6 lesson 1 concepts of ratio and proportion
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This chapter discusses discovering similar triangles and circles through properties involving proportions. It reviews key concepts like ratio, proportion, terms, and means and extremes. Students are instructed to complete warm-up practice answering activities A through F for even numbered problems only.
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1. How to simplify and perform operations on imaginary and complex numbers by writing them in terms of i, where i^2 = -1.
2. The rules for adding, subtracting, multiplying, and dividing complex numbers, which follow the same patterns as operations on binomials.
3. How to find the conjugate of a complex number and use conjugates to simplify divisions of complex numbers.
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This document introduces radical functions. It covers evaluating radical functions, finding the domain of radical functions, graphing radical functions, performing operations on functions such as addition and multiplication, and function composition. Examples are provided to illustrate evaluating functions, finding domains, graphing, performing operations, and function composition.
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This document provides instructions and examples for solving various types of equations, including:
1. Linear equations with one variable such as 4m - 2 = 6.
2. Radical equations where the radicand contains an unknown variable, along with guidelines for solving such equations by isolating radical terms and applying the principle of powers.
3. Sample radical equations are provided for practice, including x - 1 = 2, 3x + 2 = 3, and x + 1 = 3.
4. Readers are then instructed to practice solving similar equations on their own.
8.5 heron’s formula
The document describes Heron's Formula, which uses the Law of Cosines to calculate the area of a triangle based on its three side lengths. Specifically, the area equals the square root of s(s - a)(s - b)(s - c), where s is equal to half the sum of the three side lengths. This formula, credited to the Greek mathematician Heron, allows calculating a triangle's area when only its three side lengths are known.
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