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The question pertains to sign rules in multiplication and division, identifying linear equations, solving quadratic equations using the quadratic formula, and simplifying expressions with exponents.
When two positive numbers multiply, the result is positive. For instance, 2 x 3 = 6. Similarly, when two negative numbers multiply, the result is also positive, as seen in (-4) x (-3) = 12. However, when the numbers have opposite signs, the result is negative, such as (-3) x 2 = -6 or 4 x (-4) = -16. These rules apply similarly to division.
A discussion of linear equations reveals that options A, B, and C are linear because they can be written in the form y = mx + b, where m and b are constants. As for solving quadratic equations, like x² +0.0211x -0.0211 = 0, the quadratic formula can be applied because the equation is in the standard form ax² + bx + c = 0, allowing for the determination of the solution for x.
The process of simplifying expressions with exponents can be seen in re-expressing numbers, such as turning 2 x 10¹² into 2³ x 10⁵, and applying the same process to different operations. Practices involving these methods not only solve for a particular answer but also solidify the understanding of mathematical concepts.
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