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Answer: 2 < x < 7</h3>
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Explanation:
We'll use the hinge theorem here. This says (more or less) that the larger an angle is, the side opposite of that will be longer.
Imagine that the segments with the single tickmarks represent a door swinging open/shut. The more open a door is, the further the distance it is from the handle to the frame. In terms of these triangles, the segment 25 is larger than 5x-10 because the angle 90 (opposite the 25) is larger than the angle 85 degrees (opposite the 5x-10)
In symbols we say
5x - 10 < 25
We also say 5x - 10 > 0 or 0 < 5x - 10 to ensure that the segment of length 5x-10 is not 0 or negative.
Put the two inequalities together and we get 0 < 5x - 10 < 25
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Solve for x
0 < 5x - 10 < 25
0+10 < 5x - 10 < 25 + 10 .... adding 10 to all sides
10 < 5x < 35
10/5 < 5x/5 < 35/5 ... dividing all sides by 5
2 < x < 7
We have x between 2 and 7, and not equal to either endpoint.
The improper fraction form of 4 2/3 would be 14/3, if that is one of the choices.
The area of what? if those are the dimensions of a triangle, you would do base times height divided by 2.
Answer: So, your relative takes N tablets each 6 hours. a day has 24 hours, and 24/6 = 4, so he takes N tablets 4 times per day, so he takes 4*N tablets.
each tablet has 200mg, and 2.3 g (or 2300 mg) is toxic.
this means that 4*N*200mg must be less than 2300, if we are seeking for the maximum N possible, then:
4*N*200mg = 2300mg
4*N = 2300/200 = 11.5
N = 11.5/4 = 2.87
if you round up this number, you will end up taking more than 2.3g of tylenol per day, this implies that N must be equal to 2.
So your relative needs to take maximum 2 tablets per day.
