The table shows the number of hours of sleep all members of a theater group got the night before their musical.
2 answers:
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<h2>Answer:</h2>
Ques 1)
Ques 2)
Ques 1)
We know that if a graph is stretched by a factor of a then the transformation if given by:
f(x) → a f(x)
Also, we know that the translation of a function k units to the right or to the left is given by:
f(x) → f(x+k)
where if k>0 then the shift is k units to the left
and if k<0 then the shift is k units to the right.
Here the graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.
This means that the function g(x) is given by:
Ques 2)
We know that the transformation of the type:
f(x) → f(x)+k
is a shift or translation of the function k units up or down depending on k.
If k>0 then the shift is k units up.
and if k<0 then the shift is k units down.
Here, The graph of the function f(x)=|3x| is translated 4 units up.
This means that the transformed function g(x) is given by:
Bernard’s walking speed is 140 meters per minute
Bernard’s walking speed is 8.4 kilometers per hour
Step-by-step explanation:
The pace length P is the distance between the rear of two consecutive footprints
The formula, n P = 140, gives an approximate relationship between n and P where,
- n = number of steps per minute
- P = pace length in meters
- Bernard knows his pace length is 0.80 meters
- The formula applies to Bernard’s walking
We need to calculate Bernard’s walking speed in meters per minute and in kilometers per hour
∵ n = number of steps per minute
∴ n unit is number / minute
∵ P = pace length in meters
∴ P unit is meter
- That means n P unit is meters/minute
∴ n P represents the speed in meters per second
∵ The formula applies to Bernard’s walking
∵ His pace length is 0.80 meters
∵ n P = 140
∴ n(0.8) = 140
- Divide both sides by 0.8
∴ n = 175
- That means he moves 175 steps per minute
∵ The distance he walks in minute = 175 × 0.8 = 140 meters/minute
∴ His speed is 140 meters per minute
Bernard’s walking speed is 140 meters per minute
∵ 1 km = 1000 m
∵ 1 hour = 60 minutes
- Divide the meters by 1000 and the minute by 60 to change
from meters per minute to kilometers per hour
∴ His walking speed = ÷
- Change ÷ to × and reciprocal the fraction after the division sign
∴ His walking speed = ×
= 8.4 km/h
Bernard’s walking speed is 8.4 kilometers per hour
Learn more:
You can learn more about the speed in brainly.com/question/5461619
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In this question , we have a graph given, and we have to find the x coordinate of the intersection point .
From the graph , the input value is approximately 3.3 .
In the graph,
And for g(x), we need the slope and y intercept .
Slope is the ratio of rise and run .
Here rise equals 3 units and run equals 2 units. And the graph touch the y axis at -2 .
So the equation of g(x) is
We need to do
Substituting the values of the two functions, we will get
Adding 2 to both sides
Cross multiplication
So the input value is 3.3 approx