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SVETLANKA909090 [29]

3 years ago

9

Janice wants to buy carpet for a trapezoid shaped room. The bases of the trapezoid are 12 feet and 14 feet, and the height is 15

feet. If the carpet she like is $5.50 per square foot,how much will new carpet for the room cost?

1 answer:

Usimov [2.4K]3 years ago

4 0

For this case, the first thing to do is find the area of the trapezoid.
We have then:
$A = (1/2) * (b1 + b2) * (h)
$
Where,
b1: b2: Trapezoid bases
h: height of the trapezoid
Substituting values we have:
$A = (1/2) * (12 + 14) * (15)

A = 195 ft ^ 2$
Then, the cost per square foot is given by:
$C = 5.50A

C = 5.50 * 195

C = 1072.5$
Answer:
The new carpet for the room will cost:
C = 1072.5 $

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a. closed under addition and multiplication

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Step-by-step explanation:

a.

Let A be a set of all integers divisible by 5.

Let $x,y$ ∈A such that $x=5m\,,\,y=5n$

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$x+y=5m+5n=5(m+n)$

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$xy=(5m)(5n)=25mn=5(5mn)$

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$xy$ is divisible by 5.

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b.

Let A = { 2n +1 | n ∈ Z}

Let $x,y$ ∈A such that $x=2m+1\,,\,y=2n+1$ where m, n ∈ Z.

Find $x+y,xy$

$x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)$

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$x+y$ ∉ A

$xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1$

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Let $x=2,y=5$ but $x+y=2+5=7$ ∉A

Also,

$xy=2(5)=10$ ∉A

Therefore, A is not closed under addition and multiplication.

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Let $x,y$ ∈ A such that $x=17n,y=17m$

Find x + y and xy

$x+y=17n+17m=17(n+m)$

$xy=(17m)(17n)=289mn=17(17mn)$

So,

$x+y,xy$ ∈ A

Therefore, A is closed under addition and multiplication.

e.

Let A be the set of nonzero real numbers.

Let $x,y$ ∈ A such that $x=-1,y=1$

Find x + y

$x+y=-1+1=0$

So,

$x+y$ ∈ A

Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.

Therefore, A is not closed under addition but A is closed under multiplication.

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