All Answers 358149 Answers

A and B working together can finish a job in 40 days. They worked together for a number days and A left the work. B alone finished the remaining work in 24 days. For how many days did they work together? 

there will be no exact number answer if they work at different rates so I am going to assume that they both work at the same pace.

So it it takes the two 40 days to do the jobs, I will assume that it will take one 80 days.

So in 24 days one will be able to do    24/80   of the job

So that means that 56/80 was already done.

\(\frac{56}{80}*40 = 28days\)

They worked together for 28 days.  

Square the first equation,

\(\displaystyle x^{2}+y^{2}-2xy=3,\dots(1) \)

Square the  second equation,

\(\displaystyle x^{2}+y^{2}+2xy =4,\dots(2)\)

Subtract (1) from (2),

\(\displaystyle 4xy=1, \\ xy=1/4.\)

Set the equations equal

8x^2 + 6x + 1 =  2x^2 - 7x + 1          rearrange as

6x^2 + 13x   =  0       factor

x (6x  - 13)  = 0

The  x coordinates   are

x = 0                        and        6x - 13 = 0

                                                6x = 13

                                                   x  =13/6

When x = 0  y  =1

When x = 13/6, y=  2(13/6)^2 - 7(13/6) + 1   =  -43/9

The points of intersection are 

(0 , 1) , (13/6 , -43/9 )

the prob that the first one drawn is  J Q or K of hearts  is    3/52

the prob that the 2nd one drawn is  J Q or K of hdiamonds  is    3/52

the prob that the 3rd one drawn is  J Q or K of spades  is    3/52

the prob that the 4th one drawn is  J Q or K of clubs  is    3/52

These can be in any order so I would have to multiply by 4!

So I think the answer is    \(\frac{3^4}{52^4}*4!\)

6=2*3

8=2*2*2

27=3*3*3

smallest common muliple is   3*3*3*2*2*2

Thanks Builderboi  

The equations for  the circles are

(x - 2)^2 + ( y + 1)^2  = 16        (1)

(x -2)^2 + ( y - 6)^2 =    18       (2)           subtract    (1) from (2)

(y - 6)^2 - (y + 1)^2  =  2

y^2 - 12y + 36 - y^2 - 2y - 1  =  2

-14y + 35 =  2

-14y = -33

y = -33 /-14  =  33/14      this is the y coordinate for both points

To find the x coordinates

(x  -2)^2  + (33/14 + 1)^2   = 16

(x - 2)^2  +  ( 47/14)^2  =16

(x - 2)^2  =   16 - (47/14)^2

( x-2)^2  =    927 / 196        take both roots

x - 2 =   sqrt (927/196)       or        x  - 2  =  -sqrt (927/16)

x = sqrt (927/16) + 2       or           x =  -sqrt (927 /196)  + 2

AB  =     [ sqrt (927/16) + 2 ]  -  [ sqrt (927 / 196)  + 2 ]    =   2 sqrt (927 /196)

(AB)^2  =  4 ( 927 / 196)  =  927 / 49

2x - 5 ≤ -x + 12 + 3x - 7       

2x - 5  ≤ 2x + 5

This is true for  all x

x =  (-inf , inf)

sec x  + tan x =   4/3

[ Note that   tan^2 x + 1  =  sec^2x    →   tan^2 x =  sec ^2 x - 1   →  tan x = sqrt ( sec^2 x - 1)  ] 

So

sec x +  sqrt  [sec^2 x - 1 ] =  4/3

sqrt [ sec^2 x - 1 ]=  4/3  - secx          square both sides

sec^2 x  - 1  =   16/9 - (8/3)sec x + sec^2 x       simplify

-1  = 16/9 - (8/3)sec x     rearrange as

(8/3)sec x  = 16/9 + 1

(8/3)sec x =  25 / 9

sec x = (25/9)(3/8)  = 75/72  =  25/24

cos x=  24/25

sin x = sqrt [  25^2 - 24^2 ]  / 25  =  sqrt [ 49] / 25 =  7 / 25

The points    (0,1)  and (3,3)  are on the graph

Slope =   [3 - 1 ] / [ 3 - 0] =  2/3

Using this slope  and the pont (3,3)  the equation of the line is

y= (2/3) ( x - 3) + 3  

y= (2/3) x - 2 + 3

y= (2/3) x + 1      putting into  standard form we have

3y = 2x + 3

2x - 3y  =  -3

Note that B and C will always have a common divisor  !!!!!

3x - 7y  = 21 + 2x - 5y   rearrange as

x - 2y  = 21

x intercept....   let y  = 0

x =21 =  x intercept

y intercept......let x = 0

0 - 2y = 21

-2y = 21

y = -21/2  =  -10.5

Distance between intercepts =  sqrt [ (21)^2 + (-10.5)^2 ]  ≈  23.48 units

Your positive integer n ==896 - which meets all the properties.

Use the formula \(180(s-2)\) to find the sum of all the angles in a polygon with s sides. 

The prime factorization of 60 is: \(2^2 \times 5 \times 3 \).

The largest single-digit factor of 60 is 6. This will be our unit digit. 

This means the remaining numbers must multiply out to 10, which means we need a 2 and 5. 

Now, what's the smallest number possible with these 3 digits?

This is so EZ.  Just use the nth term test.

The smallest angle is 32 degrees.

The probability is 7/330.

wait why

The equation is 3x + 2y = 1.

Just one integer: 

That is when n==1

Thanks for the effort but that's wrong.

The answer is 4.

Square both sides

(z + 1/z) ^2 = 1^2

z^2 + 2 (z) (1/z)  +  1/z^2   =   1

z^2 +  2  + 1/z^2  =  1

z^2 + 1/z^2  =  1   -  2

z^2 + 1/z^2  =    -1