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Here is a graph:

Lets figure out the standard equation for a circle by completing the square

x^2-10x+25    + y^2-4x+4  = -12 +25 + 4

9x-5)^2  + (y-2)^2 = 17                                     center is h, k  = 5,2    

We want a straight line frome center through 9,3  to new center (so the circles will be tangent at 9,3)

5,2   to  9, 3    is  a change of  4,1      add that to 9, 3   to get    13,4

SO the identical tangent circle is

(x-13)^2 + (y-4)^2 = 17

6 is da answer

Two identical circles touch at the point P(9,3) 

one of the circles has equation x^2 + y^2 - 10x - 4y +12 = 0

find the equation of the other circle 

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then you can see it.

Add 2y to both sides; subtract 7 from both sides; double each term in the  resulting equation.

Multiply numerator and denominator by the complex conjugate of 1-2i; namely by 1+2i. 

Note that (1-2i)(1+2i) = 1 + 4 = 5; i.e. it no longer depends on i. 

See if if you can take it from there.

This is a miniscule written question. 

Just type it in!

NOTE:

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None of your choices provide the correct solution to what you have written!

3ⁿ⁺² + 3ⁿ⁺³ - 3ⁿ⁺¹ → 3ⁿ⁺¹(3¹ + 3² - 3⁰) → 3ⁿ⁺¹(3 + 9 - 1) → 11*3ⁿ⁺¹ 

I think you must have meant  3ⁿ⁺² / (3ⁿ⁺³ - 3ⁿ⁺¹)  → 3¹ / (3² - 3⁰) → 3 / (9 - 1) → 3/8   (where 3ⁿ⁺¹ has been factored out of the terms in both numerator and denominator).

Perhaps this graph will help:

Yes I think your answer is correct  (The image is the right half plane)

I followed your link but question 5 is different, am I missing something?

Sorry EP you are right. Your answer is good.     

Solution:

\(\text {Hugo can receive a maximum of 600 points for all tests. }\\ \text {The lowest “B” score is } (0.80 * 600) = 480 \text { points. }\\ \text {The highest “B” score is } (0.899 * 600) =539 \text { points. }\\ \text {Total points for the first four tests are } (82) + (88) + (91) + (83) = 344 \\ \text {For a “B” grade, the final score (F) must have a range of }\\ (479-344) \ge (F) \lt (540-344)\\ \hspace{2.6em} (135) \ge (F) \lt (196)\\ \; \\ \text {Answer “K” exceeds this range. }\\ \)

GA

I think it is correct, Melody.      Thnx   ~EP

You have made a little error EP

The largest one is x+1   (not x+2)

Diagram 6

now use cosine formula to finish it.

I have done it and was going to present my answer but since it is a comptetition I should leave some for you to do.

Hint:  there is a square root in the answer.

Have fun :)

diagram 5

Diagram 4

Diagram 3