4. Find the average rate ofchange, from 20 to 80 in
the table below.
х
20
40
60
80
100
y
15
35
65
105
215

Answer:

A is the correct option.

Step-by-step explanation:

The slope of the line is 2 and the y-intercept is -6.

y-intercept is the point where x is zero. Hence, the point is (0,-6)

When we graph a linear function by slope-intercept method, first of all we plot the y-intercept.

Hence, first of all we plot the point (0,-6)

Now, slope is given by

if rise is positive then we move up from the y -intercept and if negative then move down. We keep run always positive and hence we move right from the rise point.

rise = 2

run = 1

Rise is positive hence, we move 2 units up from the point (0,-6) and then move 1 unit right to get the next point. Then we draw a line passing through these points.

A is the correct option.

Answer:

cot(-53π/6) = cot(7π/6) = √(3)

Step-by-step explanation:

Remember that a trig function repeats itself every 2π, so you can add any multiple of 2π to your angle and it'll give you the same answer.

cot(-53π/6) = cot(-53π/6 + 2πk)

= cot(-53π/6 + 2π·5)

= cot(-53π/6 + 10π)

= cot(7π/6)

= [-√(3)/2] / [-1/2]

= √(3)

Answer:

r(180°,0) is a rotation of 180° degrees over the origin.

Notice that this rotation moves our figure to the opposite quadrant (so a translation of two quadrants).

Then this is equivalent to:

A reflection over the x-axis followed by a reflection over the y-axis.

Or.

A reflection over the y-axis followed by a reflection over the x-axis.

There is another possible reflection, but it depends on where is our figure.

If the figure is in the first or third quadrant, a reflection over the line y = -x is equivalent to the rotation.

If the figure is in the second or third quadrant, then the reflection over the line y = x is equivalent to the rotation.

We can combine those two and write:

A reflection over the line y = (-1)^n*x.

Where n is the number associated with the quadrant where the figure is in.

Final answer:

A rotation reflection, r(180°, O)(△BCD), can be achieved by performing two reflections over intersecting lines.

If the lines intersect at an angle of 90 degrees, the combination of the two reflections would result in a 180-degree rotation.

Explanation:

The mathematical question requires knowledge of geometrical transformations, specifically, reflections.

The rotation reflection, r(180°, O)(△BCD), means the initial triangle within the plane is reflected over a point 'O' by 180 degrees.

This reflection will result in an image equivalent to a series of two reflections over intersecting lines.

In commonly accepted mathematical conventions, it is generally accepted that any rotation can be represented by two reflections over intersecting lines.

For instance, two reflections over lines intersecting at an angle ∅/2 represent a rotation by an angle ∅, hence, a rotation by 180 degrees would mean the intersecting angle is 90 degrees.

Learn more about Geometrical Transformations here:

brainly.com/question/31737635

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