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The radius is 5*sqrt(2).

By Pythgagoras, the hypotenuse is 2*sqrt(95).

I 2x + 2y = 38

is it 10!*8!*2 = 292,626,432,000

Recall that in a 30-60-90 triangle, the hypotenuse is double the length of the shortest side. 

This means that one side of the triangle is 12 units, meaning the total perimeter is \(12 \times 3 = \color{brown}\boxed{36}\)

https://web2.0calc.com/questions/parabola_149#r1

Multiplying the entire equation by \(x^2 + 5x - 24 \) gives us: \((x + 8)C + (x-3)D = 4x - 25\). Note that \(x^2 + 5x - 24 = (x - 3) ( x+8)\)

Expanding the left-hand side gives us: \(Cx + 8C + Dx - 3D = 4x - 25\). 

Note that the only 2 terms with x in them must sum to 4x, so we have the equation: \(Cx + Dx = 4x \), meaning \(C + D = 4\)

Also note that the only 2 constants must sum to -25, giving us the equation: \(8C - 3D = -25\).

Now, we have the following system: 

\(8C - 3D = -25\) 

\(C + D = 4\)

However, solving this system yields \(C = -{13 \over 11}\) and \(D = {57 \over 11}\). 

Thus... there are no integer solutions, and no product as well....

Here is the WA link: https://www.wolframalpha.com/input?i2d=true&i=Divide%5BC%2Cx+-+3%5D+%2B+Divide%5BD%2Cx+%2B+8%5D+%3D+Divide%5B4x+-+25%2CPower%5Bx%2C2%5D%2B5x+-+24%5D

sumfor(n,251, 450, 2*n - 1)==140,000

The answer is 7 days.

Note that \(\sqrt {27} = \sqrt 9 \times \sqrt 3 = 3 \sqrt 3 \), \(\sqrt{12} = \sqrt 4 \times \sqrt 3 = 2 \sqrt 3\), and \(\sqrt{300} = 10 \sqrt 3\).

Can you take it from here?

192.50  x  1.20 ==$231.00 price of the watch after 20% markup.

231 x  [100 - 60] / 100 ==$92.40 - discount price of the watch.

Using a CPhill diagram, we have: 

D

  \(25^ \circ\)

9

   \(90^ \circ\)

E                       F

Recalling sah cah toa, we realize the only way to find side \(EF\) is by using either tan or cos. But, notice that cos uses the hypotenuse, which we don't know. This means that we have to use tan. 

So, taking the tan of \(\angle D\), we have: \(\tan(25) = {EF \over 9} \), meaning \(EF = 9 \times \tan(25) \approx \color{brown}\boxed{4.2}\)

Plug in \(x = -5\) into the first equation. Because it is a root, this equation will be true. 

Solving for p gives us: \(p = 7\). 

Now, plugging this in the second equation gives us: \(7x^2 + 7x + k = 0 \)

For the equation to have 1 solution, the discriminant must equal 0. 

Can you take it from here?

ok

367^367^367   mod11

= 367^(367^367)    mod11

= 4^(4^4)                mod11

= 4^ 256                 mod11

= 4^ 3                     mod11

=  64                      mod11

=   9                       mod11

1/2(1/3A)-21

1/6A-21

1/6A-21=2/3A-162
-21+162=2/3A-1/6A

141=(4A-1A)/6

141=3/6A

141=1/2A

A=141*2

A=282
red = 1/6A-21

      = 1/6(282)-21

      = 47-21

      = 26

The number of red bean bags were there in the basket is 26

I get the following last 4 terms:

3, 5, 2, - 3 ==7 as the sum of 2014 terms of this sequence.

x - x/6 = 5x/6

1/5 * (5x/6 - 30) = x/6 - 6

(5x/6 - 30) - (x/6 - 6)

5x/6 - 30 - x/6 + 6

$(4x/6 - 24)

$(4x/6 - 24) = $236

4x/6 - 24 = 236

4x/6 = 236 + 24 = 260

x = (260 * 6)/4

x = 340

= 390/6 - 6 = $59

$390/6 - $59 = $6

(a) $59

(b) $6

If this were my question, the first thing I would do is expand it out.

Have you done that?  What did you get?

The answerer got it with a little computer program that they wrote.

I can never remember whether

2^3^4    means     2^(3^4)      or      (2^3)^4

Just do it one bit at a time.

Let f(x) = (x - 1)/(x + 1). Compute f(f(f(5))).

f(5)=(5 - 1)/(5 + 1) = 4/6  =  2/3

\(f(f(5)) = f(\frac{2}{3}) \\ =\frac{ (\frac{2}{3}-1) }{ (\frac{2}{3}+1) }\\~\\ =\frac{ \frac{-1}{3} }{ \frac{5}{3} }\\~\\ =\frac{-1}{5}\\~\\ f(f(f(5)) )=f( f(\frac{2}{3}))=f(\frac{-1}{5}) \\ etc\)

you need to check what i have done and then finish it.

\(\frac{a}{b} = \frac{3}{5}, \frac{b}{c} = \frac{6}{15},\space and\quad \frac{c}{d} = \frac{1}{6}. \ \textcolor{red}{What \ is \ the \ value \ of \frac{a}{d}}?\)

Who cares where you got it.

It is  YOUR homework.

If you want others to do YOUR homework for free then go to some planet where it is legal and buy a few slaves.

$2 ==$1 x e^(0.1223n)

Take the natural log of both sides

Ln(2) ==0.1223n, solve for n

0.693147181 == 0.1223n

n ==0.693147181 / 0.1223

n==5.668 years - to double his money

Your sequence will look like this:

3, 5, 2, - 3, - 5, - 2, 3, 5, 2, - 3, - 5, - 2, 3, 5, 2, - 3, - 5, - 2, 3.........2014th term will be a "3". The rest of them all cancel out.

Therefore, the sum of the first 2014 terms ==3.