Answer:
n = -5
Step-by-step explanation:
Solve for n:
n + 2 = 4 n + 17
Hint: | Move terms with n to the left hand side.
Subtract 4 n from both sides:
(n - 4 n) + 2 = (4 n - 4 n) + 17
Hint: | Combine like terms in n - 4 n.
n - 4 n = -3 n:
-3 n + 2 = (4 n - 4 n) + 17
Hint: | Look for the difference of two identical terms.
4 n - 4 n = 0:
2 - 3 n = 17
Hint: | Isolate terms with n to the left hand side.
Subtract 2 from both sides:
(2 - 2) - 3 n = 17 - 2
Hint: | Look for the difference of two identical terms.
2 - 2 = 0:
-3 n = 17 - 2
Hint: | Evaluate 17 - 2.
17 - 2 = 15:
-3 n = 15
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -3 n = 15 by -3:
(-3 n)/(-3) = 15/(-3)
Hint: | Any nonzero number divided by itself is one.
(-3)/(-3) = 1:
n = 15/(-3)
Hint: | Reduce 15/(-3) to lowest terms. Start by finding the GCD of 15 and -3.
The gcd of 15 and -3 is 3, so 15/(-3) = (3×5)/(3 (-1)) = 3/3×5/(-1) = 5/(-1):
n = 5/(-1)
Hint: | Simplify the sign of 5/(-1).
Multiply numerator and denominator of 5/(-1) by -1:
Answer: n = -5
The absolute difference between the greatest and the least of these three numbers in the arithmetic sequence is 10.
The sequence is an arithmetic sequence. Therefore,
d = common difference
let
a = centre term
Therefore, the 3 consecutive term will be as follows
a - d, a, a + d
a - d + a + a + d = 27
3a = 27
a = 27 / 3
a = 9
Therefore,
(a-d)² + (a)² + (a + d)² = 293
(a²-2ad+d²) + 9² + (a² + 2ad + d²) = 293
(81 - 18d + d²) + 81 + (81 + 18d + d²) = 293
243 + 2d² = 293
2d² = 50
d² = 50 / 2
d = √25
d = 5
common difference = 5
Therefore, the 3 numbers are as follows
9 - 5 , 9, 9 + 5 = 4, 9, 14
The difference between the greatest and the least of these 3 numbers are as follows:
14 - 4 = 10
learn more on Arithmetic progression: brainly.com/question/25749583?referrer=searchResults
Answer:
36cm^2
Step-by-step explanation:
total area: 6x(4+3)=42
total area excluding the space: 42-(2x3)=36
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