Answer:
x + y - 5z = 52
Step-by-step explanation:
Given data:
Point on the plane (3,4,-9)
parallel to x + y -5z = 1
Finding the normal vector
(1 , 1 , -5)(x, y , z) = 1
the normal vector is (1 , 1 , -5)
<em>formula for finding equation the plane given the normal vector (a,b,c) and point (m,n,o) is as </em>
<em>a(x - m) + b(y - n) + c(z-o)=0</em>
Substituting the data we have
1(x-3) + 1( y- 4) - 5(z+9) =0
x-3 +y -4 -5z -45 = 0
x + y - 5z = 45 +4 +3
x + y - 5z = 52
F is located on the numbe<u>r 4.5</u><u> </u>on the number line.
<h3>
</h3><h3>
Where does point F lie on the number line?</h3>
We know that point D is at -6
Point E is at 8.
Point F is between D and E, such that the ratio:
DF:FE is 3:1
So if we divide the distance between D and E in 4 parts, 3 of these parts are DF, and one of these parts is FE.
First, the distance between E and D is:
distance = 8 - (-6) = 14 units.
Now, if we divide that by 4, we get:
14/4 = 3.5
Then we have:
DF = 3*(3.5) = 10.5
This means that F is at 10.5 units to the right of D, then:
F = D + 10.5 = -6 + 10.5 = 4.5
F is located on the numbe<u>r 4.5</u><u> </u>on the number line.
If you want to learn more about ratios:
brainly.com/question/2328454
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Answer:
Step-by-step explanation:
The sum of the ages of a Mother and her son is 78 , three years ago the mother is five times as old as the son, what is their present ages?
To solve this , let the age of the mother be x and the age of the son be y , from the first statement :
x + y = 78
Three years ago , the mother will be x- 3 and the son will be y - 3 , from the second statement:
x - 3 = 5 ( y-3)
x- 3 = 5y - 15
x - 5y = -12
The resulting equations are
x + y = 78
x - 5y = -12
This is called a simultaneous linear equation , that means it is a linear equation.
The side of a square is xcm , if the difference between the area and the perimeter is 12 , find the legth of its side.
Interpretation:
The formula for the area of a square is 
and the perimeter is 4l , from the question , we have
- 4x = 12
This is not a linear equation , it is simply a quadratic equation , so the situation is non linear
