Geometry

A shape with an interior angle of 170 degrees is a type of polygon. Specifically, it could be a concave polygon, as concave shapes can have interior angles greater than 180 degrees, but a polygon with an interior angle of 170 degrees is typically a convex polygon with multiple sides. For example, a polygon with such an angle could be a heptagon (7-sided polygon) or any other polygon that fits the angle requirement while maintaining a closed figure.

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The angles 45, 45, and 30 degrees refer to specific angles in geometry, often associated with triangles. A triangle with angles of 45°, 45°, and 30° is not a standard triangle as the sum of angles in any triangle must equal 180°. However, it can be interpreted as two 45° angles and one 30° angle in a non-triangular context, such as in a polygon or in construction. The 45° angles suggest a right isosceles triangle if paired with a 90° angle, while the 30° angle is commonly found in a 30-60-90 triangle.

Yes, copies of certain polygons can be used to tile a flat surface, a process known as tiling or tessellation. Regular polygons, such as equilateral triangles, squares, and hexagons, can perfectly tile a plane without gaps or overlaps. However, not all polygons can tile a surface; for example, irregular polygons may not fit together neatly. The specific properties of the polygon determine whether it can successfully tile a flat surface.

The amount of cocaine one person can consume varies greatly depending on individual tolerance, body weight, and the purity of the cocaine. Typically, a single line of cocaine can range from 50 to 100 milligrams, and some users may take multiple lines in a session. However, excessive use can lead to serious health risks, including overdose, which can be fatal. It's important to note that cocaine use is illegal and poses significant health dangers.

An important element of every continent during the triangle trade was the exchange of goods, people, and raw materials. Africa supplied enslaved people to the Americas, where they were forced to work on plantations producing commodities like sugar and tobacco, which were then shipped to Europe. Europe, in turn, provided manufactured goods and weapons to Africa, creating a cycle of exploitation and economic interdependence. This trade network significantly impacted the economies and societies of all continents involved.

A **Quad**rilateral is any 2-dimensional figure of four sides.

Not all quadrilaterals have right angles.

Right-angled quadrilaterals are squares and rectangles.

None right-angles quadrilaterals are parallelograms, rhombus, trapezium, and kite.

A Rectangle or a square.

The word 'rectangle' comes from Latin and means 'Right(Recto) Angles'.

Can be a Parallelogram, a Rhombus, A Kite, or a Trapezium.

However, A kite may display one right angle, depending on its angular measure.

An Asymmetric Trapezium may also display two adjacent right angles. A Symmetric Trapezium does NOT have any right angles.

NB A Square has four right angles. A RECTANGLE has four right angles.

The word 'Rectangle' is from its Latin base , meaning 'Right(rect) Angles).

NO!!!

A Rhombus is a 'lazy' square. !!!

A Rhombus has four sides all of equal length.

The opposite sides are parallel.

The adjacent angles sum to 180 degrees, but are NOT right angles.

However, alternate angles are ACUTE, OBTUSE, ACUTE, & OBTUSE.

Hence my 'silly' expression of a 'lazy' square.

Remember for the volume of a cone, the eq'n is

V(cone) = (1/3) pi r^(2) h

Algebraically rearrange

r^(2) = 3V/(pi*h).

r = sqrt[ 3V/(pi*h)]

Substituting

r = sqrt[3(400cm^(3)/(3.141592...*8.5 cm)].

r = sqrt[(1200cm^(3) / 26.70353756....cm)

r = sqrt[44.93786628... cm^(2)]

r = 6.703571159....cm

t ~ 6.7 cm ( 1 d.p.)

NB Units (cm) have been included to show how cm^(3) ( volume) is reduced to 'cm'. (linear).

NNB Also don't forget, as a last step, to square root both sides.

Remember the equation for the area of a triangle.

A = 0.5 X b X h

Algebraically rearranging

h = A / (0.5 X b)

Substituting the numbers.

h = 400/(0.5 X 20)

Do inside the BRACKETS First

h = 400 / (10)

Cancel down by '10'

h = 40 units. ( linear and at right angles to the base).

