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\(7\sqrt{50x^{15}y^{21}} \\~\\ =\,7\cdot\sqrt{2\cdot5^2\cdot x\cdot x^{14}\cdot y\cdot y^{20}} \)

\(=\,7\cdot\sqrt{5^2\cdot x^{14}\cdot y^{20}\cdot2\cdot x\cdot y} \\~\\ =\,7\cdot\sqrt{5^2}\cdot \sqrt{x^{14}}\cdot \sqrt{y^{20}}\cdot\sqrt{2\cdot x\cdot y} \\~\\ =\,7\cdot5\cdot x^7\cdot y^{10}\cdot\sqrt{2xy} \\~\\ =\,35x^7y^{10}\sqrt{2xy}\) Since  x  and  y  are not negative, we can say...

What a beautiful voice! Who is the singer? Is it you, Ginger?

I guess some of his elves aren’t. 

\(-6i\sqrt{-44} \\~\\ =\,-6\cdot i\cdot\sqrt{-44}\\~\\ =\,-6\cdot i\cdot\sqrt{-1\cdot2\cdot2\cdot11}\\~\\ =\,-6\cdot i\cdot\sqrt{-1\cdot2^2\cdot11}\\~\\ =\,-6\cdot i\cdot\sqrt{-1}\cdot\sqrt{2^2}\cdot\sqrt{11}\\~\\ =\,-6\cdot i\cdot i\cdot2\cdot\sqrt{11} \\~\\ =\,-6\cdot i^2\cdot2\cdot\sqrt{11} \\~\\ =\,-6\cdot -1\cdot2\cdot\sqrt{11} \\~\\ =\,12\sqrt{11} \)

What is it with you AngelRay?  Why do you think it’s OK to dump all your homework on here? --especially in duplicate?

Santa Clause is on break!

Sqrt[3*5*7] = sqrt[105]

Simplify the following:
sqrt(504)

Factor 504 under the radical sign.
sqrt(504) = sqrt(8×9×7) = sqrt(2^3×3^2×7):
sqrt(2^3 3^2 7)

Simplify powers.
sqrt(2^3 3^2 7) = sqrt(2^3) sqrt(3^2) sqrt(7) = 2^(3/2)×3^(2/2) sqrt(7) = 2 sqrt(2)×3 sqrt(7):
3×2 sqrt(2) sqrt(7)

Multiply 3 and 2 together.
3×2 = 6:
6 sqrt(2) sqrt(7)

For a>=0, sqrt(a) sqrt(b) = sqrt(a b). Apply this to sqrt(2) sqrt(7).
sqrt(2) sqrt(7) = sqrt(2×7):
6 sqrt(2×7)

Multiply 2 and 7 together.
2×7 = 14:
6 sqrt(14 )
 

Simplify the following:
3 sqrt(-50)

Express sqrt(-50) in terms of i.
sqrt(-50) = sqrt(-1) sqrt(50) = i sqrt(50):
3 i sqrt(50)

Simplify radicals.
sqrt(50) = sqrt(2×5^2) = 5 sqrt(2):
3 i×5 sqrt(2)

Multiply 3 and 5 together.
3×5 = 15:
15i sqrt(2)

 

Simplify the following:
4 sqrt(27) + 6 sqrt(75)

Simplify radicals.
sqrt(27) = sqrt(3^3) = 3 sqrt(3):
4×3 sqrt(3) + 6 sqrt(75)

Simplify radicals.
sqrt(75) = sqrt(3×5^2) = 5 sqrt(3):
4×3 sqrt(3) + 6×5 sqrt(3)

Multiply 4 and 3 together.
4×3 = 12:
12 sqrt(3) + 6×5 sqrt(3)

Multiply 6 and 5 together.
6×5 = 30:
12 sqrt(3) + 30 sqrt(3)

Add like terms in 12 sqrt(3) + 30 sqrt(3).
12 sqrt(3) + 30 sqrt(3) = 42 sqrt(3):
42 sqrt(3)

 

That's cause you are not an Aussie.  LOL

Everyone here knows them :))

Thanks everyone for your Great Christmas cheer :)

Thanks Melody! I have not heard those two songs before!! 

Since 1x coat of paint on the larger room requires ½x as much for the smaller room,
therefore 2x gallons for 2 coats on the larger room = ½ x 2 =1y gallons for the smaller room. But he decided not to paint the smaller room. So, we have:
A ratio of 3 to 1 gallons required to paint 3 coats for the larger room and 2 coats for the smaller room. So:
3/{3+1} x 16 =12 gallons required to paint the larger room 3 coats, or 12/3 =4 gallons per coat. The remaining 4 gallons would have been for the smaller room, or 4/2 = 2 gallons per coat.
So, he obviously has: 16 -12 = 4 gallons left.

Merry christmas to you! . Have a nice and healthy 2018, Melody!

Merry Christmas!

Merry Christmas!!

The hundreds column can be  6,7,8,or 9.   That is 4 possibilies

the tens column can be 5,6,or 7  that is 3 possibilities.

The unit column has to be 2, only one possibility

so there are   4*3*1 =        12 possible numbers

Gradient is the same thing as slope

The equation for slope  is  rise/run=   (y1-y2) / (x1-x2)  = (a-1) / (4-8) = 3/4   now solve for 'a'

a-1 = -3

a= -2

3.

5  =  log 0.9059049

10⁵  =  0.9059049

2.     I am guessing that your equation is this...

5⋅215^x  =  16

                                         Divide both sides of the equation by  5 .

215^x  =  3.2

                                         Take the log of both sides.

log( 215^x )  =  log( 3.2 )

                                         Now we can bring the  x  out like this...

x log 215   =   log 3.2

                                         Divide both sides by  log 215  .

x  =  log 3.2 / log 215       Your answer options look a bit mixed up...

Here is another post with two of the same questions on it:

Thank you!

I don't understand what you are asking but someone else might. :/