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tensa zangetsu [6.8K]
3 years ago
7

The balcony of an apartment is 4 feet by 7 feet. On a scale drawing of the apartment, the balcony is 0.8 inch by 1.4 inches, and

the kitchen is 2.4 inches by 2.8 inches.
What are the actual dimensions of the kitchen?
Mathematics
1 answer:
densk [106]3 years ago
7 0
The scale is 0.8 : 4  =  0.8/0.8 : 4/0.8  = 1: 5

so the kitchen has dimensions 2.4 * 5  and 2.8 * 5

 =  12 ft by 14 ft
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1 million

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13. The least common multiple of two non-zero integers a and b is the unique positive integer m such that (i) m is a common mult
Vlad [161]

Answer:

[a,b] divides n

Step-by-step explanation:

Let us denote the least common multiple of a and b [a,b]=m.

We want to prove that m divides n, where n is a multiple of a and b.

We suppose m does not divide n, then by the Division Theorem, there exists q and r integers such that:

(1) ... n=mq+r, where 0<r<m

As n is a multiple of a and b, there exists s and t integers such that:

sa=n and tb=n

Same thing happens to m as it is the least common multiple, there exists u and v such that:

ua=m and vb=m

So (1) has the following form:

n=mq+r ⇒ sa=uaq+r ⇒sa-uaq=r⇒(s-uq)a=r and

n=mq+r ⇒ tb=vbq+r ⇒ tb-vbq=r⇒ (t-vq)b=r

So r is a multiple of a and b, but r<m which is a contradiction as, m is the least common multiple of a and b. So this concludes the proof.

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