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history of algebra

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The history of algebra began in ancient Egypt and Babylon, where people learned to solve linear (ax = b) and quadratic (ax2 + bx = c) equations, as well as indeterminate equations such as x2 + y2 = z2, whereby several unknowns are involved. The ancient Babylonians solved arbitrary quadratic equations by essentially the same procedures taught today. They also could solve some indeterminate equations.

Algebra Formulas

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Laws of Exponents (am)(an) = am+n (ab)m = ambm (am)n = amn a0 = 1 (am)/(an) = am-n a-m= 1/(am) Quadratic Formula In an equation like ax2 + bx + c = 0 You can solve for x using the Quadratic Formula: Binomial Theorem (a + b)1 = a + b (a + b)2 = a2 + 2ab + b2 (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 ...and so on... Difference of Squares a2 - b2 = (a - b)(a + b) Rules of Zero 0/x = 0 where x is not equal to 0. a0 = 1 0a = 0 a*0 = 0 a/0 is undefined (you can't do it)

Slope and y-intercept.

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Every straight line can be represented by an equation: y = mx + b. The coordinates of every point on the line will solve the equation if you substitute them in the equation for x and y. The slope m of this line - its steepness, or slant - can be calculated like this: m = change in y-value change in x value Help from math.com

algebra history

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The history of algebra began in ancient Egypt and Babylon, where people learned to solve linear (ax = b) and quadratic (ax2 + bx = c) equations, as well as indeterminate equations such as x2 + y2 = z2, whereby several unknowns are involved. The ancient Babylonians solved arbitrary quadratic equations by essentially the same procedures taught today. They also could solve some indeterminate equations.

molarity and dilution

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Molarity Worksheet 1. Sea water contains roughly 28.0 g of NaCl per liter. What is the molarity of sodium chloride in sea water? 2. What is the molarity of 245.0 g of H2SO4 dissolved in 1.00 L of solution? 3. What is the molarity of 5.30 g of Na2CO3 dissolved in 400.0 mL solution? 4. What is the molarity of 5.00 g of NaOH in 750.0 mL of solution? 5. How many moles of Na2CO3 are there in 10.0 L of 2.0 M soluton? 6. How many moles of Na2CO3 are in 10.0 mL of a 2.0 M solution? 7. How many moles of NaCl are contained in 100.0 mL of a 0.20 M solution? 8. What weight (in grams) of NaCl would be contained in problem 7? 9. What weight (in grams) of H2SO4 would be needed to make 750.0 mL of 2.00 M solution? 10. What volume (in mL) of 18.0 M H2SO4 is needed to contain 2.45 g H2SO4?

Slope-intercept Form

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Common exercises will give you some pieces of information about a line, and you will have to come up with the equation of the line. How do you do that? You plug in whatever they give you, and solve for whatever you need, like this: Find the equation of the straight line that has slope m = 4 and passes through the point (?1, ?6). Okay, they've given me the value of the slope; in this case, m = 4. Also, in giving me a point on the line, they have given me an x-value and a y-value for this line: x = ?1 and y = ?6.

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