A roofer sketches a diagram of a house on which he is working.
2 answers:
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Option B
Trevor isn't correct because -2i must also be a root
<em><u>Solution:</u></em>
For the polynomial with roots -7, 2i and 7 their roots can be,
1. ) Real roots
2.) Imaginary roots
The real roots are: -7 and +7
The imaginary root given is: 2i
The imaginary roots come from the square root. So they will be in form of
Therefore,
For f(x) with roots -7 and +7 and we have,
Fundamental Theorem of Algebra states that a polynomial will have exactly as many roots as its degree (the degree is the highest exponent of the polynomial).
So for f(x) with 4 roots, degree of f(x) is 4
So option B is correct. Trevor is not correct because –2i must also be a root.
<h3>Answer:</h3>
Any 1 of the following transformations will work. There are others that are also possible.
- translation up 4 units, followed by rotation CCW by 90°.
- rotation CCW by 90°, followed by translation left 4 units.
- rotation CCW 90° about the center (-2, -2).
The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.
The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is <em>a sequence of transformations</em> involved, so a single rotation is probably not of interest.
If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.
If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.
Of course, rotation 90° CCW in either case is the same as rotation 270° CW.
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We have described transformations that will work. What we don't know is what is in your drop-down menu lists. There are many other transformations that will also work, so guessing the one you have available is difficult.