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Multiple of 15  =  -15

Multiple of 16  =  16

Sum   =   1

Add the first two equations

2x =  10

x = 5

Add the second two

2z = 48

z = 24

Add the first and  third

2y = 22

y = 11

x y z =    

5 *  11  *  24   = 

1320

75 mod 6  =  3

(2 + x) / 2 = 17                          ( 4 + y) / 2 =  8

(2 + x)  = 2 * 17                        (4 + y)  = 8 * 2

2 + x = 34                                  4 + y =   16

x =  34 - 2                                    y = 16 -  4

x =  32                                          y =   12

2^10 x 3^14 x 5^8 =

2^1 x 3^1 x 5^2 =150

Subtract the exponents of the same base numbers and add 1 in each case as follows:

[10 - 1 + 1] x [14 - 1 + 1] x [8 - 2 + 1] =10 x 14 x 7 = 980 such numbers.

answer from guest. the link is not working for some reason.

The base of the small right triangle =  5 / sqrt 3  =  (5/3)sqrt (3)

The  side of the triangle = twice the base =      (10/3)sqrt (3)

The perimeter = 

2 (5)  + 2 ( 5/3) sqrt (3)  + 2 ( 10/3) sqrt (3)  =

10 + (10/3) sqrt (3) + (20/3)sqrt (3)  =

10 + (30/3) sqrt (3) =

10 + 10 sqrt (3)  =

10 ( 1 + sqrt (3) ) cm  ≈   27.32 cm

thx. i saw yours. i was about to congratulate you when I saw the date that you posted it. and the number of likes you have right now! LOL

.25 R  =  (1/6)G                (note : R + 160  = G )

.25 ( R)  =  (1/6) ( R + 160)

(1/4)R =   (1/6)R + 160 / 6           

(1/4)R - (1/6)R =  160 / 6          

(2/ 24)R = 160 / 6

(1/12)R = 160 / 6

R = (160/6) ( 12 )  =   320

320  - 114  = 

206  red ones left

Triangle  APB will be isosceles  with angles   A and B  being equal

The measure of  either angle =  180  - [ (8 - 2) (180) / 8 ]  =   180 - (3/4)180  =   180  -  135  =  45°

So angle P  =  180  - 2(45)  =  90° 

Two cases

Case 1  - Last digit =  0

We have eight choices for the first digit   (2,3,4,5,6,7,8,9) 

One for the second  (1)

Seven  for the third  

Six for the fourth

8 * 1 * 7 * 6  =  336 

Case 2  -   Last digit = 5

We have seven choices for the first digit   ( 2,3,4,6,7,8,9 )

One for the second

Seven  for the third 

Six for the fourth

7 * 1 * 7 * 6  =  294

336 +  294  = 

630  such numbers

How can  f(x) + g(x)  =   -2 - x    and     f(x) + g(x)   =  x^3 + 2x + 2    ????

Initially....let the total number of beads between them = N

So, at first, Robert has (1/5)N and Robin has (4/5)N

When Robert loses (1/5)  of his he has  (1/5)(4/5)N =  (4/25) N

Then Robin gives him 152 so he has   (4/25)N + 152

And Robin now has (4/5)N  - 152....so....

(4/25)N + 152  =  (4/5)N - 152

(4/25)N + (4/5)N =  152 + 152

(4/25)N + (20/25)N =  304

(24/25)N = 304

N = 304 ( 25/24) =   1900

Robin had  1900 (4/5)  =    1520 beads at first

7, -5

Simplify to \(3x^2 - 8x + k = 0\)

If the quadratic has exactly 1 solution, then it can be expressed as \(a(x-h)^2 \), where h is the x-coordinate of the vertex. 

We know that \(a = 3\), because it is the leading coefficient of the \(x^2\) term.

Also, note that \(2h \times 3 = 8\), meaning \(h = {4 \over 3}\).

This means we have \(3(x-{4 \over 3})^2\), which expands to \(3x^2 - 8x + {16 \over 3}\), meaning \(k = \color{brown}\boxed{16 \over 3}\)

For the first digit, there are 9 choices (0 - 9)

For the second digit, there is 1 choice (it has to be 1)

For the third digit, there are 10 choices ( 0 - 9) 

For the fourth digit, there are 10 choices (0 - 9)

For the final digit, there are 2 choices (0 - 2)

So, there are \(9 \times 10^2 \times 2 = \color{brown}\boxed{1,800}\) choices. 

The sum of the possible values of h(x) is 19.

Nevermind, I'm wrong.

Thx, BuilderBoi  !!!!!

2x - 5  <= -x + 12 -3x + 7

2x - 5  <=  -4x + 19

2x + 4x < =  19 + 5

6x < =   24

x < =  24 / 6

x < = 6

y = 1  / ( ax + b)     get x by itself

y ( ax + b)  = 1

ay x  + by  = 1

ay x      = 1 - by

x = ( 1 - by) /( ay)         swap x and y

y = (1 - bx) / (ax)  =  f^-1 (x)

1 =  (1 - bx) / (ax)

ax = 1 - bx

ax - bx = 1

x ( a - b) = 1

x = 1  / ( a  -  b )

12 - 9 = cool dads only  =  3

18 - 9 = cool moms only  = 9

30 - ( 3 + 9 + 9)  = 

30  -  21  =

9   have both uncool

Sum of an infinite series =

[ First term ]  / [ 1 -common ratio]         

common ratio =  1/7

(b/7) / [ 1 - 1/7 ]  =  1

(b/7) / (6/7)  = 1

b / 6 =   1

b =  6

We actually just have 4 circles each with a radius of 5  (diameter of 10)

Area =  4 * 3.14 * 5^2  =  100 (3.14)  = 314 cm^2

Perimeter  = perimeter of  8 circles + 8 diameters =   4 * 2 * (3.14) * 5  + 4 * 10  = 165.6 cm