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It is night where I am. I am doing great as well. Good night.

I am pretty sure it is 25.

Sorry I'm late, but Happy [Belated] Birthday Rosala!

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About a month and a half I reckon

I think it might be 12

5 * 5 = 25.

Well, let's look at the equation. 

We have -3(y-1) = 9.

Divide both sides by -3 and get y-1 = -3.

Add 1 to both sides to get y= -2.

Now we have to find the value of (1/2)*y.

We know y is -2, so -2*(1/2) = -1

The answer is -1.

Oreo?

Oreo!

It simplifies to (a^2)/xy

Done F12

  z^4=81

z=3    is one answer, the others are    z=-3,    z=3i    and     z=-3i

a) 3149810398401392821

factor(3149810398401392821) = 3149810398401392821

b) 3098402938409238409

factor(3098402938409238409) = (47*589783)*111775800209

c) 9348509189323894393

factor(9348509189323894393) = ((17*31)*421)*42135645180779

d) 2309482390481134983

factor( 2309482390481134983) = ((3^3*15901)*86017)*62537737

e) 3294829348201392047

factor(3294829348201392047) = (3881*754249)*1125575263

There you go, web2.0 is a pretty cool calculator :) 

I do not know what you are asking :/

Find the equation of the parabola with coordinates of the vertex (0,0) and equation of the axis y=0 and passing through the point (3,6)

\(y^2=4ax\\ \text{sub in x=3, y=6}\\ 36=4a*3\\ a=3\\ so\\ y^2=12x\)

Rectangle \(ABCD\) is the base of pyramid \(PABCD\). If \(AB = 8\), \(BC = 4\),
\(\overline{PA}\perp \overline{AB}\), \(\overline{PA}\perp\overline{AD}\), and PA = 6, then what is the volume of \(PABCD\)?

\(\begin{array}{|rcll|} \hline V &=& \frac13 \cdot G \cdot h \\ &=& \frac13 \cdot (4\cdot 8) \cdot 6 \\ &=& 4\cdot 8 \cdot 2 \\ &=& 64 \\ \hline \end{array}\)

If jerry plays in the next two succesive games calculate the probability  of him scoring in just one of the matches.

the probability of Jerry scoring is 0.45

the probability of Jerry not scoring is 0.55

scoring in just one of the matches = 0.45 * 0.55 + 0.55 * 0.45 = 0.495

The instantaneous rate of change of f(x) = 6x² - 9 at any x is f`(x) = 12x.  This is a straight line.  Its average value between x=2 and x=b is (12b + 12*2)/2 → 6b+12

As follows:

.

Solve for x:
(sqrt(3) sqrt(x) - 4 sqrt(3))/(sqrt(x) - sqrt(2)) = (2 sqrt(2) sqrt(x) + sqrt(2))/(sqrt(6) sqrt(x) - 2 sqrt(3))

Cross multiply:
(sqrt(3) sqrt(x) - 4 sqrt(3)) (sqrt(6) sqrt(x) - 2 sqrt(3)) = (sqrt(x) - sqrt(2)) (2 sqrt(2) sqrt(x) + sqrt(2))

Subtract (sqrt(x) - sqrt(2)) (2 sqrt(2) sqrt(x) + sqrt(2)) from both sides:
(sqrt(3) sqrt(x) - 4 sqrt(3)) (sqrt(6) sqrt(x) - 2 sqrt(3)) - (sqrt(x) - sqrt(2)) (sqrt(2) + 2 sqrt(2) sqrt(x)) = 0

(sqrt(3) sqrt(x) - 4 sqrt(3)) (sqrt(6) sqrt(x) - 2 sqrt(3)) - (sqrt(x) - sqrt(2)) (sqrt(2) + 2 sqrt(2) sqrt(x)) = 26 + (-13 sqrt(2) - 2) sqrt(x) + sqrt(2) x:
26 + (-13 sqrt(2) - 2) sqrt(x) + sqrt(2) x = 0

Simplify and substitute y = sqrt(x).
26 + (-13 sqrt(2) - 2) sqrt(x) + sqrt(2) x = 26 + (-13 sqrt(2) - 2) sqrt(x) + sqrt(2) (sqrt(x))^2
 = sqrt(2) y^2 + (-2 - 13 sqrt(2)) y + 26:
sqrt(2) y^2 + (-2 - 13 sqrt(2)) y + 26 = 0

The left hand side factors into a product with two terms:
(y - 13) (sqrt(2) y - 2) = 0

Split into two equations:
y - 13 = 0 or sqrt(2) y - 2 = 0

Add 13 to both sides:
y = 13 or sqrt(2) y - 2 = 0

Substitute back for y = sqrt(x):
sqrt(x) = 13 or sqrt(2) y - 2 = 0

Raise both sides to the power of two:
x = 169 or sqrt(2) y - 2 = 0

Add 2 to both sides:
x = 169 or sqrt(2) y = 2

Divide both sides by sqrt(2):
x = 169 or y = sqrt(2)

Substitute back for y = sqrt(x):
x = 169 or sqrt(x) = sqrt(2)

