One faucet fills up a bathtub in 15 minutes while the second fills it up in 10 minutes. If both faucets are turned on, what frac
2 answers:
Faucet one fills up 
of the bathtub in one minute and faucet two fills up 
of the bathtub in one minute. If both are one then they will fill up 
So, 1/6 of the bathtub in one minute.
Answer:
Both the faucets will fill 1/6th part of the bathtub.
Step-by-step explanation:
This question can be solved with help of unitary method, means we will calculate the fraction of the bathtub filled by both the faucets individually then by adding their fractions.
∵ 15 minutes have been taken by one faucet is = 1 bathtub.
∴ in 1 minute the fraction of tub can be filled = 1/15 part of full bathtub
Similarly for the second faucet
∵ 10 minutes have been taken by second faucet is = 1 bathtub
∴ in 1 minute the fraction of bathtub will be filled = 1/10 part of bathtub.
Now we will add them to get the fraction of bathtub filled by both the faucets in one minute.
= 1/10 + 1/15=
Therefore 1/6th part of the bathtub will be filled in 1 minute by both the faucets.
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Answer:
g(x) = -3/5|x -6| +4
Step-by-step explanation:
Given the graph of an absolute value function, you want the equation for it.
<h3>Transformations</h3>The desired form is ...
g(x) = a|x -h| +k
The parameters a, h, k represent different features of the transformation of the graph of the parent function f(x) = |x|.
<h3>Vertical scale factor</h3>The parameter 'a' is the vertical scale factor. There are two features of this graph that tell you what the value is.
- the slope of the lines
- the direction of opening
The line on the left side of the vertex seems to intersect points (1, 1) and (6, 4). The slope of this line can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (4 -1)/(6 -1) = 3/5
The graph opens downward, meaning that the parent absolute value function has been reflected across the x-axis. In other words, the sign of 'a' is negative. Its magnitude is the slope we just found, so ...
- a = -3/5
When a function is translated h units horizontally and k units upward, the transformed function becomes ...
g(x) = f(x -h) +k
We notice the vertex of the graph has moved from (0, 0) to (6, 4), so we have ...
- h = 6
- k = 4
Now that we know the values of the parameters in the equation, we can write it as ...
__
<em>Additional comment</em>
Finding the vertical scale factor will work differently for different kinds of functions. In general, you want to find some vertical feature of the original function that you can recognize in the transformed function.
Here, that "feature" is the fact that an absolute value function has a rise of 1 for each run of 1 (a slope of 1) to the right of the vertex. This graph has a "rise" of -3 for a run of 5 to the right of the vertex. Effectively, the graph of the original absolute value function has been scaled by a factor of -3/5.