Answer:
You can prove this statement as follows:
Step-by-step explanation:
An odd integer is a number of the form where
. Consider the following cases.
Case 1. If is even we have:
.
If we denote by we have that
.
Case 2. if is odd we have:
.
If we denote by we have that
This result says that the remainder when we divide the square of any odd integer by 8 is 1.
Answer:
The cost of 1 doll = $ 7.5
and The Cost of 1 toy train = $ 5
Step-by-step explanation:
Let the price of 1 doll = $ x
The price of 1 toy train = $ y
Now, according to the question:
6 x + 2 y = $ 55
and 4 x + 7 y = $ 65
Solving the given system of equation,
From (1), we get
or, solving for y , we get
110y - 4y + 21 y = 195
or, 17 y = 85
⇒ y= 85/17 = 5
This implies : 6 x + 2 (5) =55
or, 6x = 55 - 10 = 45
or, x = 45/ 6 = 15/2
Hence, the cost of 1 doll = x = $ 7.5
and the Cost of 1 toy train = y = $ 5