If line rt is rotated about the origin such that its image line r't' is parallel to it, then the angle of rotation would be which of the following?
a)90 °
b)180 °
c)270 °
d)360 °

Choice B) 180 degrees

Imagine an arrow pointing directly to the east. If you rotate it 180 degrees, then it ends up pointing directly west. Both arrows will form the same straight line if you join them up together at the endpoints. This idea of rotating an arrow can also apply to rotating lines as well.

We start by setting out the inequalities

Let the number of kennels is 'k' and the number of dogs is 'd'

Inequality 1:

30 minutes per dog + 10 minutes per kennel ≤ 7 hours 
30d + 10k ≤ (7 × 60)
30d + 10k ≤ 420

Inequality 2:

Number of kennels to be cleaned is 30
k ≤ 30

Inequality 3:

Number of dogs to bathe is 10
d ≤ 10

Sketching the graph on the Cartesian axes will look like the diagram below
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PART A

From the graph, we can see two intersection coordinates that satisfy the three inequality, which we will check in turn for the greatest possible money that Nikolai could earn

First coordinate (18, 8) ⇒ This means, 18 kernels and 8 dogs
(18 × $3) + (8 × $10) = 54 + 80 = $134

Second coordinate (30, 4) ⇒ This means, 30 kernels and 4 dogs
(30 × $3) + (4 × $10) = $90 + $40 = $130

The maximum earning Nikolai could get is $134 if he cleans 18 kernels and baths 8 dogs.
-----------------------------------------------------------------------------------------------------------PART B

If Nikolai cleans all the kernels first, he'd spend 30 × 10 minutes = 300 minutes out of 420 minutes he has in total in a day

He'd have 420 - 300 = 120 minutes left to bath some dogs.

He needs 30 minutes to bath one dog
With 120 minutes he's got left, he can only bath 120 ÷ 30 = 4 dogs