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I could do this algebraically, but a  graph seem quicker

PRQ is bisected, not PQR.  

The  bisected angle PRQ  sets up  the following relationship

x + 2   /12    =  12 / 8

x + 2  / 12  =  3 / 2         multily both sides  by  12

x + 2  = 12  ( 3/2)

x + 2 =  18

x   = 16

IF P is a right angle, you can use Pythagoras' Theorem to determine the hypotenuse

of the large triangle.  Then just subtract 2 from that, and you've got the value of X. 

IF P  is a right angle, then (X+2)  =  sqrt(20²+12²)  

                                           X+2   =  sqrt(544)  =  23.3  

                                               X   =  21.3   

All this, IF you can find something that says P is a right angle.  If not, then disregard the above.  

Using  the intersecting chord theorem

RA * SA  = PA  * QA

7  * 7   =  PA  *  9

49  = PA * 9

49/9  = PA

PA + QA   =   49/9  +  9   =   [ 49 + 81]  /  9    = 130 / 9   = the diameter

So......the radius    =  1/2 of this  =  130  /18   =   65 / 9

So First of Burritos are more expensive and let Taco be T and Burrito be B

so 4T+2B=12 and 3T+3B=11.5 so 2B=4T+12

B=2T+6

3T+2T+6=11.5

5T+6=11.5

5T=5.5

T=1.1

4.4+2B=12

7.6=2B

3.8=B

Hope this helped ;)

( I have no idea how someone can eat that much unless they are small minis)

We can only  get  a 0   or   a positive from  a positive  square root

And  note  that  sqrt (x^2)  is defined as    absolute  value  (x)

So....the range  is   [ 0 , infinity )

Interior angle of a regular pentagon =   108

Interior angle  of a  regular hexagon =  120

108  / 120   =    ( 9 * 12) /  (10 * 12)   =  9  /10

If it has a domain of all real numbers, then x^2-x+c is never 0. 

If you draw out the parabola, x^2-x=y, then you find that the very end is at y=-1/4. 

So C must be greater than 1/4, and the smallest integer that works for that is 1. 

I hope this helped. :))

=^._.^=

f(-2)  =  (-2)^2  - 2  =  2

f(2)  =  2(2)  - 20  =  -16

So

2  -  16   +  f(a)  =  0

-14  + f(a)   = 0

f(a)  =  14

In  the first function  f(a) = 14  so      a^2  - 2  = 14      ⇒  a^2  = 16   ⇒  a = -4   (a  must be  < 0)

In the  second function  f(a)  = 14  so     2a  -20  = 14  ⇒  2a  =  34   ⇒  a  =  17

The positive  difference is   17 - - 4 =   21

Hello!

sin(a)^2+cosine(a)^2 = 1

(2cosine(a))^2+cosine(a)^2 = 1

I'm sure you can solve it from here. 

Good luck. :)))

=^._.^=

Dang, AnswerMachine beat me to it  !!!!

4 shepherds were watching over their flocks and they were commenting on how many sheep they each had.

If David had three more sheep, then he'd have one less sheep than Harry.

Whereas Sam has the same number as the other three shepherds put together.

If Peter had three less sheep, he'd have exactly treble the number of David.

If they were evenly distributed they'd each have eleven sheep.

How many sheep did David have?

There must be 44 sheep

Let  the  number  of David's sheep  =  D

Then Peter's sheep - 3 = 3D  or     P  = 3D + 3

And D + 3  =  H -1     or   Harry = D + 4

And Sam =   D  + 3D - 3  + D + 4

So

D + P  +  H  +  S   = 44

So

D  +  (3D + 3)  + (D + 4)  +   D + (3D + 3)  + (D + 4)   = 44     simplify

10D  +  14   = 44

10D  = 44 -14

D  = 3

P = 3(3) + 3 = 12

H = 3 + 4   = 7

S = 22

whoops, thank you for catching that :O

my bad, y should be 153/6, sorry about that !!

(...and i hope you can solve for x on your own:))

so if it was split evenly there would be 11 sheep for each and so since there are 4 sheepherds then there would be 44 sheep in all and so D+4=H and S=D+H+P and P=3D+3 and so you want to solve D then we have to subsitute all other var.  D+4+D+D+4+3D+3+3D+3+D=44 and combine like terms you get 10D+14=44 and subtract from both side you get 10D=30 so D=3

Looks good, AnswerMachine   !!!!

I belive the answer is 2, 10 and here is the ex

At $n$ o'clock, the minute hand is pointing straight up toward $12$. The hour hand must be $60^{\circ}$ away, either clockwise or counter-clockwise. Since $60^{\circ}$ is $\dfrac{1}{6}$ of a rotation and each full rotation of the hour hand lasts $12$ hours, the hour hand must be pointing $2$ hours in either direction from $12$. The possible times are $\boxed{2{:}00\text{ and }10{:}00}$.

The answer is 6

13 + 140 = 153     NOT  163  or  173 

tan(80)*12 = 68.05   ft    sorry....the web2.0 calculator was in 'Radian' mode rather than degree mode !

x ( 1 - .55)(1-.6)

 x (.45)(.4)  =0.18x       18 percent of the original price !

height of pole  = 12 tan 80°   ≈  68 ft

P.S.  -  I think the guest forgot  to change  his calcullator  mode to  degrees

tan of an angle in a right triangle is opposite side divided by adjacent side

tan 80 = height / 12

12 * tan 80 = height  = 108.04 ft

Each sheet  contains  2 pages

So...let x  be  the  number of sheets  that  were "borrowed"

So.....the  number of pages that remain = 50 - 2x

Taking the average of these  remaining  pages = 19  ......so....

( 50  - 2x )   / 2   =  19

50 - 2x   = 38

50  - 38   = 2x

12  = 2x

x  =  6  sheets were "borrowed"