Geometry

YES!!!

The 'x-axis' is by convention the horizontal axis.

It follows that the 'y-axis' is the vertical axis.

This is for a 2-dimensional graph.

In a 3-dimensional graph , drawn on paper ( 2 -dimension) , there is a 'z-axis' . This is shown as an angled line, going 'up' from left to right.

All three axes intersect at the origin.

The coordinates are ( x,y,z,) in that order. The origin is ( 0,0,0).

On a graph '

A linear Equation produces a Straight line

A Quadratic Eq'n produces a Curved line.

A graduated cylinder is better for measuring volume than a beaker because it has a narrower shape and more precise markings, allowing for more accurate readings. The design minimizes the meniscus effect, reducing parallax error, and enabling users to measure small volumes with greater precision. In contrast, beakers are typically used for mixing or holding liquids rather than for exact measurements. Thus, for accurate volume determinations, graduated cylinders are the preferred choice.

no

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Millions of sides.

However, I think you mean 'MINIMUM' number of sides for regular polygons with OBTUSE interior Angles.. The answer is '5' ( pentagon.

A Pentagon ( 5 sides) The interior angles are '108 degrees; , which are OBTUSE .

NB Regular Triangle = ACUTE

Square or Rectangle = RIGHT ANGLE.

Regular Pentagon and greater number of sided polygons are all OBTUSE.

The Cylinder.

The simple Pythagorean Triples are ;-

3,4,5, & 5,12,13.

Any multiples of these number is a Pythagorean Triple

e,g, 3,4,5, = 6,8,10 = 60,80,100 et seq.,

Remember the Trig. Functions.

Sin(Angle) = opposite / hypotenuse.

Hence algebraically rearranging.

hypotenuse = opposite / [Sin(angle))

NB You MUST know the length of the 'opposite', and the size of the angle.

So if the opposite is of length '2' and the angle is 30 degrees.

Then substituting ;=

hypotenuse = 2 / Sin(30)

From Tables or calculator 'Sin(30) = 1/2 = 0.5'

Hence

hypotenuse = 2 / (1/2) or 2/(0.5)

2/(1/2) = 4 or 2/0.5 = 4

Hence the hypotenuse is '4' units in length.

tan x

An angle that has undergone a half turn measures 180 degrees. In terms of geometric representation, this can be visualized as a straight line, where the two rays of the angle point in opposite directions. This configuration divides the plane into two equal halves.

OBTUSE /

Less 90 degrees ; ACUTE

90 degrees ; RIGHT ANGLE

Obtuse greater than 90 degrees but less than 180 degrees

180 degrees arc swept by a point on a straight line

REFLEX ; greater than 180 degrees but less than 360 degrees. ( The 'outside' of an acute or obtuse angle)/

Perimeter is NOT squared.

Squaring calculated the area inside the perimeter.

The perimeter is the addition of the lines that form the edge/perimeter.

Neither!!!

Perimeter is the addition of all the straight lines that form the perimeter.

Remember a straight line is NOT 'powered/indexed'. a^(1) or just 'a'

For Area , the power/index is 'squared' . a^(2)

For Volume, the power/index is 'cubed' a^(3)

22 divided by 7

* * * * *

That is an APPROXIMATE value of pi. The exact value cannot be calculated since pi is a transcendental number - a special kind of irrational number. It has an infinite decimal representation with no recurring pattern. That would be true in any base - binary, octal, or another base (other than pi itself, or a power of pi).

It is still being calculated.

Supa-Dupa computers have calculated 'pi' to at least 50 billion places and still going.

The ancients would have calculated 'pi' to at least 10 places. or more.

estimates for pi are 3.14, 3.1416, 3.14159 or 22/7

They are all approximations.

pi is an irrational number, which means it cannot be converted to a ratio/quotient.

The Classical Greek mathematician , Archimedes, calculated 'pi' to a degrees of estimation.

By the fact that it is a PRIME Number, it does NOT factorise, except for itself and '1'.

They named prime numbers because they do factorise.

NB Except for '2' all prime numbers are odd numbers.

However, NOT all odd numbers are prime number.

Odd numbers ending in 1,3,7,& 9. can be prime numbers. Odd numbers ending in '5' are NOT prime number

So to test for a prime number.

If it is EVEN , ending in 0,2,4,6,8 , it is NOT a Prime Number.

It is ends in '5' it is NOT a prime Number.

If the digits sum to '9' it is NOT a Prime Number. e.g. 531 ; 5 + 3 + 1 = 9

So 531/ 9 = 59 So it is NOT a Prime number.

Then divide the given number by '3' or '7', if there isa remainder then it is a prime number.

So 1253

Try '3' = 417 remainder '2'

Try '7' =179 So 1253 is NOT a prime number.

Shapes with lines of symmetry are; -

Squares, Rectangles, Rhombus, Symmetric Trapezium, Kite, Circle.

Square; Top to bottom, Side to side, Corner to corner.

Rectangle ; Top to bottom, Side to side

Rhombus, Corner to corner.

Symmetric Trapezium; to to bottom, between parallel lines

Kite ; largest angle to smallest angle

Circle ; Any radii.

YES & NO.

YES ; Equilateral triangles , Three lines of symmetry, Iine from each point to the mid point of the opposite line(Base).

Isosceles triangles One line of symmetry , from the conjunction of the two equal lines , to the opposite base.

NO ; Scalene triangles. Because no lines are of equal length.

A Right-Angled Triangle can be isosceles or scalene. Which ever one, then the above rules apply.

A symetry line is like a mirror line, if you put it in the middle of something, the other side will have to be the same thing, flipped. if you take the letter V, you can put a vertical symetry line in the middle of it, and both sides will be exactally the same, but just flipped.

A trapezoid, in general, does not have congruent sides.

Oh, dude, if the circumference of a circle is 8 inches, you just divide that by π (pi) to get the diameter. So, 8 divided by π is about 2.55 inches. There you go, now you can impress all your friends with your circle knowledge.

2x + 7y