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Math 111 Chapter 1 Sections 1 & 2 Reviews

Mixtures :

(1st % × Amt) + (2nd % × Amt) = Final % × Amt

How many gallons of cream containing 25% butter fat and milk
containing 3.5% butter fat must be mixed to obtain 50 gallons of
cream containing 12.5% butter fat?

Let x = # gal cream
Let 50- x = # gal milk

0.25x = # gal of butter fat in cream
0.35(50 - x) = # gal of butter fat in milk
0.125(50) = # gal of butterfat in mixture

0.25x + 0.035(50 - x) = 0.125(50)

x = 20.93 (rounded)

Your 8 quart radiator is full with a 30% antifreeze mixture. How
much pure antifreeze should be added to get a 50% antifreeze
mixture.

In the chemistry lab you have 20 oz of a 10% acid
solution. How much 60% acid solution should you add to
get a 35% acid solution?

Work Problems:

(part done by A ) + (part done by B) = 1 whole job

Ron, Mike, and Tim are going to paint a house together. Ron can
paint one side of the house in 4 hours. To paint an equal area,
Mike takes only 3 hours and Tim 2 hours. If the men work
together, how long will it take them to paint one side of the house?

Let t be time needed to paint the side.

(1/4)t + (1/3)t + (1/2)t = 1

Section 1.2 Quadratic Equations and Their Applications

Solve by factoring

Solve by taking the square root

Solve by completing the square

Solve by using the Quadratic Formula

The discriminant of a Quadratic Equations
Applications

A quadratic equation is an equation that can be written in the
following standard form:

ax² + bx + c = 0,

where a,b,c are real numbers and a ≠ 0

The Zero Product Principle

If A and B are algebraic expressions such that
AB = 0, then A = 0 or B = 0

1.2: Factoring and using Zero Product Principle

Solve by factoring... x² + x = 12

Solve by factoring... 2x² - 5x = 12

1.2: Square Root Procedure

If x² = c, then

Solve by using the square root method. 2x² = 48

Solve by using the square root method. (x + 2)² = 36

Geometrically

Completing the Square

1.2: Completing the Square

Solve by completing the square

1.2: Completing the Square

Solve by "completing the square"

x² - 2x- 5 = 10

2 x² + 4x - 4= 0

The Quadratic Formula

The solutions of the equation are :

a ≠ 0

Solve by using the quadratic equation :

12x² - x - 6 = 0

x² = 2x - 2

1.2: Discriminant and solutions to the quadratic equation

The equation ax² + bx + c = 0 , with real coefficients and a≠0,
has as its discriminant b² - 4ac

If b² - 4ac > 0 then two distinct real solutions.

If b² - 4ac = 0 then one real solution.

If b² - 4ac < 0 then two distinct nonreal complex
solutions. The solutions are conjugates of each other

Determine discriminant and state the number of solutions

a) 4x² - 5x + 3 = 0

b) x² + 2x - 15 = 0

c) 4x² + 12x + 9 = 0

Now graphically

1.2: Applications

The Pythagorean Theorem

If a and b denote the lengths of the legs of a right
triangle and c the length of the hypotenuse, then

a² + b² = c²

Garfield's Proof of the Pythagorean Theorem

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More Algebra Help

Math 111 Chapter 1 Sections 1 & 2 Reviews