Answer:
9.55 minutes
Step-by-step explanation:
x hours to go to the river
0.25-x hours to come back, since 15 minutes is 0.25 hr.
to the river 40 mph * x hours =40x miles
from the river 70 mph (0.25-x) hours=17.5-70x
those two are equal
40x=17.5-70x
110x=17.5
x=17.5/110=0.159 hours
9.55 minutes
Using translation concepts, the equation of g(x) is given as follows:

<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the parent function is given by:

For a horizontal compression by a factor of 1/5, we have to find f(1/5x), hence:

For a vertical stretch by a factor of 7, we have to multiply by 7, hence:

For a reflection in the y-axis, we have to find g(-x), hence:

For a translation of 10 units left, we have to find g(x + 10), hence:

For a translation of 1 unit down, we have to subtract one, hence:

More can be learned about translation concepts at brainly.com/question/28174785
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Answer:
Praetors
Step-by-step explanation:
The praetors administered civil law and commanded provincial armies, and, eventually, began to act as chief judges over the courts.Praetors were part of the judicial branch, they were elected yearly by the people of Rome, and acted as judges.
Answer:
W = 
Step-by-step explanation:
To transpose the equation with a given subject means to isolate that variable. To move W to the other side, you must first multiply both sides by W:
TW = 2π
Finally, divide both by T to isolate W:
W = 
Answer:
8.8
Step-by-step explanation:
Normally, to find the distance between two points, you would use the distance formula, but these two points have the same x-coordinate, meaning they will form a vertical line when connected. To find the length of a vertical line you find the distance between the y-coordinates, in this case -4.7 and 4.1. Finding the distance is the same as finding the absolute value of the difference:
|4.1 -(-4.7)|
|4.1 + 4.7|
|8.8|
8.8