Answer:
the prices were $0.05 and $1.05
Step-by-step explanation:
Let 'a' and 'b' represent the costs of the two sodas. The given relations are ...
a + b = 1.10 . . . . the total cost of the sodas was $1.10
a - b = 1.00 . . . . one soda costs $1.00 more than the other one
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Adding these two equations, we get ...
2a = 2.10
a = 1.05 . . . . . divide by 2
1.05 -b = 1.00 . . . . . substitute for a in the second equation
1.05 -1.00 = b = 0.05 . . . add b-1 to both sides
The prices of the two sodas were $0.05 and $1.05.
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<em>Additional comment</em>
This is a "sum and difference" problem, in which you are given the sum and the difference of two values. As we have seen here, <em>the larger value is half the sum of the sum and difference</em>: a = (1+1.10)/2 = 1.05. If we were to subtract one equation from the other, we would find <em>the smaller value is half the difference of the sum and difference</em>: b = (1.05 -1.00)/2 = 0.05.
This result is the general solution to sum and difference problems.
Answer:
950.00
Step-by-step explanation:
Answer:
a) Observe that
![G=\left[\begin{array}{ccc}2&6\\4&0\end{array}\right] =2\left[\begin{array}{ccc}1&3\\2&0\end{array}\right] =2F](https://tex.z-dn.net/?f=G%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%266%5C%5C4%260%5Cend%7Barray%7D%5Cright%5D%20%3D2%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%5C%5C2%260%5Cend%7Barray%7D%5Cright%5D%20%3D2F)
Then, 
b) The zero matrix satisfies that for every matrix B such that the product is well defined, 
Since the matrix G is the zero matrix then 
c) The identity(Id) matrix satisfies that for that for every matrix B such that the product is well defined Id*B=B=B*Id. Observe that G is the identity matrix, then FG=F*Id=F=Id*F=GF
d) Observe that
![G=\left[\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right] =3\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] =3Id](https://tex.z-dn.net/?f=G%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%260%260%5C%5C0%263%260%5C%5C0%260%263%5Cend%7Barray%7D%5Cright%5D%20%3D3%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D%20%3D3Id)
.
Then 
For this case we have the following equation:
y = -8
The equation is a horizontal line.
The horizontal line cuts to the axis and in the following point:
(x, y) = (0, -8)
The horizontal line does not cut to the x axis.
Answer:
b. No x-intercept y-intercept is (0, -8)
