PLEASE HELP. WORTH 50 PINTS IF CORRECT. A gate casts a shadow that is 5 feet long. A nearby cactus is 9 feet tall and casts a sh
adow that is 15 feet long. What is the height of the gate?
2 answers:
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Answer:
-2 < x < 4/3
Step-by-step explanation:
A graphing calculator can show you the solution. I like to recast the equation as a comparison to zero, since a graphing calculator often can display zeros of a function easily. Here that means ...
|6x +2| -10 < 0
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If you want to solve this by hand, you can "unfold" the absolute value to get ...
-10 < 6x +2 < 10
-12 < 6x < 8 . . . . . . subtract 2
-12/6 < x < 8/6 . . . . divide by 6
-2 < x < 4/3 . . . . . . simplify
This graphs on the number line as a solid line between open circles at -2 and 4/3. On the attached graph, the boundary values are shown as dotted blue lines, and the solution space is shown in blue.
