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sell 1/2 ....then 1/2 left

1/2 left   sell 1/2   then   1/4 left

1/4 * 20 = 5 left to sell

6a = 5 g    initially       g = 6/5 a

a - 1/2a =  g + 1/2 a  - 60      sub in red equation

1/2a      = 6/5a + 1/2a -60

6/5a = 60

a = 60 * 5/6 = 50 toys initially

L = 3p      l = 12     so  p = 4

w = 6p        w = 6(4) = 24

  12 + 4 + 24 = 40 prizes               

7 is to 56    as    2  is to x

7/56 = 2/x

x = 2  * 56/7 = 16  magnets

56 is divisible by 7, so this problem is very easy.

7 * 8 = 56

2 * 8 = [16] magnets Jason has

Squaring both sides of the original equation, we get \(a^2 = 4+\sqrt{5+a}.\)
Subtracting 4 from both sides and squaring again gives \((a^2-4)^2 = 5+a.\)
Expanding this out and subtracting 5 + a from both sides, we have \(a^4-8a^2-a+11 = 0.\)
Similar manipulations on the other equations give \(\begin{align*} b^4-8b^2-b+11 &= 0, \\ c^4-8c^2+c+11 &= 0, \\ d^4-8d^2+d+11 &= 0. \end{align*}\)
(Note the signs carefully.)

Let \(f(x)=x^4-8x^2-x+11\). Then a and b are roots of f(x), while c and d are roots of  \(x^4-8x^2+x+11\), which is f(-x). It follows that -c and -d are roots of f(x). Since -c and -d are negative and hence distinct from a and b, we have four roots of f(x). Since f(x) has degree four, we know we have found all the roots.

By Vieta's formulas, the constant term of f(x) is the product of the roots. Thus, 

\(\begin{align} abcd = (a)(b)(-c)(-d) = \boxed{11}. \end{align}\)

The smallest x, y, z are:

x = 14,   y = 70,   z = 126

x + y + z = 14 + 70 + 126 = 210

This has been asked and answered many times before.

there are 21 possible chords and you want 4 of them so that is   21C4 = 4985 possible combinations.

To make a bow tie you need just 4 points out of 7   which is  7C4 = 35 combinations

But how many possible bow ties can you get out of a specific 4 points?  You work it out.

And then you finish it.

Any help would be greatly appreciated :)

I think it is a stupid question too.

I will assume that all the socks of each colour are identical.

At a minimum 2.  she might get lucky

At a maximum 6.  She might pull out one of each colour before finally pulling out a second of any.

Ok, sorry that explains it.

You can always send a private message to  a moderator asking them to unlock a question.

Also you can still put a link to the original and explain that it is, and, may continue to be locked.

You could also comment on my new answer on the old thread, as that thread is no longer locked.

r = ratio

a2 = a1*r

a3 = a1*(r^2)

a4 = a1*(r^3)

a5 = a1*(r^4)

a2/a4 = a1*r/a1*(r^3)=1/r^2

1/r^2 = 3

r*2 = 1/3

a5/a3 = a1*(r^4)/a1*(r^2) = r^2 = 1/3

Thx for the attempt guest but that isn't right does anyone else have an aswer please

The answer is 25/27.

thank you but i keep getting 166.93 it the wrong answer for the norman window 

3x  +  2y  +  xy  =  115

3x  +  xy   =    115  -  2y

x  ( 3 + y)   =  115  -  2y

x =   (115  -  2y) /  ( 3 + y)

Note  that  when y  =  8

x =  (115  - 2*8)  / ( 3 + 8)  =   99 / 11  = 9

So

x = 9  and y = 8

So

x +  y  =  17

please hel cphill 

also cphill did you create this website

Thank you so much CPhil god bless you

If  you  can  imagine  this.....

BA  will  intersect  p   at an  angle of 90°  since  A  is refected  over  p  to B

And  CA   will intersect q  at 90°  since  A  is reflected over q to C

So  angle  BAC   =    360  - 90  -90  - 38   =  142°

Also Cphill you are my favorite. And huerka

1.A 26-inch bicycle is pedaled so that the tires rotate at a rate of 200 revolutions per minute. A 20-inch bicycle is pedaled so that its tires rotate at a rate of 200 revolutions per minute, as well. What is the linear velocity of each bicycle? State your answers in inches per minute, rounded to the nearest tenth.

Linear  velocity f 26 inch  bike =  13  * 2pi * 200  =  16336.3 in /min

Linear  velcity of 20 inch  bike  =  10 * 2pi *200  =   12566.5 in / min

2.Typically, the speed at which a bicycle moves is expressed in miles per hour. Convert the linear velocity of the 26-inch bicycle and the 20-inch bicycle to miles per hour. Round your answer to the nearest tenth.

26 in bike  =   16336.3 in  x    1 ft  / 12 in  x   1 mile  / 5280 ft   x 60  =  15.5 mph

20 in bike  =    12566.5 in  x   1 ft / 5280 x     1mile  / 5280 ft x   60   =   11.9 mph

3.How many more revolutions must the 20-inch bicycle complete to have the same linear velocity as the 26-inch bicycle? Round your answer to the nearest tenth.

10 * 2pi  *  R   =   16336.3

R  =  16336.3  / ( 20pi)    =  260

So....the  20 in bike  must rotate  60  more  revs per minute  to have  the  same linear velocity as  the 26 in bike

4.What is the angular velocity of each bicycle? Write your answer in exact form in radians per second.

Since  each  rotates  200 times in a minute....they  have  the  same  angular velocity

This  is     200 * 2pi  /60   =  (20/3) pi  rads   /sec

5.How many complete rotations does either bike complete in one second? 

(20/3) pi   =  6 + 2/3 rotatations per sec  =   6 full rotations per sec

Number 1. I got 7539.8 don't really have time to explain also can anybody go to my post it is the one abount two line p and q intersect at X at an angle of 38 degrees. thx