Answer:
y = 30
Step-by-step explanation:
Use the direct variation equation, y = kx
Plug in 20 as y and 8 as x, then solve for k:
y = kx
20 = k(8)
2.5 = k
So, the equation is y = 2.5x
Plug in 12 as x, and solve for y:
y = 2.5x
y = 2.5(12)
y = 30
So, when x = 12, y = 30
Answers:
- Plane EFGH
- Angle 2 and angle 3
- Alternate exterior angles
- See the explanation below
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Explanation:
Problem 1
The plane ABCD is the floor of the box or room.
The ceiling plane EFGH is parallel to the floor.
Parallel planes never intersect, must like how parallel lines in 2D never intersect. As such, parallel planes are the same distance apart.
In contrast, something like plane ABFE intersects with ABCD along the segment AB. This shows ABFE is not parallel to ABCD.
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Problem 2
Same side interior angles, aka consecutive interior angles, are inside the parallel (or nearly parallel) lines. One such example is angle 2 and angle 3. The other pair being angle 6 and angle 7. They must be on the same side of the transversal.
In contrast, alternate interior angles would be something like the pair angle 2 and angle 7. The other pair being angle 3 and angle 6. This time the angles are on alternating or opposite sides of the transversal.
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Problem 3
Angles 1 and 8 are exterior of the parallel (or nearly parallel) lines. They are on alternating sides of the transversal. Therefore, we consider them to be alternate exterior angles.
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Problem 4
The use of "alternate" refers to the idea the angles are on opposite or alternating sides of the transversal line. The transversal line is the line that crosses the two other lines that are almost parallel.
I like to think of the parallel (or nearly parallel) lines as train tracks. The transversal is the roadway that crosses both train tracks. Then we could have locations 1 and 8 on opposite sides of the roadways to represent the alternate exterior angles.
As you can probably guess or know by now, the "exterior" is from the angles being outside or exterior of the parallel (or nearly parallel) lines.
Answer:400
Step-by-step explanation:
3 hours: 400 times 2=800
6 hours: 800 times 2=1600
9 hours: 1600 times 2=3200
12 hours: 3200 times 2=6400
15 hours: 6400 times 2= 12800
18 hours: 12800 times 2=25,600
21 hours: 25,600 times 2= 51200
24 hours: 102,400
