The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
I am unable to read all of the options in the picture you provided but I hope this helps! (:
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A carousel would be a rotation. Since a carousel is stationary, it would not be a translation.
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Use the geometric mean for right triangles here. Like this

. Cross multiply to get

, and

. That simplifies down to

. Pull out the 9 as a perfect square of 3 and you're left with

, first choice above.
Answer:
x > -5 in the answer
Step-by-step explanation:
(5 - 3x) / 4 < 5
multiplying both sides by 4:-
5 - 3x < 20
-3x < 15
x > 15/-3
x > -5 (Note the inequality sign is flipped because we are dividing by a negative number)