Find the equation of the line that is perpendicular to y = –2x + 5 and contains the point
(2,–1).

The given equation is:

To find the line perpendicular to it, we interchange coefficients and switch the signs of one coefficient.

The equation to a line perpendicular to it is:

$ 2y-x=c$

where, $c$ is some constant we have determine using the condition given.

It passes through $(2,-1)$

Put the point in our equation:

$2(-1)-(2)=c$

$c=-2-2$

$c=-4$

The final equation is:

$\boxed{ 2y-x=-4}$

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0