Answer:
x = 7
y = -4
Step-by-step explanation:
5x = 35
x=7
14 + 2y = 6
2y = -8
y = -4
Answer:
<em>5.5</em>
Step-by-step explanation:
Given the set of data
5, 4, 2, 1, 1, 2, 10, 2, 3, 5.
The average of the least and the greatest value is known as the midrange
The formula for calculating the midrange is expressed as shown:
Midrange = (Greatest value + Least value)/2
Given
Greatest value = 10
Least value = 1
Midrange = 10+1/2
Midrange = 11/2
Midrange = 5.5
<em>Hence the midrange of the data is 5.5</em>
Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).
topjm [15]
Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)
We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>
The vector product pq x pr gives a vector perpendicular to both pq and pr. This vector is the normal vector of a plane passing through all three points
pq x pr
=
i j k
-4 -2 -4
-3 5 1
=<-2+20,12+4,-20-6>
=<18,16,-26>
Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>
The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).
The equation of the required plane is therefore
Π : 9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π : 9x+8y-13z=24
Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.
The answer is 22.5 so the reminder will be 1/2 or .5
6n+1 = 25
subtract 1 from each side
6n+1-1 = 25-1
6n = 24
divide each side by 6
6n/6 = 24/6
n =4
