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Length of Side of Cube and Hypotenuse of a Triangle

1) How do I solve the following equations?
a)
Answer:

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b) .
Answer:

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c) .
Answer:

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2) Is an identity (true for all values of x)?
Answer:

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3) For the equation , perform the following:
a) Solve for all values of x that satisfies the equation.
Answer:

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b) Graph the functions and on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.

Please show the graph here:

c) How does the graph relate to part a?
Answer:

4) A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90° angle). How do I find the hypotenuse when the other 2 sides' measurements are 3 feet and 4 feet?
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5) Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point?
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If the volume of a cube is given by V = s3. How do I find the length of a side of a cube if the Volume is 729 cm3?
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6) While the radical symbol is widely used, converting to rational exponents has advantages. How do I explain an advantage of rational exponents over the radical sign? I need to include in my answer an example of an equation easier to solve as a rational exponent rather then a radical sign.

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Solution Summary

Solving Word Problems with Radicals and Exponents is investigated.

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