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Given the metric space (X, p), prove that |p(x, z) - p(y, u)| < p(x, y) + p(z, u) (x, y, z, u is an element of X);
Find (and describe) all the regular tessellations of the plane. Note that septagons, nonagons, and 11-gons are not provided.
Forest rangers use degree measures to identify directions and locate critical spots such as fires.
Suppose you travel north for 65 kilometers then travel east 75 kilometers. How far are you from the starting point?
A patient is being treated with laser therapy to remove a tumour that is located behind a vital organ. The tumor is 5.7 cm below the skin.
Discuss how these strategies and processes encourage students to persist through difficult problems.
The preferred seating area of a music theater has a base that measures 34 yd and a height of 39.6 yd.
Explain how to derive the distance formula (assuming that the distance formula is not yet known), first in 2 dimentional and then in 3 dimentional.
Let's say you hgave an area with 100 feet of fence. Two configurations were a circle and a rectangle.
An isosceles triangle has two equal sides of length 10cm. Let theta be the angle between the two equal sides.
Find the area of the shaded region on the following geoboard if the unit of measurement is 1 cm2.
Start by drawing an equilateral triangle: we will call this T1 as it is the first step in the process.
How would you explain the difference between angle-angle-side, angle-side-angle, and side-angle-side to a classmate who thinks the letters look alike?
Find five triangles with integers sides (without no commun divisors) such that the median AD from angle A to side BC is m(a) = b + c - a.
Draw 3 different shapes, then draw a shape you can make by combining the 3 shapes.
Angles PQR and ABC are supplementary angles, and angle PQR is nine times as large as angle ABC. Determine the measure of each angle.
Construct the quadrature of 3 squares. Let a = 3 be a line segment that extends along the y-axis from the origin O to the point B at (0,3).
Use Pascal's triangle to expand (x + y)6 How is the sum of the entries in row 5 in Pascal's triangle related to powers of 2?
Write an inequality in the variable x for the degree measure of the smallest angle of a triangle given that the degree measure of the smallest angle.
Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle.
A 5 foot post is supposed to be vertical, but it is 4 inches out of alignment at the top. What is the angle of lean, round to the nearest tenth of a degree?
Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians, which is the point that lies one-third of the way.
Suppose instead of working on the Euclidean plane we study geometry on a sphere in (Euclidean) three space.
In a triangle the sum of the angles is 180 degrees. If Angle A is four times Angle B and Angle C is 27 degrees more than three times Angle A.
The formal definition of a rectangle is a quadrilateral with four right angles therefore this figure does not exist in hyperbolic geometry.