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"The quantity sqrt(45) + 2*sqrt(5) + sqrt(360)/sqrt(2) can be expressed as sqrtN, where N is an integer. Find N."

sqrt(45) + 2*sqrt(5) + sqrt(360)/sqrt(2) = sqrt(9*5) + 2*sqrt(5) + sqrt(2*5*36)/sqrt(2)

= 3*sqrt(5) + 2*sqrt(5) + sqrt(2)*sqrt(5)*sqrt(36).sqrt(2) 

=  3*sqrt(5) + 2*sqrt(5) + 6*sqrt(5) 

= 11*sqrt(5)  

= sqrt(11^2 * 5) 

= sqrt(605)

N = 605

and you answer is completly incorrect

can you please explain how you got that answer

The determinat of the quadratic formula must = 0 for only one solution to the equation

  b^2 - 4ac = 0

20^2 - 4(a)(7) = 0         solve for 'a' ...........   you can finish, right?

Each sticker is 2x2 = 4 in²

The poster is   2 FEET   x  3 FEET                   1 foot = 12 inches

                        2 * 12      x  3 * 12   = 864 in²

864 / 4 = 216 stickers needed

Total distance  50 miles

30 minutes @ 60 m/ hr = 30 miles       20 miles to go

30 minutes @ 25 m/hr  = 12.5 miles    7.5 miles to go

last 30 minutes she went 7.5 miles       30 minutes = 1/2 hr     7.5 miles / (1/2 hour) = 15 m/hr during last 30 minutes

Try expanding (3x+5/3)^2 and see what you get. :))

=^._.^=

w + x + y = -2

w + x + z = -4

w + y + z = 19

x + y + z = 12

~~~~~~~~~~~~~~~~~

w + x + z = -4

w + y + z = 19

y = x + 23                     y = 12 ¹/₃

~~~~~~~~~~~~~~~~~~

w + y + z = 19

x + y + z = 12

w = x + 7                      w = - 3 ²/₃

~~~~~~~~~~~~~~~~~~~

w + x + y = -2

(x + 7) + x + (x + 23) = -2

                                     x = - 10 ²/₃

~~~~~~~~~~~~~~~~~~~

x + y + z = 12

z = 12 - (-10 ²/₃) - (12 ¹/₃)

                                     z = 10 ¹/₃

~~~~~~~~~~~~~~~~~~~~

w*x + y*z = 166 ⁵/₉ 

 I will try to figure it out for more. Keep sharing such informative post keep suggesting such post.   
 

Oops!!! I made boo-boo

b = 46.

There are 6 solutions.

The correct ordering is S, P, Q, R.

Important:

When two chords intersect inside a circle, then the measures of the segments of each chord multiplied with each other are equal to the product from the other chord.

~~~~~~~~~~~~~~~~~~~~~~~~~~~

LJ = 16

HJ = 40

LJ * HJ = MJ * NJ

640 = MJ * NJ

MN = √2560     or      16√10

If that answer's the best, then what's mine??? 

    21₄    =    2 (4) + 1   =  9₁₀

 -  12₄   =     1(4)  + 2   =  6₁₀

                                      ____

                                         3₁₀  =  3₄

A  -  B  =   

2  -  1   = 

    1

Note -12 is the largest whole number in -12.1, and 13 is the largest whole number in 13.3

...- -12- -11- -10- -9- -8-...-7-8-9-10-11-12-13-...

So the numbers we have here are -12 to 13. notice that when we add the numbers up, they cancel, like -12 and 12. So, the only number we have left is $\boxed{13}$ 

Extend  F  thru  E   to   G

Angle   GEC   is supplemental  to  angle AEF

So    GEC  =   180 - ( 10BAC  - 22)   =    202  - 10BAC  =  angle DAC

And  BAC  = (1/2)DAC

So

202 -  10 (1/2)DAC  =  DAC

202  -  5DAC   =  DAC

202  =   6DAC

DAC  =   202  / 6   ≈  33.66° 

x =  81  ,  324  ,  441

This  equation doesn't  match  the  data  given.........

Since the arc of 8x - 5 and 6x + 10 are the same, they should be the same too. 

8x - 5 = 6x + 10

2x = 15

x = 7.5

10x - 10 = XY

10(7.5) - 10 = XY

65 = XY

=^._.^=

No solutions.....see  here  :  https://web2.0calc.com/questions/ordered-triple

3xy  -4x^2 -36y  +48 x   = 0

3xy  - 36y  -  4x^2  +  48x  =  0

3y ( x - 12)    -  4x(x - 12)  =  0

(x - 12)  ( 3y  - 4x)   =  0

x =  12                  and       3y  = 4x    ⇒     y  =  (4/3)x

Using the  first  solution  in  the  second equation, we  have

x^2 - 2y^2  =  16

12^2  - 2y^2  = 16

12^2 -  16  = 2 y^2

144 - 16  = 2y^2

128   =  2y^2

64   = y^2 

y = 8    and  -8

So   (12, 8)  and (12 , -8)  are  solutions

And 

x^2  - 2  [( 4/3)x]^2  =   16

x^2  -  (32/9)x^2  =  16

(-23/9)x^2   =  16

x^2  =  16  (-9 / 23)

x^2  = -144/23

So

x = -12i / sqrt (23)         and  x =  12i / sqrt (23)

And  y  =  (4/3) (-12i) / sqrt 23   =   -16i/sqrt 23           and   16i / sqrt (23)

So

( -12i/sqrt 23, -16i/sqrt 23)   and  ( 12i/sqrt 23  , 16i/sqrt 23)     are also solutions

C(8,3) *  C (6, 3)    =

56  *    20   =

1120  combos