Hello anonymous and CPhill !

What is the equation of the line which passes through (3,1) and (-2,-4)?

y1 = 1   x1 = 3   y2 = -4   x2 = -2

m = (y2 - x2) / (y1 - x1) = (-4 - (-2)) / (1 - 3) = -2 / -2

m = 1

y = mx + b

y1 = m * x1 +b

b = y1 - m * x1 = 1 - 1 * 3 = 1 - 3

b = - 2

y = ƒ(x) = mx + b

y = ƒ(x) = x - 2

The equation of the line which passes through (3,1) and (-2,-4) is

y = ƒ(x) = x - 2

Greetings   :- )

Hallo anonymous!

a times b equals -8. a plus b equals 7. what is a and b?

a * b = - 8

a + b = 7

a = - 8 / b

a = 7 - b

- 8 / b = 7 - b

- 8 = 7b - b²

b² - 7b - 8 = 0

b1;2 = - (p/2) ±√((p/2)² -q)

b1;2 = 3,5 ±√ (3,5² + 8)

b1;2 = 3,5 ±√ 20,25 = 3,5 ± 4,5

b1 = 8

b2 = -1

a1;2 = 7 - b

a1 = -1

a2 = 8

test :

a1 * b1 = - 8                 

-1 * 8  = - 8   okey

a1 + b1 = 7

-1 + 8 = 7      okey

a2 * b2 = - 8

8 * (- 1) = - 8 okey

a2 + b2 = 7

8 + (-1) = 7 okey

greetings   :- )

Hallo anonymous!

5c - 4 - 2c + 1 = 8c + 2                      both sides : - 8c + 4 - 1

5c - 2c - 8c = 2 + 4 - 1

- 5c = 5                                              both sides :  / ( - 5 )

c = - 1

:- )

Hallo anonymous!

solve 3x^2-8x-11=0

3 x² - 8 x - 11 = 0                    [ / 3

x² (- 8 / 3) x (- 11 / 3) = 0

p = - 8 / 3      q = - 11 / 3

x(1;2) = - p / 2 ±√ ((p / 2)² - q)

x(1;2) = 4 / 3 ±√ ((4 / 3)² + 11 / 3)

x(1;2) = 4 / 3 ±√ (16 / 9 + 33 / 9) = 4 / 3 ±√ (49 /9) = 4 / 3 ± 7 / 3

x1 = 11/3 = 3  2/3

x2 = - 3/3 = - 1

x1 = 3 2/3

x2 = - 1

test:

3 x² - 8 x - 11 = 0

3*(11/3)²-8*(11/3)-11=0

0=0     okey

3*(-1)²-8*(-1)-11=0

0=0     okey

:- )

Hello friends!

The whole backwards.

(2 sqrt(sqrt(3)-3 x) sqrt(sqrt(3)+3 x))/sqrt(3)

= (2 * √ ( √ (3) - 3x ) * √ ( √ (3) + 3x )) / √ (3)

= (2 √ (3 - 9x²)) / √ (3)

= √ ( 12 - 36 x²) / √ (3)

= ( √ (3) * √ (4 - 12 x²)) / √ (3)

= √ ( 4 - 12 x² )

√ ( 4 - 12 x² ) = (2 sqrt(sqrt(3)-3 x) sqrt(sqrt(3)+3 x))/sqrt(3)

Q. E. D.

Greetings    :- )

Hallo anonymous!

Calculate the average speed if a golf cart runs 140 meters in 10 seconds .

v = s / t

v = 140 m / 10 sec = 14 m / sec * (3600 sec / 1 h) * (1 km / 1000m) = 50.4 km / h

The average speed is 14 m / sec or 50.4 km / h.

Greetings  :- )

Hallo anonymous!

0.001% of $5,958,334.00

P = G * p / 100

P = $5 958 334.00 * 0.001 / 100 = $5 958 334.00 * 0.000 001 = $59.58334

0.001% of $5,958,334.00 ar $59.58334

:- )

Hallo anonymous!

sqrt (4-12x^2)

sqrt (4-12x^2) = sqrt (4 * (1 - 3x²)) = 2 * sqrt (1 - 3x²)

= 2 * √(1- 3x²) = 2 * √[(1 + x√3) * (1 - x√3)]

sqrt (4-12x^2) = 2 * √[(1 + x√3) * (1 - x√3)]

Further calculations would result in no additional simplification.

 :- )

Hallo anonymous!

What is y = - x + 4 if x is - 6?

Replace x with (- 6) .

y = - (x) + 4

y = - (-6) + 4

Y = 6 + 4

y = 10

y = 10     if x is - 6

:- )

Hallo anonymous!

what is 1.0x10^14 ?

10 high-14 is a 1 with 14 zeroes.

1,0 x 10^14 = 100 000 000 000 000

This are 100 Billionen in germany. 

These are 100 trillion in england and the united states of america.