2. the general equation of a plane is ax + by + cz = d, where a, b, c, and d are real numbers and a is nonnegative. find the equation of the plane containing the points (3, 0, 0), (0, 8, 0), and (0, 0, 6). show each step of your process. then graph the plane.

The standard equation is 8x+3y+4z= -24.

Step-by-step explanation:

Given : The general equation of a plane is Ax + By + Cz = D, where A, B, C, and D are real numbers and A is non negative.

We have to find the equation of the plane containing the points (3, 0, 0), (0, 8, 0), and (0, 0, 6).

If given coordinates of three points lying on a plane are defined then the plane equation can be found using the formula,

For the given coordinates, A(3, 0, 0), B(0, 8, 0), and C(0, 0, 6)

Substitute, we have,

Solving further, we get,

Evaluate along row !, we get,

We get,

Simplify , we get,

Thus, the standard equation is 8x+3y+4z= -24

47 - 90 = 43

43 - 180 = x

x = 137

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.