Are the fractions equal? Explain why or why not.
2 answers:
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Answer:
Lets a,b be elements of G. since G/K is abelian, then there exists k ∈ K such that ab * k = ba (because the class of ab, is equal to
, thus ab and ba are equal or you can obtain one from the other by multiplying by an element of K.
Since K is a subgroup of H, then k ∈ H. This means that you can obtain ba from ab by multiplying by an element of H, k. Thus, . Since a and b were generic elements of H, then H/G is abelian.
Answer:
The cost of the 1 muffin is $1.5 and 1 quart of milk cost is $3 .
Step-by-step explanation:
Let us assume that the cost of one muffins be x.
Let us assume that the cost of one 1 quarts of milk be y.
As given
The cost of 8 muffins and 2 quarts of mil is $18.
Than the equation becomes
8x + 2y = 18
As given
The cost of 3 muffins and 1 quart of milk is $7.50.
Than the equation becomes
3x + 1y = 7.50
Two equations are
8x + 2y = 18 and 3x + 1y = 7.50
Multiply 3x + 1y = 7.50 by 2 and subtracted from 8x + 2y = 18 .
Thus
8x - 6x + 2y - 2y = 18 - 15
2x = 3
x = 1.5
Put x = 1.5 in 3x + 1y = 7.50
3 × 1.5 + y = 7.50
y = 7.50 - 4.5
y = 3
Therefore the cost of the 1 muffin is $1.5 and 1 quart of milk cost is $3 .