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1 answer:
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Part A
There is a perfect positive correlation going on here, so r = +1 or simply r = 1. This is because all of the points are on the same straight line, and this line has a positive slope. Each time x goes up by 1, y goes up by 3. The slope is m = (change in y)/(change in x) = 3/1 = 3
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Part B
The slope is 3 as mentioned back in part A. Further confirmation can be shown if you pick any two points and use the slope formula m = (y2-y1)/(x2-x1). I'll use the first two points
m = (y2-y1)/(x2-x1)
m = (7-4)/(1-0)
m = 3/1
m = 3
Note how (x,y) = (0,4) is on the line so the y intercept is 4.
So we go from y = mx+b to y = 3x+4
Plug x = 0 into y = 3x+4 and you should get y = 4. Plug x = 1 into y = 3x+4 and you should get y = 7. Etc etc
The function that perfectly fits the data is y = 3x+4
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Part C
The slope is 3 tells us how fast the plant grows per day. In this case, it grows 3 centimeters per day. You can think of this as the unit rate.
The y intercept is the starting height of the plant, which is 4 cm. On day 0 (starting day) the plant is 4 cm tall. The y intercept is the point where the graph crosses the y axis as shown in the attached image below.
Answer:
∠1=∠3=∠5=∠7=168°
∠6=∠4=∠2=∠8=12°
Step-by-step explanation:
We are given two angles of the same side of parallel lines is 1:14
Please see the attachment to see all angles of parallel lines.
In figure, ∠6 and ∠3 are same side angles.
∠6 : ∠3 = 1 : 14
Therefore, ∠6 = x , ∠3=14x
Sum of angles of same side of parallel lines is 180°
∠6 + ∠3 = 180°
x+14x=180°
x=12
∠6=12°
∠3=168°
∠3=∠1=168° (Vertically Opposite angles)
∠3=∠5=168° (Alternate interior angles)
∠3=∠7=168° (Corresponding angles)
Therefore, ∠1=∠3=∠5=∠7=168°
∠6=∠8=12° (Vertically Opposite angles)
∠6=∠4=12° (Alternate interior angles)
∠6=∠2=12° (Corresponding angles)
Therefore, ∠6=∠4=∠2=∠8=12°
