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I can't find "gcd" on this calculator.  I think the best you can do here is to use the "factor" function:

factor(7788) gives 2²*3*11*59

factor(1386) gives 2*3²*7*11

Take the highest power of each prime that is common to both and multiply them together.

Here that is:  2*3*11 → 66

x^2+bx +c   ...  b  = c + 1  ....so....

x^2 + (c + 1)x + c

If this has one real root, the discriminant  = 0

So

(c + 1)^2  - 4(1)(c)  = 0  simplify

c^2 + 2c + 1  - 4c   = 0

c^2 - 2c + 1  = 0    this factors as

(c - 1)^2  = 0      take the square root

c - 1  = 0    ⇒   c  =  1

We can divide the parallelogram into 2 equal triangles by drawing a diagonal

The  area  is  2 (1/2) (6 * 8) / √2  = 48 / √2  =  24√2 ≈   33.94 units^2

Simplify

\(\large{i^1+i^2+i^3+\cdots+ i^{97} + i^{98}+i^{99}.} \)

Geometric sequence:

\(\begin{array}{|rcll|} \hline s &=& i^1+&i^2+i^3+\cdots+ i^{97} + i^{98}+i^{99} \quad & | \quad \cdot i \\ i\cdot s &=& &i^2+i^3+i^4+\cdots+ i^{98} + i^{99}+i^{100} \\\\ \hline s-i\cdot s &=& i^1 - i^{100} \\ s(1-i) &=& i^1 - i^{100} \\\\ \mathbf{s} &\mathbf{=} & \mathbf{ \dfrac{i - i^{100}}{1-i} } \quad & | \quad i^{100}= \left(i^2 \right)^{50}=(-1)^{50}=1 \\\\ s & = & \dfrac{i-1}{1-i} \\ s & = & -\left( \dfrac{1-i}{1-i} \right) \\ \mathbf{s} &\mathbf{=} & \mathbf{-1} \\ \hline \end{array}\)

\(\boxed{\large{i^1+i^2+i^3+\cdots+ i^{97} + i^{98}+i^{99} = -1}}\)

\(\dfrac 2 3 t - 1 < t+7 \leq -2t + 15 \\ \dfrac 2 3t-8

Yes, it is cool :)

Note....There are  ≈ 39.37 inches to one meter

So we have

4000   =  2 * pi^2 * (.59 * 39.37) * r^2

( 4000 / [ 2 * pi^2 * (.59 * 39.37) ] )  = r^2    take the square root of both sides

2.95  in ≈  r

And there are ≈ 2.54 cm to  one in

So....radius  ≈  2.54 * 2.95   ≈  7.493 cm

\(\dfrac{12+x}{23}=2\)

Note the repeating pattern  of  length  4

i^1   = i

i^2  = -1

i^3  = -i

i^4  =  1

So....the sum of this series  from i^1  to  i*96   = 0

So...the sum of the last  three terms   = i^97  + i^98  + i^99  = i + -1 +  -i   = -1

So...this series sums  to  0 + (-1)  = -1

(1/2) f (x - 2)  =  (1/2)  ( l  (x - 2) - 2 l - 5 )   =  (1/2) l x - 4 l   - 5/2   =  g(x)

To find the y intercept, let x  = 0  and we have

y  = (1/2)  l 0 - 4 l - 5/2  = (1/2) (4) - 5/2  =  2 - 5/2  =  -1/2

To find the x intercepts, let y  =  0

0  = (1/2) l x - 4 l  - 5/2   multiply through by 2

0  = l x  - 4  l - 5    add 5 to both sides

5  =  l x - 4  l

So either   

x  - 4  = 5    or             x  - 4   =  -5

x  = 9          or             x  = -1

(c)  Your answer is correct !!

(d) a  = 150    r  = 3m

Arc Length  =  2pi * 3 * (150 / 360)  ≈  7.85 m

(b) a = 74   r  = 2 ft

Arc Length  =  2 pi * 2 * (74 / 360) ≈ 2.58 ft

(a)  a  = 60     C  = 48 cm

Arc Length  =   48 * (60 / 360)  =  48 * (1/6)  =  8 cm

Why not help me?

\(\displaystyle \sum \limits_{k=1}^n~\alpha^k =\dfrac{\alpha \left(\alpha ^n-1\right)}{\alpha -1}\)

letting \(\alpha=i,~n=99,~\text{and assuming }i=\sqrt{-1}\)

\(\displaystyle \sum \limits_{k=1}^{99} ~i^k = \dfrac{i(i^{100}-1)}{i-1} = 0\)

By the way, f(x)= |x-2|-5

Sombody help me plz

Let P  be the original price

The new  price  is   P(1.5)(.25)  = .375 P

So....to return to the original price.....we must increase this new price by

  1 / .375  ≈  2.66 ≈  266%

Thanks for all the answers guys! I really appreciate the help. Isn't it cool how many different solutions this problem has?

Didn't you like my explanation Chris?    

Actually, I do like yours, but mine is simpler because it has no algebra.

Thanks!!!

Yeah! That was what I got for no.1 and I thought I was wrong... :( THANK SO MUCH!

thanks

1)  Try a = 23/2. With this value, equation 1 multiplied by 2 is exactly the same as equation 2.

2) Try dividing 2005/3 + 2005/4 - 2005/6. Ignore the fractional parts.

3) If you are allowed to repeat the letters, then you should have: 3^3 = 27

yea this problem is weird