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Answer:
AB = BC = 2√2
Step-by-step explanation:
Start by focusing on the 45 degree angle. The unknown AB is the side adjacent to this 45 degree angle, and the hypotenuse is known to be 4.
Thus,
cos 45 degrees = adj / hyp = AB / 4, or
AB = 4 cos 45 degrees = 4 (1 / √2) =
4 √2
----------- * --------- = 2√2
√2 √2
Since this is a 45-45-90 triangle, the two shorter sides are equal, and so BC = 2√2 also.
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Answer:
2/3
Step-by-step explanation:
Simplify the following:
3/4 - 1/12
Put 3/4 - 1/12 over the common denominator 12. 3/4 - 1/12 = (3×3)/12 - 1/12:
(3×3)/12 - 1/12
3×3 = 9:
9/12 - 1/12
9/12 - 1/12 = (9 - 1)/12:
(9 - 1)/12
9 - 1 = 8:
8/12
The gcd of 8 and 12 is 4, so 8/12 = (4×2)/(4×3) = 4/4×2/3 = 2/3:
Answer: 2/3
As we can tell, the first number is 3, so we'll have a y-intercept in our equation and overall. Secondly, we can tell it's increasing by 7 each time, so we can tell that's the rate. But, it won't just be 3+7x, if we plug 1 in, it would be 10 and not 3. We need to put in the parenthesis 3+7(x-1). If we put one in, we would receive three. Let's make sure this works.
3+7(5-1)
3+7(4)
3+28
31
31 is the fifth terms.
So the expression would be 3+7(x-1).
Let's find the 100th term.
3+7(100-1)
3+7(99)
3+693
696
So the 100th term would be 696.
