Answer:
3x + 6y = 64.50________equation 1
9x + 8y = 106.00_______equation 2
Price of a bag of popcorn is $3(300 cents) WHILE the price of one drink is $8.75(875 cents)
Step-by-step explanation:
The question here says that Kayden and Carter go to the movie theater and purchase refreshments for their friends.
Kayden spends a total of $64.50 on 3 bags of popcorn and 6 drinks.
Carter spends a total of $106.00 on 9 bags of popcorn and 8 drinks.
Now let's assume that the price of each bag of popcorn is X and the price of one drink as Y
It means that
3x + 6y = 64.50________equation 1
9x + 8y = 106.00_______equation 2
Make "x" the subject of the formula in equation 1
3x = 64.50 - 6y
X = (64.50 - 6y)/3
Apply the above in equation 2 and we have
9[ (64.50 - 6y)/3] + 8y = 106
9(21.5 - 2y) +8y = 106
193.5 - 18y + 8y = 106
193.5 - 10y = 106
Y= (193.5 - 106)/10
Y= $8.75 (price of one drink)
Now substitute Y = 8.75 in equation 1
3x + 6y = 64.50
3x + 6(8.75) = 64.50
3X = 64.50 - 52.5
X = 12/3
X = 3
Then the original price was $42
Because it is half off we multiply 21 by 2 and get 42.
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: (0, -2)
Step-by-step explanation: