Please help me on how to solve this question, it is really confusing, pleaseeeee

Mathematics

1 answer:

mezya [45]3 years ago

6 0

D is halfway between A and B

so the coordinates of D are (2,2)

E is halfway between A and C so the coordinates of E are (-1,1)

now you need to find the gradient/slope of DE and BC using the formula:

y2 - y1 ÷ x2 - x1

Gradient of DE:

SUB IN COORDINATES OF D AND E

1-2 ÷ -1-2

therefore the gradient of DE is 1/3.

Gradient of BC:

SUB IN COORDINATES OF B AND C

- 2 - 0 ÷ - 3 - 3

therefore the gradient of BC is -2/-6 which simplifies to 1/3.

therefore, BC and DE are parallel as they both have a gradient/slope of 1/3 and parallel lines have the same gradient

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(c) $100=2^2\cdot5^2$ ; there are 50 multiples of 2, and 20 multiples of 5, between 1 and 100; 10 of these are counted twice (the multiples of 2*5=10), so a total of 50 + 20 - 10 = 60 distinct numbers not coprime to 100, leaving us with $\varphi(100)=100-60=40$ .

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