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 The diagonal of the square is     \(\sqrt{2R^2}\)

You need to check my working for stupid errors.

Thanks a lot!

The question is slightly ambiguous.  "The same scores" could mean identical scores for each individual problem, or it could mean the same total score.  I'll assume the latter.

With 22 problems and the three possible scores of 0, 1 and 3 per problem, the total score could be any of the numbers from 0 to 66.  Hence there are 67 possible totals.  Therefore we need a minimum of 68 candidates to ensure at least two have the same total score.

Write the ratio in lowest terms with whole numbers in the numerator and denominator . 0.3 km to 0.09 km

Hello Fhhenakwnrn!

\(0.3km\ :\ 0.09km=1\ :\ 3/10=1\ :\ \large \frac{3}{10}\)

  !

(√2r² - r) : r = (√2r² + r) : R 

Hint:

Use the difference of two squares         3 times.

Please no one expand on this.

If it says 31/9 is wrong, then try entering it in a different way.

I will assume tan y    is   tan S

Tans = opp / adj   =   x / (x+14)  = 8/15   

                                  8(x+14)  = 15x

                                   x = 16

Pythag theorem      16^2  +   30^2  = QS^2     solve for QS

cos RQS = adj / hyp = 16/(the value you found for QS above) = .........

Solve the system of equations

10b+5v+5z=55  
3b+5v+5z=34
5b+6v+3z=42

10b+5v+5z=55               5z=55-10b-5v
3b+5v+5z=34                 5z=34-3b-5v

55-10b-5v=34-3b-5v   | + 5v                    system of equations        

55-10b=34-3b             | -34+10b

21=7b                          | /7

b=3

3b+5v+5z=34              |deploy b=3         system of deploy
5b+6v+3z=42              |deploy b=3

9+5v+5z=34                | * 3 
15+6v+3z=42              | * 5

27+15v+15z=170        | subtr.                 system of addition

75+30v+15z=210

48+15v=40                  | -48

15v=-8                         | /15

v=\(-\frac{8}{15}\)

27+15v+15z=170        | deploy \(v=-\frac{8}{15}\)   

27-8+15z=170            | - 19

15z=151

\(z=10\frac{1}{15}\)

  !

I do not like any of those answers.

b  is absolutely incorrect.

d  perhaps not really related

a , well not really, but if you are talking very near future then I guess that is correct.  

c, the slope of a lined is always an integer.

So I guess we are left with only one possibility.

-18917

watch this.

sorry, i meant simplified fraction

then what number base is 3.444444 supposed to be converted from

Yes. They want the decimal 3.44444...  converted to base 10 as a simplified answer

put 31/9 into a calculator, it is equal to 3.444444

is the base 10 part supposed to mean something? i just assumed it meant that it didn't want the fraction to be in base 7 or anything.

i tried 31/9 but it says it is wrong

to start, we will ignore the 3 and come back to it later

we are left with the fraction .4444444444444

i see this and reconize that it is 4/9, but if you dont there is a way we can get there algabraicly

x=.444444444

multiply by 10

10x=4.44444444444

subtract the original equation

9x=4

divide by 9, and you get x=4/9

coming back to the 3

4/9+3=(3(9)+4)/9

=31/9

(r*s)(t) means r(s(t)), where you plug t into the function s, and then put the value you get from that into r.

for option a, substituting s(t)=t+f into r is 2(t+5)+1

=2t+10+1

=2t+11

this is the result we were looking for, so the answer is a