Hello from MrBillDoesMath!
Answer:
Choice A, "n"
Discussion:
n/4 + n/4 + n/4 + n/4 = 4 (n/4) = n
which is choice A
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MrB
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Answer: 2/4 or 1/2
Step-by-step explanation:
M=rise/run
-2/4 +1
2/4
1/2
We'll use the exponent rule that a^(b+c) = a^b*a^c
to break up 17^16 into 17^(14+2) = 17^14*17^2
That allows us to factor like so
17^16+17^14
17^14*17^2+17^14*1
17^14(17^2 + 1)
Computing 17^14 is a lot more difficult compared to computing 17^2 + 1, assuming you only could use paper and pencil.
Note that 17^2 = 17*17 = 289, so 17^2 + 1 = 289+1 = 290
Because 290 ends in a 0, this means that 5 is a factor
290 = 5*58
This makes 5 to be a factor of the original expression.
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So overall,
17^16+17^14 = 17^14(17^2 + 1) = 17^14*290 = 17^14*5*58 = 5*17^14*58
The stuff "17^14*58" doesn't matter. All we care about is that factor of 5.
Since 5 is a factor, this means that 17^16+17^14 is a multiple of 5, or 17^16+17^14 is divisible by 5.
Phrased another way, 17^16+17^14 all divided over 5 leads to some integer. In this case, the integer would be the result of 17^14*58.
Answer:
7.6 seconds
Step-by-step explanation:
To solve this problem we can use the following equation:
S = So + 113*t + at^2/2
Where S is the final position, So is the inicial position, Vo is the inicial speed, a is the acceleration and t is the time.
In this problem, we have that S = 0, So = 65, Vo = 113 and a = -32 ft/s2 (The acceleration of gravity)
So we have that:
0 = 65 + 113t - 16t2
16t2 - 113t - 65 = 0
Using Bhaskara's formula, we have:
Delta = 113^2 + 4*65*16 = 16929
sqrt(Delta) = 130.11
t = (113 + 130.11) / (2*16) = 7.597 seconds
Rounding to nearest tenth, we have t = 7.6 seconds
