Each car can hold 5 students and each minibus can hold 15 students.
1 answer:
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Answer:
- vertical scale ×2; translate (-1, -5); (-1, -5), (0, -3), (-2, -3)
- vertical scale ×1/2; translate (3, 1); (3, 1), (1, 3), (5, 3)
- reflect over x; vertical scale ×2; translate (-3, -4); (-3, -4), (-2, -6), (1, -8)
Step-by-step explanation:
Transformation of parent function f(x) into g(x) = c·f(x-h)+k is a vertical scaling by a factor of c, and translation by (h, k) units to the right and up. If c is negative, then a reflection over the x-axis is also part of the transformation. Once you identify the parent function (here: x² or √x), it is a relatively simple matter to read the values of c, h, k from the equation and list the transformations those values represent.
For most functions, points differing from the vertex by 1 or 2 units are usually easily found. Of course, the vertex is one of the points on the function.
<h3>1.</h3>(c, h, k) = (2, -1, -5)
- vertical scaling by a factor of 2
- translation 1 left and down 5
Points: (-1, -5), (-2, -3), (0, -3)
__
<h3>2.</h3>(c, h, k) = (1/2, 3, 1)
- vertical scaling by a factor of 1/2
- translation 3 right and 1 up
Points: (3, 1), (1, 3), (5, 3)
__
<h3>3.</h3>(c, h, k) = (-2, -3, -4)
- reflection over the x-axis
- vertical scaling by a factor of 2
- translation 3 left and 4 down
Points: (-3, -4), (-2, -6), (1, -8)
_____
<em>Additional comment</em>
For finding points on the parabolas, we use our knowledge of squares and roots:
1² = 1, 2² = 4
√1 = 1, √4 = 2
Answer:
The number of bacteria after
days is given by
where is the initial number of bacteria.
Step-by-step explanation:
The number of bacteria in the sample triples every 10 days, this means after the first 10th day, the number of bacteria is
where is the initial number of bacteria in the sample.
After the 2nd 10th days, the number of bacteria is
after the 3rd day,
and so on.
Thus, the formula we get for the number of bacteria after the <em>n</em>th 10-days is
where is is the <em>n</em>th 10-days.
Since, is 10 days, we have
or
Substituting that into , we get: