Metric Conversions

Metric Conversions

Below are the rules for converting metric and english systems of measurement.

Multiply	By	To Find
Centimeters	.0328	feet
Centimeters	.3937	inches
Feet	30.4801	centimeters
Feet/minutes	.507	cent./seconds
Foot-pounds	.1383	meter-kilograms
Gallons	3,785.4	cubic centimeters
Gallons	3.7853	liters
Grams	.0353	ounces
Grams	.0022	pounds
Inches	2.54	centimeters
Inches	.0833	feet
Kilograms	2.2046	pounds
Kilometers	3,280.833	feet
Kilometers	.6214	miles
Kilometers/hour	54.68	feet/minute
Kilometers/hour	.6214	miles/hour
Knots	1.8532	kilometers/hour
Liters	1.0567	quarts
Meters	3.2808	feet
Meters	39.37	inches
Meters	1.0936	yards
Meter-kilograms	7.2307	foot-pounds
Meters/minute	1.667	centimeters/second
Meters/minute	.0547	feet/second
Miles	1.6093	kilometers
Miles/hour	.8684	knots
Miles/hour	1.6093	kilometers/hour
Miles/hour	.447	meters/second
Ounces	28.3495	grams
Ounces	2.8349x10(2)	kilograms
Pounds	453.5924	grams
Pounds	.4536	kilograms
Quarts	.946	liters
Quarts (dry)	67.2	cubic inches
Quarts (liquid)	57.75	cubic inches
Sq. centimeters	.0011	square feet
Sq. kilometers	.3861	square miles
Sq. kilometers	1.196x10(6)	square yards
Sq. meters	10.7639	square feet
Sq. meters	1.196	square yards
Sq. miles	2.59	square kilometers
Sq. yards	.8361	square meters
Yards	91.44	centimeters
Yards	.9144	meters

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Prime Numbers up to 1000

What is Prime Number?

 A prime number can be divided, without a remainder, only by itself and by 1. For example, 17 can be divided only by 17 and by 1.

Some facts:

• The only even prime number is 2. All other even numbers can be divided by 2.
• If the sum of a number's digits is a multiple of 3, that number can be divided by 3.
• No prime number greater than 5 ends in a 5. Any number greater than 5 that ends in a 5 can be divided by 5.
• Zero and 1 are not considered prime numbers.
• Except for 0 and 1, a number is either a prime number or a composite number. A composite number is defined as any number, greater than 1, that is not prime.

 

Here is a table of all prime numbers up to 1,000:

	2	3	5	7	11	13	17	19	23
29	31	37	41	43	47	53	59	61	67
71	73	79	83	89	97	101	103	107	109
113	127	131	137	139	149	151	157	163	167
173	179	181	191	193	197	199	211	223	227
229	233	239	241	251	257	263	269	271	277
281	283	293	307	311	313	317	331	337	347
349	353	359	367	373	379	383	389	397	401
409	419	421	431	433	439	443	449	457	461
463	467	479	487	491	499	503	509	521	523
541	547	557	563	569	571	577	587	593	599
601	607	613	617	619	631	641	643	647	653
659	661	673	677	683	691	701	709	719	727
733	739	743	751	757	761	769	773	787	797
809	811	821	823	827	829	839	853	857	859
863	877	881	883	887	907	911	919	929	937
941	947	953	967	971	977	983	991	997

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Polygons

Polygons

A polygon is a closed figure where the sides are all stock segments. Each side must intersect exactly two others sides but on your own at their endpoints. The sides must be noncollinear and have a common endpoint.
Polygons
A polygon is usually named after how many sides it has, a polygon once n-sides is called a n-gon. E.g. the building which houses United States Department of Defense is called pentagon in assistance it has 5 sides.
Sides                  Polygon
3                           triangle
4                           quadrilateral
5                           pentagon
6                           hexagon
7                           heptagon
9                           nonagon
10                        decagon
A regular polygon is a polygon in which each and every one sides are congruent and all the angles are congruent.

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Measure and classify an angle

A line that has one defined endpoint is called a ray and extends endlessly in one direction. A ray is named after the endpoint and another point on the ray e.g.

AB→$$\overrightarrow{AB}$$

The angle that is formed between two rays with the same endpoint is measured in degrees. The point is called the vertex

The vertex is written as

∡CAB$$\measuredangle CAB$$

In algebra we used the coordinate plane to graph and solve equations.  You can plot lines, line segments, rays and angles in a coordinate plane.

In the coordinate plane above we have two rays

BA→andBD→$$\overrightarrow{BA}and\overrightarrow{BD}$$

That form an angle with the vertex in point B.

You can use the coordinate plane to measure the length of a line segment. Point B is at (-2, -2) and C (1. -2). The distance between the two points is 1 - (-2) = 3 units.

Angles can be either straight, right, acute or obtuse.

An angle is a fraction of a circle where the whole circle is 360°. A straight angle is the same as half the circle and is 180° whereas a right angle is a quarter of a circle and is 90°.

You measure the size of an angle with a protractor.

Two angles with the same measure are called congruent angles. Congruent angles are denoted as

∠A≅∠B$$\mathrm{\angle }A\cong \mathrm{\angle }B$$

Or could be shown by an arc on the figure to indicate which angles that are congruent.

Two angles whose measures together are 180° are called supplementary e.g. two right angles are supplementary since 90° + 90° = 180°.

Two angles whose measures together are 90° are called complementary.

m∠A+m∠B=180∘$$m\mathrm{\angle }A+m\mathrm{\angle }B={180}^{\circ }$$

m∠C+m∠D=90∘

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Conjecture

If we look at data over the precipitation in a city for 29 out of 30 days and see that it has been raining every single day it would be a good guess that it will be raining the 30^th day as well. A conjecture is an educated guess that is bases on known information.

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Example

If we are given information about the quantity and formation of section 1, 2 and 3 of stars our conjecture would be as follows.

This method to use a number of examples to arrive at a plausible generalization or prediction could also be called inductive reasoning.

If our conjecture would turn out to be false it is called a counterexample.

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How to solve linear equations

Fundamentals in solving equations in one or more steps

Formulas are very common within physics and chemistry, for example, velocity equals distance divided by time. Thus we use the common symbols for velocity (v), distance (d) and time (t) and express it thus:

v=dt$$v=\frac{d}{t}$$

We may beneficially describe a formula as creature a variable and an ventilation estranged by an equal sign along in the middle of them. In new words a formula is the same as an equation.

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Example

A book club requires a membership fee of $10 in addition to the $2 levied for each book ordered. If we were to list the cost of ordering a number of books, it would look like:

Number of books	Cost
1	10 + 2 ∙ 1 = 12
2	10 + 2 ∙ 2 = 14
3	10 + 2 ∙ 3 = 16
4	10 + 2 ∙ 4 = 18
5	10 + 2 ∙ 5 = 20
x	10 + 2x

If we designate the total book club cost as C, we may derive the following formula for the expression:

C=10+2x$$C=10+2x$$

If we furthermore suffering sensation to know how many books we may get your hands on from the sticker album club for $30 we can either continue filling in the table above or use the properties of equations that we handled in the last section.

30=10+2x$$30=10+2x$$	C was the cost, i.e. it is now $30
30−10=10+2x−10$$30-10=10+2x-10$$	we subtract $10 from each side
20=2x$$20=2x$$	simplify
202=2x2$$\frac{20}{2}=\frac{2x}{2}$$	divide both sides by 2 to isolate x
10=x$$10=x$$	x equals 10

We may purchase 10 books for $30.

When we want to solve an equation including one unknown variable, as x in the example above, we always aim at isolating the unknown variable. You can say that we put everything else on the other side of the equal sign. It is always a good idea to first isolate the terms including the variable from the constants to begin with as we did above by subtracting or adding before dividing or multiplying away the coefficient in front of the variable. As long as you do the same thing on both sides of the equal sign you can do whatever you want and in which order you want.

Above we began by subtracting the constant on both sides. We could have begun by dividing by 2 instead. It would have looked like

302=10+2x2$$\frac{30}{2}=\frac{10+2x}{2}$$

302=102+2x2$$\frac{30}{2}=\frac{10}{2}+\frac{2x}{2}$$

15=5+x$$15=5+x$$

15−5=5+x−5$$15-5=5+x-5$$

10=x$$10=x$$

Again the same answer just proving the point.

If your equation contains like terms it is preferable to begin by combining the like terms before continuing solving the equation.

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Example

5x+14+2x+2=30$$5x+14+2x+2=30$$

Begin by combining the like terms (all terms including the same variable x and all constants)

(5x+2x)+(14+2)=30$$\left(5x+2x\right)+\left(14+2\right)=30$$

7x+16=30$$7x+16=30$$

Now it's time to isolate the variable from the constant part. This is done by subtracting 16 from both sides

7x+16−16=30−16$$7x+16-16=30-16$$

7x=14$$7x=14$$

Divide both sides by 7 to isolate the variable

7x7=147$$\frac{7x}{7}=\frac{14}{7}$$

x=2$$x=2$$

If you have an equation where you have variables on the subject of the subject of both sides you get your hands on basically the same event as in the in the past. You compilation all as soon as terms. Before you have worked by first collecting all constant terms on one side and save the adaptable terms regarding the added side. The same applies here. You entire sum every single one share of portion of constant terms upon one side and the adjustable terms upon the new side. It's usually a innocent idea to whole every variables upon the side that has the adjustable as soon as the highest coefficient i.e. in the example knocked out there are more x:es in relation to speaking the left side (4x) compared to the right side (2x) and hence we combined all x:es concerning the subject of the left side.

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Example

4x+3=2x+11$$4x+3=2x+11$$

subtract 2x from both sides

4x+3−2x=2x+11−2x$$4x+3-2x=2x+11-2x$$

Now it looks like any other equation

2x+3=11$$2x+3=11$$

subtract 3 from both sides

2x+3−3=11−3$$2x+3-3=11-3$$

2x=8$$2x=8$$

Divide by 2 on both sides

2x2=82$$\frac{2x}{2}=\frac{8}{2}$$

x=4$$x=4$$

In the beginning of this section we showed the formula for calculating the velocity where velocity (v) equals the distance (d) divided by time (t) or

v=dt$$v=\frac{d}{t}$$

If we by some chance want to know how far a truck drives in 3 hours at 60 miles per hour we can use the formula above and rewrite it to solve the distance, d.

dt⋅t=v⋅t$$\frac{d}{t}\cdot t=v\cdot t$$

d=v⋅t$$d=v\cdot t$$

When that's done we can just put our numbers in the formula and calculate the answer

d=60⋅3=180$$d=60\cdot 3=180$$

The truck travels 180 miles in 3 hours.

This holds true for all formulas and equations.

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