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a) Option B Direct variation, y=1.8x is correct option.
b) Option A Not a direct variation is correct option.
Step-by-step explanation:
a) for the data in the table tell whether y varies directly with X if it does write an equation for the direct variation
The direct variation is represented by:
We need to find k.
Given the values of x and y in table we will find k. if value of k is constant, so x and y varies directly
Since value of k is constant i.e 1.8 so, y varies directly with x.
Option B Direct variation, y=1.8x is correct option.
b) For the data in the table tell whether Y varies directly with x if it does write an equation for the direct variation.
The direct variation is represented by:
We need to find k.
Given the values of x and y in table we will find k. if value of k is constant, so x and y varies directly
Since value of k is not constant so, y doesn't varies directly with x.
Option A Not a direct variation is correct option.
Keywords: Direct variation:
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<h3>Answer: A) 35</h3>
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Short Explanation:
Subtract the arcs and divide by 2 like so
angle 1 = (longerArc - shorterArc)/2
angle 1 = (100 - 30)/2
angle 1 = 70/2
angle 1 = 35 degrees
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Longer explanation:
Refer to the diagram below. I have replaced the 100 and 30 degree arcs with A and B respectively. I've also added in the arc measures of y and z.
Note how the smaller circle arc pieces A, B, y and z all form a complete full circle. So those values add to 360. We get A+B+y+z = 360. We'll use this later.
In the diagram, I've also drawn a blue segment to form a triangle. The angle x we want to find has replaced angle 1. The angles (y+B)/2 and (z+B)/2 are found through the inscribed angle theorem.
Focus on the triangle. The three angles of any triangle always add to 180, so,
(z+B)/2 + (y+B)/2 + x = 180
we can multiply both sides by 2 and we end up with
z+B + y+B + 2x = 360
z+y+2B + 2x = 360
Since we have 360 on the right hand side of this equation, and the equation A+B+y+z = 360, this means that the left sides of each equation are the same.
We can then say the following
z+y+2B + 2x = A+B+y+z
2B+2x = A+B
2x = A+B-2B
2x = A-B
x = (A-B)/2
This is the formula used in the "short explanation" section above. In this case, A = 100 and B = 30, so
x = (A-B)/2
x = (100-30)/2
x = 70/2
x = 35
The measure of angle 1 is 35 degrees.
Side note: With that formula above, we always have A > B.