'09 TMSCA #11

[nsguy1350]

8. The graph of [unparseable or potentially dangerous latex formula] is _________
D. 2 intersecting lines -- I knew that taking the discriminant (b^2 - 4ac, in conics too) gives a hyperbola, but I didn't know what degenerate conic to pick out of the line, point, 2 intersection lines, 2 parallel lines, or no curve offered.
12. Joe left Elkhart and traveled 22 miles due south. Then he changed directions and traveled 18 miles on a bearing of 240. What bearing will he need to travel straight back to Elkhart? (nearest degree)
A. 27
I can find the distance, and find the angle of the triangle that was formed, but I tried to find the bearing and gave up during the test once my methods didn't work.
21. Joe's Pizzeria offers 9 varieties of pizza during their lunch buffet. How many ways could Mary select 4 slices of pizza?
B. 495 -- I got 126, and I don't know why a simple 9C4 doesn't work. Factoring 495 gives 11 x 5 x 9, and I don't see how you would get that.
30. Which number is a lucky prime?
C.193 -- need a method for determining lucky numbers...
31. Two circles [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] intersect at 2 points. Find the x-intercept of the line passing through the points of intersection.
A. -20 -- I tried subtracting the equations during the test, but the resulting line got me nowhere - in-depth explanation please?
47. Find the sum of the ten's digit and unit's digit of [unparseable or potentially dangerous latex formula].
A. 9 --- how do you determine this again? Something using relatively prime and something? Help please!

292... did 49, missed 1, skipped 10, my worst test of the day. I took four math tests today!! Cramming for TMSCA State so hard... gotta improve here, then improve in Calculator, study some Science, and make sure I have the TMSCA format down for Number Sense.

[Salvadoramerican]

On 47 normally you would on a ti-89 put in as 9^4*2mod(100) and that would give you the tens and 1s digits

On number 31 when expanded the two circles are x^2-4x+4+y^2-14y+49-144=0 and x^2+2x+1+y^2+16y+64-36=0
when subtracted they come out to be y=.2x-4 where the x-intercept is 0=.2x-4 when solve = 20

12 would be easier to explain if i had a diagram to show you but when you find the angle its about 33 degrees. You have to remember that the 240 comes down to 30 so add that 30 to the 33 you get 63 and 90-63=27 degree bearing.

#21 its a ball and pins type problem because we can repeat having 4 slices of the same pizza so the formula for that is n+r-1Cr where n is the pizza and r is the slices

#8 two intersecting lines are a degenerate graph of a hyperbola wikipedia degenreate conics and it goes more in depth

[nsguy1350]

Too lazy to check LateX, that's what happens. Should be 9^(42).

[Salvadoramerican]

Sorry it still works out 9^42mod(100)=81 8+1=9

[Salvadoramerican]

If you find a method for finding lucky number quickly tell cause i'm wanting to know too

[nsguy1350]

Ok, I see, thanks! I'll go research lucky numbers, and tell you if I find anything.