Which of these is the algebraic expression for "6 less than 5 times some number?" 6n − 5 5n − 6 5 − 6n 6 − 5n
2 answers:
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Answer:
Step-by-step explanation:
To solve for the leg of the missing right triangle, one must use the Pythagorean theorem. The Pythagorean theorem states the following,
Where (a) and (b) are the sides adjacent to or next to the right angle. (c) is the side opposite the right angle. Substitute in the given values and solve for the unknown,
Substitute,
Simplify,
Inverse operations,
Answer:
Only d) is false.
Step-by-step explanation:
Let be the characteristic polynomial of B.
a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)
b) Remember that . 0 is a root of p, so we have that
.
c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.
d) det(B)=0 by part c) so B is not invertible.
e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.
Answer:
n = 36
Step-by-step explanation:
The opposite sides of a parallelogram are congruent , that is
AB = DC , substitute values
n - 5 =
n + 7 ( multiply through by 3 to clear the fractions )
2n - 15 = n + 21 ( subtract n from both sides )
n - 15 = 21 ( add 15 to both sides )
n = 36