Solve the inequality in terms of intervals and illustrate the solution set on the real number line. (x − 1)(x − 8) > 0
1 answer:
Answer:
The solution set of the given inequality is (-∞,1) ∪ (8,∞).
Step-by-step explanation:
The given inequality is
The related equation is
Two numbers 1 and 8 divide the number line in three intervals. (-∞,1), (1,8) ,(8,∞).
Intervals check point (x -1)(x -8) > 0 True or False
(-∞,1) 0 (-1)(-8)=8>0 True
(1,8) 2 (2-1)(2-8)=-6>0 False
(8,∞) 9 (9-1)(9-8)=8>0 True
The given inequality is true for (-∞,1) and (8,∞).
Therefore, the solution set of the given inequality is (-∞,1) ∪ (8,∞).
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The question is incomplete. Here is the complete question.
To set up a game of billiards, the first player moves the balls contained within a triangular rack as shown. What happens to the distance between each billiard during this rigid transformation?
A. The distance remains constant throughout the transformation.
B. The distance decreases at the start and increases after all motion stops.
C. The distance stays the same at the start but decreasesexactly when motion ends.
D. The distance increases at the start and then decreases as the rack gets further from the player.
Answer: A. The distance remains constant throughout the transformation.
Step-by-step explanation: In a <u>rigid</u> <u>motion</u>, all moving points in the plane are moving in way such tha:
1) relative distance between them stays the same and
2) relative position of the points stays the same
There are four types of rigid motions: translation, rotation, reflexion and glide reflection.
<u>Translation</u>: every point or object is moved by the same amount and in the same direction;
<u>Rotation</u>: the object rotates by the same amount around a fixed point;
<u>Reflexion</u>: the object exchange points from one side of a line with points on the other side of the line at the same distance from the line;
<u>Glide</u> <u>Reflection</u>: is a mirror reflection followed by a translation parallel to the mirror.
In the game of billiards, because all the balls are inside the triangular rack, the distance, and also the position, between them stays the same, limited by the rack. Since they are moving by the same amount in the same direction, the rigid transformation is a translation.
Therefore, the distance of the balls in the triangular rack remains constant throughout the transformation.
