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The official logo of the TAKS test. Mainly based on the TAAS test's logo. The Texas Assessment of Knowledge and Skills (TAKS) was the fourth Texas state standardized test previously used in grade 3-8 and grade 9-11 to assess students' attainment of reading, writing, math, science, and social studies skills required under Texas education standards. [1]
As the name implies, a quarter note's duration is one quarter that of a whole note, half the length of a half note, and twice that of an eighth note. It represents one beat in a bar of 4 4 time. The term "quarter note" is a calque (loan-translation) of the German term Viertelnote.
Microsoft Math was originally released as a bundled part of Microsoft Student. It was then available as a standalone paid version starting with version 3.0. For version 4.0, it was released as a free downloadable product [4] and was called Microsoft Mathematics 4.0.
In abstract algebra, a subset of a field is algebraically independent over a subfield if the elements of do not satisfy any non-trivial polynomial equation with coefficients in . In particular, a one element set { α } {\displaystyle \{\alpha \}} is algebraically independent over K {\displaystyle K} if and only if α {\displaystyle \alpha } is ...
The maximum independent set problem is NP-hard. However, it can be solved more efficiently than the O(n 2 2 n) time that would be given by a naive brute force algorithm that examines every vertex subset and checks whether it is an independent set. As of 2017 it can be solved in time O(1.1996 n) using polynomial space. [9]
for (t 1, t 2, ... , t k) ≠ (u 1, u 2, ... , u k). [note 3] If v 1, ..., v k are linearly independent, then the coordinates t 1, ..., t k for a vector in the span are uniquely determined. A basis for a subspace S is a set of linearly independent vectors whose span is S. The number of elements in a basis is always equal to the geometric ...
The equations 3x + 2y = 6 and 3x + 2y = 12 are independent, because any constant times one of them fails to produce the other one. An independent equation is an equation in a system of simultaneous equations which cannot be derived algebraically from the other equations. [1] The concept typically arises in the context of linear equations.
GeoGebra's creator, Markus Hohenwarter, [4] started the project in 2001 as part of his master's thesis at the University of Salzburg. After a successful Kickstarter campaign, GeoGebra expanded its offering to include an iPad, an Android and a Windows Store app version. [5] In 2013, GeoGebra incorporated Bernard Parisse's Xcas [6] into its CAS ...