G If S is the subspace of R 3 containing only the zero vector, what is S ⊥? If S is spanned by (1, 1, 1), what is S ⊥? If S is spanned by (1, 1, 1) and (1, 1, −1), what is a basis for S ⊥?

step-by-step explanation:

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mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

answer:   y=2x-3

step-by-step explanation: