The equation of the plane that goes through these points is:
6x + 2y + z = 10.
<h3>How to find the equation of a plane given three points?</h3>
The equation of the plane is found replacing the points into the following equation:
ax + by + c = z.
For point A, we have that:
3b + c = 4.
For point B, we have that:
a + 2b + c = 0.
For point C, we have that:
-a + 6b + c = 4.
Hence the system is:
From the first equation, we have that:
c = 4 - 3b.
Replacing in the second, we have that:
a + 2b + 4 - 3b = 0
a - b = -4.
Replacing in the third, we have that:
-a + 6b + 4 - 3b = 4.
-a + 3b = 0.
a = 3b.
We have that a - b = -4, hence:
3b - b = -4
2b = -4
b = -2.
a = 3b, hence a = -6.
c = 4 - 3b -> c = 10.
Hence the equation is:
ax + by + c = z.
z = -6x - 2y + 10
6x + 2y + z = 10.
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Answer:
12.6 square feet
Step-by-step explanation:
So first we set it up:
18ft is 100% of the original
and the area of the copies are 70%
Copies: x
x/70 = 18/100
70(18) = 1260
1260/100 = 12.6
x = 12.6
Answer: the distance of the base of the house to the foot of the ladder is 6.84 feet
Step-by-step explanation:
The scenario is shown in the attached photo.
Right angle triangle ABC is formed when the ladder leans against the wall of the house.
AC = the height of the ladder
AB = x feet = distance of the base of the house to the foot of the ladder
BC is the wall of the building.
To determine x, we will apply trigonometric ratio
Cos # = adjacent/hypotenuse
Where
# = 70 degrees
Hypotenuse = 20
Adjacent = x
Cos 70 = x/20
x = 20cos70
x = 20 × 0.3420
x = 6.84 feets
The steps on the construction of a segment bisector by paper folding, and label the midpoint M is given below.
<h3>What are the steps of this construction?</h3>
1. First, one need to open a Compass so that it is said to be more than half the length of the said segment.
2. Without altering it, with the aid of the compass, do draw an art above and also below the said line segment from one of the segment endpoints.
3. Also without altering it and with use the compass, do draw another pair of arts from the other and points. One arc will be seen above the segment and the other or the second arc will be seen below.
4. Then do draw the point of intersection that is said to exist between the pair of arts below the line segment and also in-between the pair of arts as seen below the line segment
5. Lastly, do make use of a straight edge to link the intersection points between the both pair of arts.
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I think the answer is 1/2. C.
