Answer:
The rate is 1.75 feet/seconds or 105 feet/minute.
Step-by-step explanation:
Given that,
Li walks at a constant rate of 7 feet in 4 seconds
To find the constant of proportionality, divide 7 feet by 4 seconds.
So,
1.75 ft/s is the constant of proportionality
We know that, 1 minute = 60 seconds
k = 105 feet/minute
So, the rate is 1.75 feet/seconds or 105 feet/minute.
Answer:
25.968
Step-by-step explanation:
The Google calculator will reliably use PEMDAS to evaluate an expression.
= (2.1 +30.36)×0.8
= 32.46×0.8
= 25.968
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If entering this expression into your calculator gives a different result, get a better calculator.
Answer:
Step-by-step explanation:
These are the transformations of interest:
g(x) = k·f(x) . . . . . vertical scaling (expansion) by a factor of k
g(x) = f(x) +k . . . . vertical translation by k units (upward)
g(x) = f(x/k) . . . . . horizontal expansion by a factor of k. When k < 0, the function is also reflected over the y-axis
g(x) = f(x-k) . . . . . horizontal translation to the right by k units
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Here, we have ...
g(x) = 1/3f(-1/3(x+1)) +3
The vertical and horizontal transformations can be applied in either order, since neither affects the other. If we work left-to-right through the expression for g(x), we can see these transformations have been applied:
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<em>Additional comment</em>
The "working" is a matter of matching the form of g(x) to the forms of the different transformations. It is a pattern-matching problem.
The horizontal transformations could also be described as ...
The initial translation in this scenario would be reflected to a translation left 1/3 unit, then the horizontal expansion would turn that into a translation left 1 unit, as described above. Order matters.
Answer:
The farmer have at first <u>202</u> chickens.
Step-by-step explanation:
Given:
A farmer had twice as many chickens as ducks on his farm. After he sold 166 chickens and ducks, he had half as many chickens as ducks left.
Now, to find the chickens farmer have at first.
Let the chickens be
And, the ducks be
<em>As, the farmer had twice as many chickens as ducks on his farm.</em>
So, ......(1)
<em>As, given the farmer after selling 166 chickens and ducks, he had half as many chickens as ducks left.</em>
According to question:
Substituting the value of from equation (1) we get:
<em>By cross multiplying we get:</em>
<em>Adding both sides 332 we get:</em>
<em>Subtracting both sides by </em><em> we get:</em>
<em>Dividing both sides by 3 we get:</em>
Now, to get the number of chickens substituting the value of in equation (1):
Therefore, the farmer have at first 202 chickens.