Answer:
(D) he should have found that there are no solutions because the statement is false
35 pounds of black tea is needed to be mixed to get the final mixture for 2.10 per pound
<h3>What is an equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of black tea worth 1.80 per pound to be mixed to get the final mixture for 2.10 per pound, hence:
2.4(35) + 1.8(x) = 2.1(x + 35)
x = 35 pounds
35 pounds of black tea is needed to be mixed to get the final mixture for 2.10 per pound
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Step-by-step explanation:
Use the method of TOA CAH SOH.


Perimeter of triangle = Sum of all sides =

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.