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ankoles [38]
3 years ago
13

Find an equation of the plane that passes through the origin and its perpendicular to the vector [1,-2,5]

Mathematics
1 answer:
Volgvan3 years ago
8 0

Answer:

x - 2y + 5z = 0

Step-by-step explanation:

The standard equation is of the form, Ax + By + Cz = 0

The equation of the plane that passes through the origin(0, 0, 0)  and is perpendicular to [1, -2, 5] is

A = 1, B = -2, C = 5

x = y = z = 0 (at origin)

A(x-0) + B(y-0) + C(z-0) = 0

(x - 0) -2(y-0) + 5(z-0) = 0

x - 2y + 5z = 0

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What is the factored form of x2 − 4x − 5?
laiz [17]
Factored Form:
x^2 - 4x - 5
Simplifying:
x^2 +  - 4x +  - 5 = 0

Reorder the terms:
- 5 +  - 4x + x^2 = 0

Solving for variable " x":
Subproblem 1:
Set the factor ( - 1 +  - 1x) equal to Zero and attempt to solve.

Simplifying:
- 1 +  - 1x = 0

Solving:
- 1 +  - 1x = 0
Move all terms containing x to the left, all other terms to the right

Add 1 to each side of equation:
- 1 + 1 +  - 1x = 0 + 1

Combine Like Terms: 0 + 1 = 1
x =  - 1


Divide each side by - 1
x =  - 1

Simplifying:  x =  -  1


Subproblem 2: Set the factor (5 +  -  1x) equal to Zero attempt to solve

Simplifying:
5 +  - 1x = 0

Move all terms containing x to the left, all other terms to the right
Add - 5 to each side of the equation
5 +  - 5  +  - 1x = 0 + 5

Combine Like terms:  5 +  - 5 = 0
0 +  - 1x = 0 +  - 5
- 1x = 0 +  - 5

Combine Like Terms: 0 +  - 5 = - 5
- 1x =  - 5

Divide each side by - 1
x = 5

Simplifying:
x = 5

Solution:
x = { - 1,  5}





Answer when factored:
(x + 1)(x - 5)







hope that helps!!!
4 0
2 years ago
Read 2 more answers
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