Solving Equations, Length of a Cube and Pythagorean Theorem

1. a. square root of x-2 = 1 show work
b. square root of x cubed = 27 show work
c. 3 x the square root of x squared = 9 show work

2. Is the square root of x squared = x an identity (true for all non values of x?)
Explain answer

3. For the equation x - 2 times square root of x on the same graph (by plotting points if necessary) Show the points of intersection of these two graphs.

4. In a right triangle, the sides are related by Pythagorean Theorem c squarred + a squared + b squared where c is the hypotenuse ( the side opposite the 90 degree angle) Find the hypotenuse when the other 2 sides' measurements are 6 feet and 8 feet. Show work

5. Should you travel north for 65 kilometers then travel east 75 kilometers. How far are your from your starting point? Show work

6. The volume of a cube is given by V= s cubed. Find the length of a side of a cube if the volume is 1000 cm cubed. Show work

Solution Summary

Solving Equations, Length of a Cube and Pythagorean Theorem are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

The Numbers 3,4, and 5 are called Pythagorean triples since 3^2 + 4^2 = 5^2. The Numbers 5,12, and 13 are also Pythagorean triples since 5^2 + 12^2 =13^2. Can you find any other Pythagorean triples? Actually, there are alot of formulas that will generate as infinite number of Pythagorean Triples.
Make sure you select at least

Use the PythagoreanTheorem to determine if an angle is the right angle (3-4-5 triangle).
What would you use the PythagoreanTheorem for? List one example either from work or personal life or any other application.

Solving Quadratic Equations by Factoring is Chapter 13.7 page 955
1) Quadratic Equation is in STANDARD FORM (ax^2 + bx + c = 0 where a is positive)
Factor trinomial: x^2 + bx +c =(X + m)( X +n)=0 ,which :(mn=C),and (m+n=b)
(X + m)=0 ---->X = - m , and (X + n)=0----> X= - n
2) PythagoreanTheorem in Right triangle (

Find the length of the diagonal of a rectangular billboard whose sides are 5 feet and 12 feet. Note that the length of the diagonal of a rectangle with length = a and width = b is given by the PythagoreanTheorem c^2 = a^2 + b^2.

Measure the height of your computer monitor to the nearest tenth of a centimeter of sixteenth of an inch. Measure the width of your monitor as well. Use the Pythagoreantheorem to find the length of the diagonal of your monitor.
In your post, include the height, the width, and the calculations needed to determine the length

The PythagoreanTheorem can also be proved directly, by choosing 0 at the right angle of a right-angled triangle whose other two vertices are u and v.
Show that |v - u|^2 = |u|^2 + |v|^2 under these conditions, and explain why this is the Pythagoreantheorem.

A radio station is going to construct a 12 foot tower for a new antenna on top of a tall building. The tower will be supported by three cables, each attached to the top of the tower and to points on the roof of the building which are 5 feet from the base of the tower. What is the total length of these three cables? 39 feet
Ca

Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point? Can you show me how you got the answer?