Select the correct answer. Which factor of production includes human-made resources used to produce a good or a service? A. Land
1 answer:
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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).)
Answers:
- 300 = 12i+36s
- i = 10
- Yes it's reasonable
- i = -11
Refer to the diagram below.
The explanation for each part is below as well.
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Part 1
i = number of individual nail polish bottles
s = number of sets of 4
12i = money earned from just selling the individual bottles only
36s = money earned from just selling the sets of 4 only
12i+36s = total money earned = 300
12i+36s = 300 is the equation to set up
This is the same as 300 = 12i+36s because A = B is the same as B = A.
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Part 2
Plug in s = 5 to represent she sold 5 sets. Let's solve for i
12i+36s = 300
12i+36(5) = 300
12i+180 = 300
12i = 300-180
12i = 120
i = 120/12
i = 10
If she wants to sell $300 worth of product overall, and she already sold 5 sets so far, then she needs to sell 10 individual bottles to reach this monthly goal.
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Part 3
Yes it's reasonable to reach this goal. This is because the value of i (from part 2) was some positive whole number.
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Part 4
We'll repeat part 2 but with s = 12
12i+36s = 300
12i+36(12) = 300
12i+432 = 300
12i = 300-432
12i = -132
i = -132/12
i = -11
As the instructions state, we get a negative value. This is not reasonable because we can't sell a negative number of items. A negative number of items in general doesn't make sense.
The instructions further state that $432 was already made and that she exceeded her goal. Meaning that she doesn't have to worry about selling the individual bottles if selling the sets has her reach something over $300.
