Take an arbitrary vector (<em>x</em>, <em>y</em>, <em>z</em>), which goes from the origin to some point (<em>x</em>, <em>y</em>, <em>z</em>) on the plane we want to find.
Subtract from this vector, the vector that points to 
, which is (-3, 3, 1). This translates the first vector so that it starts at the point and is directed at some point (<em>x</em>, <em>y</em>, <em>z</em>). We get a new translated vector, (<em>x</em> + 3, <em>y</em> - 3, <em>z</em> - 1), which lies in the plane.
The normal vector to the plane is orthogonal to every vector in the plane. So taking the dot product of any vector in the plane with the normal to the plane will always result in 0. We use this to find the plane's equation:
and so the answer is D.
Answer:
66.67
Step-by-step explanation:
20-12=8
8/12=0.6666667
0.6666667x100=66.67
To write the rule or equation of the linear function we need to find the slope of the function first. Using any two points we can find the slope.
Using the first two points (-3, -1) and (0, 2).
Slope (m) of the function would be:
Using slope and the point (0,2) we can write the equation of the line as:
y - 2 = 1(x-0)
y = x + 2
Thus, the correct rule for the given linear function is x+2
Step-by-step explanation:
Given:
Two Equations
y = x + 5 ..................(1)
y = (3/2) x - 5 ...................(2)
Both are considered as Equation (1) and (2) respectively,
Equating the equation 1 and 2, we get
⇒ x + 5 = (3/2) x - 5
⇒ x - (3/2) x = - 5 - 5
⇒ (2x - 3x) /2 = - 10
⇒ - x = - 20
⇒ x = 20
Now substituting "x = 20" in equation (1), we get
⇒ y = 20 + 5
⇒ y = 25
Thus, we get the value of x = 20 and value of y = 25.
