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Colt1911 [192]
3 years ago
5

A rectangular room is 3 meters longer than it is wide, and its perimeter is 22 meters. Find the dimension of the room. The lengt

h is : meters and the width is: meters.
Mathematics
1 answer:
lyudmila [28]3 years ago
4 0

Answer:

Width = 4 m

Length = 7 m

Step-by-step explanation:

given:

perimeter of a rectangle = 22m

L = 3 + W

perimeter = 2L + 2W

perimeter = 2 (3 + W) + 2W

22 = 6 + 2W + 2W

22 - 6 = 4W

W = 16 / 4

W = 4 m

L = 3 + W

L = 3 + 4

L = 7 m

check:

perimeter = 2L + 2W

22 = 2(7) + 2(4)

22 = 14 + 8

22 = 22  ---- OK

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Select all the expressions that are equivalent to (2)^n+³
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Answer:

The expressions which equivalent to  (2)^{n+3} are:

4(2)^{n+1}  ⇒ B

8(2)^{n} ⇒ C

Step-by-step explanation:

Let us revise some rules of exponent

  • a^{m} × a^{m}  = a^{m+n}
  • (a^{m})^{n} = a^{m*n}

Now let us find the equivalent expressions of  (2)^{n+3}

A.

∵ 4 = 2 × 2

∴ 4 =  2^{2}

∴  (4)^{n+2} =  (2^{2})^{n+2}

- By using the second rule above multiply 2 and (n + 2)

∵ 2(n + 2) = 2n + 4

∴  (4)^{n+2} =  (2)^{2n+4}  

B.

∵ 4 = 2 × 2

∴ 4 =  2²

∴  4(2)^{n+1} = 2² ×  (2)^{n+1}

- By using the first rule rule add the exponents of 2

∵ 2 + n + 1 = n + 3

∴   4(2)^{n+1} =  (2)^{n+3}

C.

∵ 8 = 2 × 2 × 2

∴ 8 =  2³

∴  8(2)^{n} = 2³ ×  (2)^{n}

- By using the first rule rule add the exponents of 2

∵ 3 + n = n + 3

∴  8(2)^{n} =  (2)^{n+3}

D.

∵ 16 = 2 × 2 × 2 × 2

∴ 16 = 2^{4}

∴  16(2)^{n} = 2^{4}  ×  (2)^{n}

- By using the first rule rule add the exponents of 2

∵ 4 + n = n + 4

∴  16(2)^{n} =  (2)^{n+4}

E.

(2)^{2n+3} is in its simplest form

The expressions which equivalent to  (2)^{n+3} are:

4(2)^{n+1}  ⇒ B

8(2)^{n} ⇒ C

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