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1/a + 1/b = 4/17.

If x, y, and z are real numbers for which

x + y - z = -8

x - y + z = 18

-x + y + z = 30

Then what is xyz?

2x =10

2y = 22

2z = 48

xyz = 1320

3a  + b +  c =  -3

a   + 3b  + c  =  9

a  + b  +  3c  =  -19

add  these

5a + 5b + 5c   = - 13

5 ( a + b + c)   = -13

a  + b +  c   = - 13 / 5

b + c   = -13/5  -  a

Subbing this into  the first  equation and simplifying  we  get  that

2a  = -3  + 13/5

2a  = -2/5

a = -2/10

a  = -1/5

Subbing  this  value  into  the swcond and third equations  we have  that

-1/5  + 3b + c  =  9    ⇒    3b + c =  9 + 1/5  ⇒  3b + c  =  46/5 ⇒    -9b - 3c =  -138/5

-1/5  +  b + 3c  = -19 ⇒   b +  3c  = -19 + 1/5  ⇒  b + 3c  =  -94/5⇒  b  + 3c  =  -94/5

Add the last two equations  and  we have  that

-8b  =  -232/ 5

b  =  -(232/ 5) (-1/8)  =  29/5

And     

b + c  = -13/5  - a

29/5  + c  = -13/5  -(- 1/5 )

29/5  + c =  -12/5

c = -41/5

So

abc =   (-1/5) (29/5) ( -41/5)   =  1189 /  125

Charlie had 90 stamps, gave 30 (1/3) to Don, leaving 60 stamps.

Don had 50 stamps, received 30 from Charlie, making 80, then gave 20 (1/4) to Egan, leaving Don with 60 stamps.

Egan had 40 stamps, received 20 from Don, giving Egan also a total of 60 stamps.

Try adding 2 equations together, that will isolate one variable and give you the value for them.

=^._.^=

(1+y)/(2-y) = 15

1 + y = 30 - 15y

16y = 29

y = 29/16

=^._.^=

g(16) = sqrt(16) + 3 = 7

t(7) = 3 - g(7)

g(7) = sqrt(7) + 3

t(7) = 3 - (sqrt(7) + 3)

t(7) = -sqrt(7)

=^._.^=

1.  Larry  has  9  (or more)  books

2. 

A .    16   ≥  3   +  x

B.   Pat  has   13  books  ( or less)

thank you for the explanation!

Let Charlie, Don and Egan have c, d and e number of stamps initially.

At the end, all 3 will have 60 stamps each. So after giving away 1/3 of his stamps, Charlie is left with 2/3c stamps. Similarly, Don is left with 3/4d stamps.

Now. 2/3c=60 => c=90

3/4d=60 => d=80

Thus, e= 180-(c+d)= 10

Verification: 1/3c + 1/4d + e = 60

Ans: 90, 80 and 10

1/ x   +   1/y    =  1/18

x and y  must  be  >  18

Let   z = 18

Let   x =   z +  a

Let y =  z  +  b

So  we  have  that

1 / ( z + a)   +  1  /(z + b)  =  1 /  z   simplify

[ z + b + z + a ]  / [ (z + a) (z + b) ]    =  1  / z    cross-multiply

z  [2z  + a + b ]   =     (z + a) ( z + b)

2z^2  + az + bz   =  z^2 + az  + bz  +  ab

z^2  =   ab

This implies  that

18^2   =  ab

324  =  ab

Factors of 324   are   1 | 2 | 3 | 4 | 6 | 9 | 12 | 18 | 27 | 36 | 54 | 81 | 108 | 162 | 324 (15 divisors)

x  +  y   is minimized   when     a  = 12   and  b = 17

So....x = z + a  =  18  + 12  =  30

And  y  = z + b  =   18  + 27  =   45

So  x  + y =   30  +  45    =  75

abc = 76.

The sum of the values of k is 22.

1.  Larry has at least 3 more books than Pat. If Pat has 6 books, what do you know about the number of books Larry has?

2.  Suppose Larry has 16 books and Pat has x books. (Larry still has at least 3 more than Pat.)
A.  Use <, ≤, >, or ≥ to write an inequality to compare the number of books Larry has to
the number of books Pat has.
B.  What do you know about the number of books Pat has?

1.  Larry  has  9  (or more)  books

2. 

A .    16   ≥  3   +  x

B.   Pat  has   13  books  ( or less)

The 'x' coordiante of the parabola will be   - b / 2a   =   - -6/(2*3/4)       use this value in the quadratic to calculate the 'y' coordinate of the vertex.

Here is a Venndiagram to help you out.....

You poopy face really think that is the d'm answer

sorry if i'm wrong but i think it's 5%

how did you get the minimum

a + b = 44.

6t  - t/5  = 4  +  (2 - t)  / 3

Multiply through  by  LCM  of 3, 5  =  15

90t  - 3t   = 60  +  5 ( 2 - t)

90t  - 3t   =  60  + 10   - 5t

87t  =  70  - 5t

87  +  5t  =  70

92t   = 70

t  =  70  / 92     =   35  / 46

Let X be shirt cost, Y be tie cost

X + Y = 43, 4X + 4Y = 172

4X + 2Y = 152

4X + 4Y = 172, subtract equations

-2Y = — 20,

Y = $10, X = $33, check work

4 × 33 + 2 × 10 = 152

132 + 20 = 152

152 = 152, yeah!!!