Saying that 4<(sq.root of x)<9 is equivalent to saying what about x ?

a. 0<x<5
b. 0<x<65
c. 2<x<3
d. 4<x<9
e. 16<x<81

Please help.
Does this problem relate to 'x'values on the xy coordinate system ? If so please explain the concept here.

If not please explain this problem anyway.

A million thank yous.

First write the problem.

4 < x^(1/2) < 9
Square each term. There are no negative signs, so the inequality signs will not change.
Squaring...

16 < x < 81

To determine the equivalent inequality for the given statement, let's consider each option and simplify the inequalities.

a. 0 < x < 5: If we square both sides of this inequality, we get 0 < x^2 < 25. However, this does not match the given inequality since it includes values greater than 9.

b. 0 < x < 65: If we square both sides of this inequality, we get 0 < x^2 < 4225. Again, this does not match the given inequality.

c. 2 < x < 3: Squaring both sides of this inequality gives us 4 < x^2 < 9. This matches the given inequality, so we can consider option (c) as a potential answer.

d. 4 < x < 9: If we square both sides of this inequality, we get 16 < x^2 < 81. This also matches the given inequality, so we can consider option (d) as a potential answer.

e. 16 < x < 81: If we take the square root of both sides of this inequality, we get 4 < sqrt(x) < 9. This does not match the given inequality.

Based on our analysis, the answer to the question is either option (c) or option (d).

Regarding your question about whether this problem relates to "x" values on the xy coordinate system, the answer is yes. The inequalities represent the possible values for "x," which can be plotted on the x-axis of a coordinate plane. However, in this case, we are only considering the range of values for "x" and not their actual coordinates on the xy plane.

I hope this clears up the problem for you. Let me know if you have any further questions!