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The unique pair of values a, b satisfying the first two equations is (a, b) = (1, 1); since these values also satisfy the third equation, there do in fact exist a, b such that a times the original first equation plus b times the original second equation equals the original third equation; we conclude that the third equation is linearly ...
Hence, zero is the (global) minimum of the square function. The square x 2 of a number x is less than x (that is x 2 < x) if and only if 0 < x < 1, that is, if x belongs to the open interval (0,1). This implies that the square of an integer is never less than the original number x.
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
The equations 3x + 2y = 6 and 3x + 2y = 12 are inconsistent. A linear system is inconsistent if it has no solution, and otherwise, it is said to be consistent. [7] When the system is inconsistent, it is possible to derive a contradiction from the equations, that may always be rewritten as the statement 0 = 1. For example, the equations
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If the original fact were stated as "ab = 0 implies a = 0 or b = 0", then when saying "consider abc = 0," we would have a conflict of terms when substituting. Yet the above logic is still valid to show that if abc = 0 then a = 0 or b = 0 or c = 0 if, instead of letting a = a and b = bc , one substitutes a for a and b for bc (and with bc = 0 ...
That possession ended with a touchdown anyway on Mixon's 45-yard sprint up the middle, and he ran wide for a 1-yard score and 14-0 lead. Mixon had 109 yards rushing and set up a field goal with a ...
(The Center Square) – Missouri state Sen. Jill Carter, R-Granby, plans to file bills in the state legislature to increase border security measures and ensure law enforcement agencies have the ...