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Elina [12.6K]
3 years ago
9

Prove that the sum of five consecutive natural numbers is even​

Mathematics
1 answer:
ELEN [110]3 years ago
6 0

Answer:

Conversely, if n is divisible by 5, then n is the sum of five consecutive integers. In particular, this gives n = 5m + 10 = 5(m + 2) and, since m + 2 is an integer, this shows n is divisible by 5

Step-by-step explanation:

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The park service that administers a state park estimates that there are 495 deer in the park. They decide to remove deer accordi
Vlada [557]

Answer:

your answer is (A.)

Step-by-step explanation:

6 0
3 years ago
A 47-foot-long piece of pipe is to be cut into three pieces. The second piece is three times as long as the first piece, and the
DanielleElmas [232]
A = first piece, b = second piece, c = third piece

a + b + c = 47
b = 3a
c = 5a + 2

a + (3a) + (5a + 2) = 47.....combine like terms
9a + 2 = 47
9a = 47 - 2
9a = 45
a = 45/9
a = 5 ft

b = 3a.....b = 3(5)....b = 15 ft
c = 5a + 2....c = 5(5) + 2.....c = 25 + 2....c = 27 ft

longest piece (c) = 27 ft
7 0
3 years ago
PLEASE HELP, GIVING 55 POINTS IF YOU ANSWER (08.03/08.05 MC) A pair of equations is shown below: y = 3x − 5 y = 6x − 8 Part A: E
Andrew [12]

Answer:

  A. (1, -2)

  B. the lines intersect at the solution point: (1, -2).

Step-by-step explanation:

A. The equations can be solve by substitution by using the y-expression provided by one of them to substitute for y in the other.

This gives ...

  3x -5 = 6x -8

Adding 8-3x to both sides, we get ...

  3 = 3x

Dividing both sides by 3 gives ...

  1 = x

Substituting this value into the first equation, we can find y:

  y = 3(1) -5 = -2

The solution is (x, y) = (1, -2).

__

B. The lines intersect at the solution point, the point that satisfies both equations simultaneously. That point is (1, -2).

8 0
3 years ago
Replace ∗ with a monomial so that the derived expression may be represented as a square of a binomial: * +14b+49
anyanavicka [17]

Answer:

  * = b²

Step-by-step explanation:

You know that the square of a binomial is of the form ...

  (x + y)² = x² + 2xy + y²

Matching given terms, we have ...

  49 = y²

  2xy = 14b

Solving the first of these relations for y, we have

  y = √49 = 7

Putting that in the second relation and solving for x, we find ...

  2x·7 = 14b

  14x = 14b

  x = b

Then the first term of the expansion, x², will be b².

The missing term is b².

7 0
3 years ago
According to the distributive property, a(5 + b) =
WINSTONCH [101]
The answer would be B
7 0
3 years ago
Read 2 more answers
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