3x - 6y = -2
-6y = -3x - 2, divide through by -1
6y = 3x + 2, divide through by 6
y = 3x/6 + 2/6
y = x/2 + 1/3
The sum of the angle 5 and angle 6 is 180 degrees. Then the correct option is C.
<h3>What is Supplementary angle?</h3>
When two angles are said to be supplementary angles if their sum is 180 degrees.
A triangle is shown with its exterior angles.
The interior angles of the triangle are angles 2, 3, 5.
The exterior angle at angle 2 is angle 1.
The exterior angle at angle 3 is angle 4.
The exterior angle at angle 5 is angle 6.
We know that the sum of interior and exterior angle of the triangle is 180 degrees.
∠1 + ∠2 = 180°
∠3 + ∠4 = 180°
∠5 + ∠6 = 180°
Then the correct option is C.
More about the Supplementary angle link is given below.
brainly.com/question/15767203
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Answer:
4.5
Step-by-step explanation:
0.5p-3.45=-1.2
add 3.45 to -1.2 which would leave the equation to look like
0.5p=2.25
then divide 0.5 to both sides cancelling 0.5 leaving the answer to be
p=4.5
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.
Answer:
-1
Step-by-step explanation:
4 + (-2) - (-3) - 6
4 - 2 + 3 - 6
2 - 3
-1