OR

you can do the ca;cu;ation by

h = 400 /( 0.5 x 20)

Cancel down by '20'

h = 20/(0.5)

Divide '20' by '0.5'

h = 40 units ( as before).

Remember for ANY triangle, the area is one half multiplied to the base length multiplied to the perpendicular height length .

Algebraically expressed as

A = 0.5bh

Substituting 10 ft & 6 ft.

A = 0.5 X 10ft X 6ft =

A = 0.5 x 60 sq.ft.

A = 30 sq.ft.,

Providing '6' & '10' are orthogonal (right-angles/ 90 degrees) to each other, then the area is 6 x 10 = 60 units^(2)

The saddest chord is often considered to be the minor chord, particularly the minor seventh chord. This chord evokes a sense of melancholy and longing due to its unique intervals, which create a haunting sound. In music theory, the C minor chord, for example, combines a root, minor third, and perfect fifth, contributing to its emotional resonance. Ultimately, the perception of sadness in music can vary among listeners, influenced by personal experiences and cultural contexts.

To divide any single triangle into six equal-area parts, find the midpoints of all three sides and draw the medians (lines connecting each vertex to the midpoint of the opposite side). These three medians intersect at a single point, the centroid, dividing the triangle into six smaller triangles with equal area.

Cot(68) = 1/ Tan(68)

One the calculator

1/Tan*68( = 1/2.475086853.... )

Hence 1 / 2.475086853... = 0.40402885....

Another way is

Cot = Cos / Sin

Hence

Cot(68) = Cos(68) / Sin(68) =

0.374606583... / 0.937193954...

= 0.404026225.... =

The Einsatzgruppen ABCD were mobile killing units formed by Nazi Germany during World War II, primarily tasked with the mass execution of Jews, Roma, communists, and other perceived enemies of the Third Reich in occupied territories. Their purpose was to carry out systematic extermination to facilitate the Nazi goal of racial purity and to eliminate opposition. Operating mainly in Eastern Europe, these units were responsible for the deaths of hundreds of thousands of people through mass shootings and other brutal methods. Their actions laid the groundwork for the Holocaust and exemplified the extreme measures taken by the Nazis to implement their genocidal policies.

The circumradius ( R ) of a triangle can be calculated using the formula ( R = \frac{abc}{4K} ), where ( a ), ( b ), and ( c ) are the lengths of the triangle's sides, and ( K ) is the area of the triangle. The area ( K ) can be found using Heron's formula: ( K = \sqrt{s(s-a)(s-b)(s-c)} ), where ( s ) is the semi-perimeter ( s = \frac{a+b+c}{2} ). Alternatively, if you know the angles of the triangle, you can use the formula ( R = \frac{a}{2\sin A} ), where ( A ) is the angle opposite side ( a ).

NO!!!

45 degrees is an ACUTE angle.

The 'outside' angle is 360 - 45 = 315 degrees is a REFLEX ANGLE.

Reflex is 360 - 98 = 262 degrees,

NB Reflex angles are those between 180 degrees and 360 degrees, but NOT including 180, nor 360. It is the 'outside' angle of acute, right angle and obtuse angles.

An angle of 98 degrees is an obtuse angle

An angle consists of two rays or lines having the same endpoint (vertex).

An angle is formed when two rays meet at an endpoint. The endpoint is called the vertex of the angle. The measure of an angle tells how far one side is turned from the other side -0 degrees is no turn and 360 degrees is one full turn. You can name angles by how their measures compare to 90 degrees or 180 degrees. There are 4 types of angles, acute angle, right angle, obtuse angle, and straight angle. An acute angle is an angle that measures less than 90 degrees. A right angle is an angle that measures exactly 90 degrees. A straight angle measures exactly 180 degrees.

Yes!!!

In 2-dimensional polygons, the sum of the internal angles is related to the number of sides.

Hence

3 ; 180

4 ; 360

5 ; 540

6 ; 720

7 ; 900

8 ; 1080

9 ; 1260

10 ; 1440

et seq.,

For each extra side , add 180.

A Square and a Rectangle.

NOT a parallelogram, nor a rhombus, nor a kite. nor a trapezium.