Find q, r in \mathbb{z} so that 105 = 11q + r
with 0 \leq r < 11 as in the division algorithm

Step-by-step explanation:

Division Algorithm :

As per division algorithm , for numbers a and b , there exist numbers q and r such that

Here ,

a = Dividend

b = Divisor

q = quotient

r = remainder

Given : 105 = 11q + r such that

Here, clearly a = 105 , b = 11

To find : q and r

Solution : On dividing 105 by 11 , we get

On comparing with , we get

this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)

hope this !

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step-by-step explanation: