002 8224^2 =26. So, the continued fraction is the square root of 26.

We have \(9x, 10y, -9y, 10\), so our like terms are  \(10y, -9y\) or the first option. (A). 

I think I can convert this into LaTex. Does it look like this \(\left(\frac{\left(-\frac{3}{5}+\frac{1}{10}\cdot \:3\right)}{\left(\frac{\frac{9}{20}}{\left(-\frac{1}{4}-\frac{1}{5}\right)}\right)}\right)-\frac{3}{4}-\frac{\frac{2}{5}}{\frac{\left(\frac{1}{20}-\frac{1}{4}\right)}{\left(-\frac{5}{6}-\frac{1}{13}\left(\frac{5}{4}-\frac{1}{6}\right)\right)}}\) . Sorry, it's a bit hard to read. First, try to start from the bottom.

I think you mean: \(y=x^2-5x-6\) and \(x+y=-3.\) Taking \(x\) to the other side in our second equation, we have \(y=-3-x\) . This means \(-x^2-5x-6=-3-x\), so by using the quadratic formula, we get \(x=-3,\:x=-1.\) . 

From here, first by plugging \(x=-3\) in the second equation to solve for \(y\), we get      \(​​-3+y=-3, y=-3+3, y=0.\) Consequently, by plugging in \(x=-1\)\(\), we get    \(-1+y=-3, y=-3+1, y=-2.\) Finally, our two ordered pairs are \(\boxed{(-3,0), (-1,-2)}\) , so (A) or the first option. 

We have these three digit numbers

102, 109, 120, 129, 190, 192, 201, 209, 210, 219, 290, 291,901, 910, ,902, 912, 920, 921

And their average is    =   429 1/3

2+0+1+9 divide by how many there are which is 4

 so answer is 3

All of angles are interior angles, right?

So, \(x+(2x+4)+60=180, 3x+4=120, 3x=116, x=\frac{116}{3}.\)

joe paid=x

mary paid=x

m=j+2, joe paid: 2/5j-1 and mary paid 1/3(j+2). Now, we have an equation: 2/5j-1=1/3j+2/3, 1/15j=1 2/3, so j=5/3*15, j=25.

So, Mary paid 25+2=$27. Thus, the answer is $25+$27=$52.

Sorry, I think I need to say that ABCD must be a quadrilateral. Is it always true when that is the case?

We need to find the constant of proportionality, k

b(x)  = k * x        and we  know that

4325 = k * 25         divide both sides by 25

k = 173

So when x = 19

b(x) = 173 * 19 = 3287

http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

6 laps / 5 1/3 laps =12.5% is runner B faster than runner A.

If runner B run a mile in 7.5 minutes, then:

7.5 x 1.125 =8.4375 - minutes for runner A to run a mile.

8.4375 - 7.5 =0.9375 - minutes longer that takes runner A to run a mile.

0.9375 x 60 =56.25 seconds longer for runner A to run the same mile.

See the following:

Let the amount Joe had =J
Let the amount Mary had =J+$2
1/3(J+2) =2/5J -  1, solve for J
J = $25 - the amount Joe started with
$25 + 2 =$27 - the amount Mary started with
$25 + $27 =$52 - they had together.

could i use quadratic equation ?

What do you call a deer with no legs or eyes?

Still no Idea

(its still, it can't move)

so so. You?

Fraction of red paint = (3/5)/(16/3) = 9/80.

Yes that is right, what is the problem ?

55( mod 34) also equals 21