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:
it is c
Step-by-step explanation:
brainly plz
Answer:
Step-by-step explanation:
g(x) = x^2 - x
g(2/3) = (2/3)^2 - 2\3 = 4/9 - 2/3 = 4/9 - 6/9 = -2/9
Answer:
22 miles per hour
Step-by-step explanation:
Against the current, the boat's rate of travel is ...
(120 mi)/(6 h) = 20 mi/h
With the current, the boat's rate of travel is ...
(120 mi)/(5 h) = 24 mi/h
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The sum of boat speed (b) and current speed (c) is 24 mph. The difference is 20 mph. This lets us write the equations ...
b + c = 24
b - c = 20
Adding these two equations together, we get ...
2b + 0c = 44
b = 22 . . . . . . . . divide by 2
The rate of the boat in still water is 22 miles per hour.
Answer:
x + 2700 ≥ 5000 → x ≥ 2300
Step-by-step explanation:
The inequality is: x + 2700 ≥ 5000 with x being the number of points
To solve we need to subtract 2700 from both sides to get: x ≥ 2300
