Which case allows for more than one triangle with the given measures to be constructed?
1 answer:
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Option C
The distance of a spin of one full rotation is 31.4 feet
<em><u>Solution:</u></em>
Given that,
A circular merry-go-round has a radius of 5 feet
Radius = 5 feet
We have to find the distance of spin for one full rotation
Distance covered in 1 full of rotation is equal to circumference of circle
<em><u>The circumference of circle is given as:</u></em>
Where "r" is the radius
Thus the distance of a spin of one full rotation is 31.4 feet
Answer:
A. y = (x -7)² +9
B. y = -(x +3)² -11
C. minimum, (7, 9)
D. maximum, (-3, -11)
Step-by-step explanation:
The general steps to rewriting the function in vertex form are ...
1. factor out the leading coefficient (if not 1) from the first two terms
2. add inside parentheses the square of half the x coefficient; subtract the same amount outside parentheses. The factor in front of the parentheses must be taken into account when adding the same amount outside.
3. rewrite the content of parentheses as a square, collect terms outside parentheses.
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A. y = x² -14x +58
y = (x² -14x) +58 . . . . . . . . . . step 1
y = (x² -14x +49) +58 -49 . . . step 2
y = (x -7)² +9 . . . . . . . . . . . . . step 3
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B. y = -x² -6x -20
y = -(x² +6x) -20
y = -(x² +6x +9) -20 -(-9)
y = -(x +3)² -11
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C. In vertex form, the function for vertical scale factor "a" and vertex (h, k) looks like ...
y = a(x -h)² +k
When a < 0, the vertex is a maximum (the graph opens downward); when a > 0, the vertex is a minimum (the graph opens upward).
The function of part A has a minimum at the vertex (7, 9). 9 is the minimum value.
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D. The function of part B has a maximum at the vertex (-3, -11). -11 is the maximum value.
