If the line is perpendicular, then its slope is the reciprocal of the given line's slope. This new line's slope is 1/2. We plug it into slope-intercept form
y = 1/2x + b
Now plug in the given point of (2, 10) and solve for b.
10 = 1/2(2) + b
10 = 1 + b
9 = b
So your equation is y = 1/2x + 9
15,000 + 1,250=16,250 add the distance above ground and under water to get the total distance.
The triangle height = 5√3 cm
So....the area =
(1/2) base x height = (1/2) (5) (5√3) = (25/2)√3
≈ 21.7 cm
Answer:
165 ways
Step-by-step explanation:
Selection deals with combination
There are a total of 11 from which 3 are to be selected
11C3 = 11!/3!(11-3)!
= 11!/(3!x8!)
=(11x10x9x8!)/(3x2x8!)
=11x10x9/6
=11x5x3 = 165 ways
We are told that every 9th person gets free popcorn and every 6th person gets free apple juice at the movie theater. We want to show if the 36th person is the first to get both free popcorn and apple juice.
Since every 9th gets free popcorn, then the 9th and 18th and 27th and 36th people get it. We can use numbers and show this as multiples of 9.
9, 18, 27, 36, 45, 54, ...
And we repeat it for every 6th and the free juice.
6, 12, 18, 24, 30, 36,....
Shani thinks 36 comes first, and she's wrong. 18 appears on the list before 36 as something that's common. What are we finding is the lowest common muliple of 6 and 9.
6 = 2 x 3
9 = 3 x 3
The lowest common multiple will have a 2, a 3, and a second 3 (because we don't double count). 2 x 3 x 3 = 18. This matches up to the list of multiples.
Thus, Shani is wrong that the 36th person gets both free items, as she did not account for the 18th person gettting both free items
