(21 + 34 + x + 25 + 37 + 22) / 6 = 30
(139 + x) / 6 = 30 .....multiply both sides by 6
139 + x = 30 * 6
139 + x = 180
x = 180 - 139
x = 41......so during week 3, she rode her bike 41 miles
125 = 5 * 5 * 5 = 5^3
Its a perfect cube.
This question boils down to this:
"What is the diagonal of a square with a side length of 90 ft?"
The key to this question is the properties of squares.
All of the angles in a square are right, (90°) but that diagonal is going to bisect two of those into 45° angles.
Now we have two triangles, each with angle measures of 45°, 45°. and 90°.
(an isoceles right triangle)
This 45-45-90 tirnalge is one of two special triangles (the other being the 30-60-90) and here is its special property: the sides opposite these angles can be put as x, x, and x√2 respectively. Why? Well, we know that our triangle is isoceles (the congruent base angles ⇔ congruent sides) and so we call those x...by the Pythagorean theorem...a² + b² = c²...2x² = c²...x√2 = c!
In our case here, that diagonal, being the hypotenuse of our triangle, is going to be 90√2 feet, or approximately 127.3 feet.
