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Rudik [331]
3 years ago
14

Wes measures the floor area of rectangular living room to replace the carpet with tiles. The length of the room is 2.6 feet grea

ter then the width. The width of the room is 9.8 feet. How many square feet of tile will Wes need?
Mathematics
1 answer:
Oliga [24]3 years ago
3 0

Answer:

Wes need 121.52 square feet of tile.

Step-by-step explanation:

Given:

Wes measures the floor area of rectangular living room to replace the carpet with tiles

The length of the room is 2.6 feet greater than the width.

The width of the room is 9.8 feet.

Now, to find the square feet of tiles Will Wes need.

Width = 9.8 feet.

Length = 2.6 feet + 9.8 feet = 12.4 feet.

So, to get the square feet of tile we get the area of the room:

Area = length\times width

Area=12.4\times 9.8

Area=121.52\ square\ feet.

Therefore, Wes need 121.52 square feet of tile.

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Check whether the relation R on the set S = {1, 2, 3} is an equivalent
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Answer:

R isn't an equivalence relation. It is reflexive but neither symmetric nor transitive.

Step-by-step explanation:

Let S denote a set of elements. S \times S would denote the set of all ordered pairs of elements of S\!.

For example, with S = \lbrace 1,\, 2,\, 3 \rbrace, (3,\, 2) and (2,\, 3) are both members of S \times S. However, (3,\, 2) \ne (2,\, 3) because the pairs are ordered.

A relation R on S\! is a subset of S \times S. For any two elementsa,\, b \in S, a \sim b if and only if the ordered pair (a,\, b) is in R\!.

 

A relation R on set S is an equivalence relation if it satisfies the following:

  • Reflexivity: for any a \in S, the relation R needs to ensure that a \sim a (that is: (a,\, a) \in R.)
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  • Transitivity: for any a,\, b,\, c \in S, if a \sim b and b \sim c, then a \sim c. In other words, if (a,\, b) and (b,\, c) are both in R, then (a,\, c) also needs to be in R\!.

The relation R (on S = \lbrace 1,\, 2,\, 3 \rbrace) in this question is indeed reflexive. (1,\, 1), (2,\, 2), and (3,\, 3) (one pair for each element of S) are all elements of R\!.

R isn't symmetric. (2,\, 3) \in R but (3,\, 2) \not \in R (the pairs in \! R are all ordered.) In other words, 3 isn't equivalent to 2 under R\! even though 2 \sim 3.

Neither is R transitive. (3,\, 1) \in R and (1,\, 2) \in R. However, (3,\, 2) \not \in R. In other words, under relation R\!, 3 \sim 1 and 1 \sim 2 does not imply 3 \sim 2.

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