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1)     12x - 28 = 7x + 12         solve for x

2)     (9y - 77) + (12x - 28) = 180        solve for y

please look up modular artihmetic rules on mathstackexchange instead of begging for an answer it is quite elementary indeed

formula for sum of geometric series is S(n) = (a_1*(1-r^n))/1-r where r is not equal to 1. use it 

multiply the denominators of both fractions by the conjugate to rationalize the denominator (because you get difference of squares). subsequently u multiply by the lcd of the two get rid of a fraction in the denominator and then do any simplifying u need to u should get it in that form :)

standard form of a circle = (x-a)^2 + (y-b)^2 = r^2 where (a,b) is the center and r is the radius

now, we have to account to complete the squares. since r = 7, r^2 = 49. 

(x+4)^2 = x^2 + 8x + 16

(y+2)^2 + y^2 + 4y + 4 

x^2 + 8x + 16 + y^2 + 4y + 4 + 49 = 0 

this makes up a circle if you break it down into standard form... now lets add up what we have added onto it

49 + 4 + 16 = 49 + 20 = 69 

Write 5 = 3 + 2, and expand using the Binomial Theorem.  Then appy the Reduction Lemma to finish.

ratio of AC : BD = 7 : 12    or    7/12

CP = BC = sqrt( 61 - 5²) = 6

It turns out that there really isn't a good strategy; you should guess whichever card to be the card with the highest number on it, so the best you can do is 1/3.

Reference: https://math.stackexchange.com/questions/3474127/what-is-the-best-betting-strategy-to-maximize-probability-of-winning/

Angle CXA = 23 degrees.

cos angle ABM = 4/7.

Compute i + i^2 + i^3 + i^4 + ... + i^(2020).

sum_(n=1)^2020 i^n = 0

Go to this link and see all the details of the reactions:

https://www.wolframalpha.com/input/?i=2+C3H3+%2B+O2+%E2%86%92+2+CO2+%2B+H2O

I should have included units to make things clearer perhaps, but often the units can clutter the equation and lead to confusion:

6200 N  * 95000 m = ......... j

Thanks so much for the explanation!

I'd convert them both to base 10, do the multiplication and then convert back.

(Hint: 1 kN= 1000 N)    as given in the Q

k stand for kilo which means 1000 times bigger.

So

6.2kN = 6.2 thousand Newtons = 6.2*1000 =  6200 N

Same for Km

Turn all of those numbers into decimals (with a calculator). And tell us what the question becomes.

how'd you converted 6.2 kN and 95 km?