Greg's distance is 3 times than Jed. so, 25 yards * 3 = 75 yards. And RJ ran only 0.1 times than Greg (75 yards). So, it should be 7.5 yards
Answer:
19
Step-by-step explanation:
15z-14z=12+7
z=19
You use distributive property to distribute the numbers out.
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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:
POSTULATE
Step-by-step explanation:
<em>A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven
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<em>In geometry, the theorem is considered valid or correct with which its assertion is practically not refuted by almost anyone, whether it is really true or not.
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<em>This, in practice, implies that all students of the subject share the same criteria on the theory. Thus, the postulates, in short, have the following characteristics:
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<em> They are presumed true by most of the scholars in the field.
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<em>Its contradiction goes against the very essence of the subject.
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<em>Postulate 6: If two planes intersect, then their intersection is a line.</em>
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<em>See Attachment for Details ^^</em>
<em>The image attached represents the statement given in the question (If two distinct planes intersect, then their intersection is a line)</em>
<em>Therefore</em><em>,
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<em>The Geometry term that represents the statement above is POSTULATE</em>