Raise both sides to the power of two:
x = 169 or x = 2

(sqrt(3) sqrt(x) - 4 sqrt(3))/(sqrt(x) - sqrt(2)) ⇒ (sqrt(3) sqrt(2) - 4 sqrt(3))/(sqrt(2) - sqrt(2)) = ∞^~
(2 sqrt(2) sqrt(x) + sqrt(2))/(sqrt(6) sqrt(x) - 2 sqrt(3)) ⇒ (sqrt(2) + 2 sqrt(2) sqrt(2))/(sqrt(6) sqrt(2) - 2 sqrt(3)) = ∞^~:
So this solution is incorrect

(sqrt(3) sqrt(x) - 4 sqrt(3))/(sqrt(x) - sqrt(2)) ⇒ (sqrt(3) sqrt(169) - 4 sqrt(3))/(sqrt(169) - sqrt(2)) = -(9 sqrt(3))/(sqrt(2) - 13) ≈ 1.34548
(2 sqrt(2) sqrt(x) + sqrt(2))/(sqrt(6) sqrt(x) - 2 sqrt(3)) ⇒ (sqrt(2) + 2 sqrt(2) sqrt(169))/(sqrt(6) sqrt(169) - 2 sqrt(3)) = (9 sqrt(6))/(13 sqrt(2) - 2) ≈ 1.34548:
So this solution is correct

x = 169 - Courtesy of Mathematica 11 - !!!!

[ √[3x] - 4√3 ]   =   2√[2x] + √2

__________       __________

√x  - √2                 √[6x] - 2√3

[ √3 (√x - 4) ]  =  [ √2 ( 2√x + 1) ]

__________     _____________ 

√x  - √2               √[6x] -  √12 

[ √3 (√x - 4) ]  =  [ √2 ( 2√x + 1) ]

__________     _____________

√x  - √2               √6 [ √x - √2 ]

[ √3 (√x - 4) ]  =  [ √2 ( 2√x + 1) ]

                           _____________

                               √6

[ √3 (√x - 4) ]  =  [ ( 2√x + 1) ] / √3

3[√x -  4]    =     2√x + 1

3√x - 12   =   2√x + 1

√x  =  13

x  = 169

I am going to try to simplify the denominators first.

The second denominator is  sqrt(6x) - 2·sqrt(3).

However, 2·sqrt(3) can be written as sqrt(4)·sqrt(3) = sqrt(12)

     and sqrt(12) can be written as sqrt(6)·sqrt(2),

so sqrt(6x) - 2·sqrt(3) becomes sqrt(6)·sqrt(x) - sqrt(6)·sqrt(2),

and, factoring, becomes:  sqrt(6)[sqrt(x) - sqrt(2)].

This is almost the same as the first denominator, which is simply [sqrt(x) - sqrt(2)].

This means that if x = 2, these denominators are zero, so if we get an answer of 2, we'll have to throw it out.

Now, let's multiply both sides by sqrt(6)[sqrt(x) - sqrt(2)].

This cancels the denominator on the left side of the equation, but puts a factor of sqrt(6) on the left side.

This completely cancels the denominator on the right side of the equation.

We now have:  sqrt(6)·[sqrt(3x) - 4sqrt(3)]  =  2sqrt(2x) + sqrt(2)

Let's square both sides:

Left side:     [ sqrt(6)·[sqrt(3x) - 4sqrt(3)] ]²  = 6·[ sqrt(3x) - 4sqrt(3) ]²  =  6[ 3x - 2·4·sqrt(3x)·sqrt(3) + 16·3 ]

     =  6[3x - 8·3·sqrt(x) + 48]  =  18x - 144sqrt(x) + 288

Right side:     [ 2sqrt(2x) + sqrt(2) ]²  =  4·2x + 2·2·2·sqrt(x) + 2  

     =  8x + 8sqrt(x) + 2

Setting these two equal:     18x - 144sqrt(x) + 288  =  8x + 8sqrt(x) + 2

Simplifying:     10x - 152sqrt(x) + 286 = 0

Dividing by 2:     5x - 76sqrt(x) + 143  =  0

Using the quadratic formula to find sqrt(x);     sqrt(x)  =  [ 76 +/1 sqrt(76² - 4·5·143) ] / 10

----->     sqrt(x)  =  13 or 2.2

----->     x = 169  or  x = 4.84

Checking both possible answers, 169 works but 4.84 is an extraneous root introduced by the squaring process.

N mod  1,117 =43,  N mod 3,037 =949,  N mod 2,017 =1,064.

We have the following equalities:

1,117A + 43 = 3,037B + 949 =2,017C + 1,064 =N

By simple iteration we get:

A = 28, B = 10, C = 15. Therefore:

N =1,117 x 28 + 43 = 31, 319

N =3,037 x 10 + 949 = 31,319

N =2,017 x 15 + 1,064 = 31, 319 - which is the smallest positive integer that satisfies all 3 equations.

However, the LCM of {1,117, 3,037, 2,017} =6,842,327,593. It follows that:

N = 6,842,327,593D + 31,319, where D =0, 1, 2, 3, 4.......etc.

\(4000(0.85)^4-3 = 2085.025​\)

(2×10^4) (3×10^7)

We can rearrange this as

( 2 x 3) ( 10^4 x 10^7)  =

( 6) [ 10^ (4 + 7) ] =

6 x 10^11  =

600,000,000,000