Workers in an office of 40 staff were asked their favourite type of take-away.
2 answers:
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Answer:
Step-by-step explanation:
The table shows a set of x and y values, thus showing a set of points we can use to find the equation.
1) First, find the slope by using two points and substituting their x and y values into the slope formula, . I chose (-3, 13) and (0,17), but any two points from the table will work. Use them for the formula like so:
Thus, the slope is .
2) Next, identify the y-intercept. The y-intercept is where the line hits the y-axis. All points on the y-axis have a x value of 0. Thus, (0,17) must be the y-intercept of the line.
3) Finally, write an equation in slope-intercept form, or format. Substitute the
and
for real values.
The represents the slope of the equation, so substitute it for
. The
represents the y-value of the y-intercept, so substitute it for 17. This will give the following answer and equation:
Answer:
A: The transformations are a rotation and a translation.
Step-by-step explanation:
The function f(x) is shown in the attachment as a dashed red line. The function g(x) is shown as the blue line.
The two lines have different slopes. The change in slope can be accomplished by horizontal or vertical scaling, or by rotation. The offered answer choices only include <em>rotation</em> as an option for changing the slope.
The two lines have different intercepts. To move the line from one intercept to another, generally translation is involved.
The simplest transformation is rotation and translation.
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<em>Comment on the answer choices</em>
If the reflection is done across a line other than an axis, or if the rotation is done about a point other than the origin, then <em>any combination of rotation, reflection, and translation can be used to make the transformation seen</em>. (Translation alone is not sufficient.)
For example, reflecting the line across the bisector of the angle between the lines (a line with a slope of (√13 -2)/3 through (5, 5)) will give the desired transformation in one step.
Similarly, a rotation of about 33.69° about the point (5, 5) will give the transformation in on step. (That angle is 45°-arctan(1/5).)
