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The area of the WHOLE circle is the area of the central angle of 2pi

Let's set up a ratio     2pi  / (3pi/13)   =   x / 19    

and solve for 'x'    =   2pi / (3pi/13)    x   19   = 26 / 3     x 19 =  494 / 3 =164 2/3 m^2

Just add the 'like terms'

(7+(-8)) + (3i+9i)  =   -1 + 12i 

3  2/5 as a decimal.    The '3' will still be a '3' and you just divide the  2 by 5 for the decimal fraction to get :  3 . 4 

Is that 1,092 . 58 ?        = 3.03845 

Thanks Alan,

I never doubted you but I'd still like to see it done in a more general way. ://

With a root of -1/2 it is likely that 2x^2 + 15x + p = 0 can be written as:

(2x + 1)*(x - a) = 0   This has roots of -1/2 and a

Expanding this we get:   2x^2 +(1 - 2a)*x - a = 0

For this to match we must have:  1 - 2a = 15  or  a = -7

We must also have  p = -a  so p = 7

.

Here's another example with completely different functions, but with the same values of f`(5), g(2) etc.:

Still get 96.  More than a coincidence!

(7/4) (21^2) <tan (180/7)^-1 What is this answer?  

I am not really sure what your question is

(7/4) (21^2) tan^-1(180/7)

=(7/4)*(21^2)*atan (180/7) = 67738.7765028982455

or (the second one makes more sense.)

(7/4) (21^2) (tan (180/7))^-1

=(7/4)*(21^2)/(tan (180/7)) = 1602.5553878031321963

Cinema tickets costs 110 $ for adults and 90 $ for kids. They sold 120 tickets for a total of 11640 $. How many adults saw the show?

K+A=120

so   K=120-A

110A+90K=11640

divide both sides by 10

11A+9K=1164

Sub in K=120-A

11A+9(120-A)=1164

11A+1080-9A=1164

2A=84

A=42

42 adults saw the show :)

Greetings Herr Heureka,

When I saw this post, I thought a thousand people could look at this and will think this is a childish troll attempting to annoy with a 1+1 post and inadvertently typed an exclamation point (“!”) along with the one (1).

I also thought if Heureka sees this, he will solve the “Derangement!”  You didn’t disappoint!  ROFLMAO

The only reason I know what a Derangement is (outside of the psychological condition caused by a psychosis), is because of this:

It is really great to see you back Heureka :))

Yes, I think that Ginger is correct.  Does your book's answer agree with Ginger's answer ?

You seem to have the right idea; you just need to multiply each combination by the available number of suits.  As each suit is selected, there is one less suit to consider. 

\(\binom{13}{6} \cdot (4) \cdot \binom{13}{5} \cdot (3)\ \cdot \binom{13}{2} \cdot (2) \\\\ \text { } \\ = 4,134,297,024 \text { Combinations}\)

GA

Is there a pattern to 0,6,24,60,120,210? This is fiendishly hard. Or how about 0,4,10,20,35. Please save me and solve!

\(\begin{array}{|r|rcr|} \hline n & n\cdot(n+1)\cdot(n+2) \\ \hline 0 & 0\cdot 1 \cdot 2 &=& 0 \\ 1 & 1\cdot 2 \cdot 3 &=& 6 \\ 2 & 2\cdot 3 \cdot 4 &=& 24 \\ 3 & 3\cdot 4 \cdot 5 &=& 60 \\ 4 & 4\cdot 5 \cdot 6 &=& 120 \\ 5 & 5\cdot 6 \cdot 7 &=& 210 \\ 6 & 6\cdot 7 \cdot 8 &=& 336 \\ 7 & 7\cdot 8 \cdot 9 &=& 504 \\ 8 & 8\cdot 9 \cdot 10 &=& 720 \\ \cdots & \cdots \\ \hline \end{array}\)

!1+1

\(\begin{array}{|rcll|} \hline !1 &=& 1! \cdot \left( 1- \frac{1}{1!} \right) \\ &=& 1 \cdot \left( 1- 1 \right) \\ &=& 1 \cdot 0 \\ &=& 0 \\\\ !1+1 &=& 0 + 1 \\ &=& 1 \\ \hline \end{array}\)

The quadratic equation 2x2 + 15x + p = 0 has a root of -1/2 when p has a whole number value of what? Please explain steps as well

p=7

A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?

2,727 / 27 =101 gallons used up in driving 2,727 miles.

101 x $4.04 =$408.04 cost of gas.

Solve for d:
d/6+2/3 = (d-2)/4

Put each term in d/6+2/3 over the common denominator 6: d/6+2/3 = d/6+4/6:
d/6+4/6 = (d-2)/4

d/6+4/6 = (d+4)/6:
(d+4)/6 = (d-2)/4

Multiply both sides by 12:
(12 (d+4))/6 = (12 (d-2))/4

12/6 = (6×2)/6 = 2:
2 (d+4) = (12 (d-2))/4

12/4 = (4×3)/4 = 3:
2 (d+4) = 3 (d-2)

Expand out terms of the left hand side:
2 d+8 = 3 (d-2)

Expand out terms of the right hand side:
2 d+8 = 3 d-6

Subtract 3 d from both sides:
(2 d-3 d)+8 = (3 d-3 d)-6

2 d-3 d = -d:
-d+8 = (3 d-3 d)-6

3 d-3 d = 0:
8-d = -6

Subtract 8 from both sides:
(8-8)-d = -6-8

8-8 = 0:
-d = -6-8

-6-8 = -14:
-d = -14

Multiply both sides of -d = -14 by -1:
-d/(-1) = 14

(-1)/(-1) = 1:
Answer: |d = 14

29!/(29-14)!14! =77,558,760

3/4x+1/8=3/4(x+8)

\(\frac {3}{4}x+ \frac {1}{8}=\frac {3}{4} (x+8)\)

\(\frac {3}{4}x+ \frac {1}{8}=\frac {3}{4}x+\frac {24}{4}\)

\({\color{red} \frac {1}{8}\neq \frac {24}{4}}\)

so

\(\frac{3}{4x}+\frac{1}{8}=\frac{3}{4\left(x+8\right) }\)

\(\frac{6+x}{8x} =\frac{3}{4\left(x+8\right) } \)

\(4(6+x)(x+8)= 24x\)

\((6+x)(x+8)= 6x\)

\(6x + 48 + x² + 8x = 6x\)

\(x^2+8x+48=0\)

No real solution.

asinus :- )  !

x=7 and y=12

42 is the meaning of life the universe and everything.

−9.8+(−5.9)+u=−12.4

\({\color{red}-9.8+(-5.9)+u = -12.4}\)        { - [- 9,8 + (-5.9) ]

\(u = -12.4 +9.8 -(-5.9)\)       

\(u = -12.4 +9.8 +5.9\)

\({\color{blue}u=3.3}\)   !

I think you may have misrepresented the equation. f(x) = 12(x)² is probably what you meant to put?

the expression f(x) means function of x, therefore there must be an x on the right side of that equation somewhere. If the equation is supposed to be f(x) = 12(x)²  then f(-2) = 12(-2)²  = 48