Answer:
1408 multiply 64 by 22 for a total of 1,408
The normal vector to the plane <em>x</em> + 3<em>y</em> + <em>z</em> = 5 is <em>n</em> = (1, 3, 1). The line we want is parallel to this normal vector.
Scale this normal vector by any real number <em>t</em> to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:
(1, 0, 6) + (1, 3, 1)<em>t</em> = (1 + <em>t</em>, 3<em>t</em>, 6 + <em>t</em>)
This is the vector equation; getting the parametric form is just a matter of delineating
<em>x</em>(<em>t</em>) = 1 + <em>t</em>
<em>y</em>(<em>t</em>) = 3<em>t</em>
<em>z</em>(<em>t</em>) = 6 + <em>t</em>
The vertices of the triangle are the points where any pair of lines intersect.
We start by setting up the system
Using one of the two equations we can derive the correspondent y value:
So, one vertex is (1, 1)
We choose the other two pairs of lines to find the other vertices:
So, the three vertices are (1, 1), (2, 0), (-1, -3).
Answer:
B. The second choice.
Step-by-step explanation:
A function cannot have two points with the same x-coordinate.
If you graph two different points that have the same x-coordinate, they will both lie on the same vertical line. Therefore, if in a relation, more than one point lie on the same vertical line, then the relation is not a function.
Answer:
Step-by-step explanation:
Givens
The triangle is equilateral. Given
<K = < M = 60 Property of an equilateral triangle.
IE = IE Reflexive property
Proof
- <IEK = <IEM = 90 Property of perpendicular
- <EIK = 180 - 60 - 90 All triangles have 180 degrees
- <EIK = 30 Subtraction
- <MIK = 180 - 60 - 90 All triangles have 180 degrees
- <MIK = 30 Subtraction
- <MIE = <KIE Both = 30 degrees
- IE = IE Reflexive property
- <IEK = <MEI Both are right angles.
- ΔMIK ≡ΔKIE ASA
