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1 answer:
Answer: A) No, because it has a constant rate of change
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Explanation:
Each time x goes up by 1, y drops by 2.
This means,
slope = rise/run
slope = (change in y)/(change in x)
slope = (y drops by 2)/(x goes up by 1)
slope = -2/1
slope = -2
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We can pick two points from the table to plug into the slope formula. I'll pick the first two rows
m = slope
m = (y2-y1)/(x2-x1)
m = (2-4)/(7-6)
m = -2/1
m = -2
If you tried every pair of rows possible for this table, you'll get the same slope each time. This is why the rate of change is constant.
This means the data is linear instead of nonlinear. Plotting the points leads to a single straight line going through all four points. See the diagram below. The graph was made with GeoGebra.
The equation of that red line is y = -2x+16 which is equivalent to 2x+y = 16.
In the graph, going from A to B has us go down 2 and to the right 1, which is one visual way of seeing the slope is -2/1 = -2.
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Answer:
57.3°
Step-by-step explanation:
A 25 feet ladder leans against a building.
The ladder's base is 13.5 feet from the building.
The ladder, the wall of the building and the ground form a right-angled triangle of:
Hypotenuse = 25 feet
Base = 13.5 feet
We are to find the angle of elevation which the ladder makes with the ground (or rather the angle created by hypotenuse and base)
Let's say the angle = X°
According to a trigonometric equation;
cos X° = adjacent side ÷ hypotenuse = = 0.54
= 57.5=3° (Answer rounded up to nearest one decimal place).
∴ The angle of elevation = 57.3°
Answer:
15. 31.42 cm^2
16. 25.73 m^2
17. Fly A
Step-by-step explanation:
15.
The blue shaded region is a sector of a circle. The formula for area of sector =
Where is the central angle and r is the radius
<em>For the diagram, we have 80° arc and 180° arc as the "white" area. Since the whole circle is 360°, the shaded region arc is 360 - (80+180) = </em><em>100°.</em><em> this is and the radius is 6. </em>
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Plugging in it in the formula we get:
Area of shaded region = cm^2
16.
We can say that area of shaded region = area of parallelogram - area of circle
Now,
Area of Parallelogram = b * h
where
b is the base (it is 6+3=9) and h is the height (diameter of the circle is the height = 6)
Area of Parallelogram = 9 * 6 = 54
Area of Circle = πr^2 where r is the radius, which is 6/2=3
Area of Circle = π(3)^2 = 9π
Now,
Area of Shaded Region = 54 - 9π = 25.73 m^2
17.
For the first figure (rectangle) we could let the height be h (since not given). So area of yellow region would be 4h (area of rectangle is base * height)
And area of whole ruler would be 8*h = 8h
So probability of landing in yellow region would be
For 2nd figure, the yellow region has area of π(2)^2 = 4π ( radius of yellow circle is 2 and area of circle is πr^2)
Area of whole circle is π(4)^2 = 16π
So probability of landing in yellow region would be
<em>Hence, </em><em>Fly A is more likely to land in a yellow region.</em>