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Alex Ar [27]
3 years ago
14

Your family is putting in a rectangular pool in the back yard. The pool's perimeter equals 28 feet. The contractor want the leng

th to equal 5 more feet than 3 times the width. What will the width of your garden be?
Mathematics
1 answer:
meriva3 years ago
4 0

Answer:

2.25 ft

Step-by-step explanation:

Perimter= 28ft

W= x ft

L= 3x+5

but

P=2L+2W

substitute

28=2*(3x+5)+2x

28=6x+10+2x

collet like terms

28=8x+10

28-10= 8x

18=8x

divide both sides by 8

x= 18/8

x=2.25 ft

Hence the width is 2.25 ft

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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.

So this means that \frac{ab}{m} is and integer.

As m= vb, then \frac{m}{b} is an integer, lets say \frac{m}{b}=v; and as m=ua, then \frac{m}{a}=u.

So \frac{ab}{m}v=\frac{ab}{m}\frac{m}{b}=a, so \frac{ab}{m} divides a; on the other hand, \frac{ab}{m}u=\frac{ab}{m}\frac{m}{a}=b, so \frac{ab}{m} divides b. From this we can conclude that \frac{ab}{m} is a common divisor of a and b.

4 0
3 years ago
Help me please help ​
Dmitry_Shevchenko [17]
That would be A :D It would be A because you would do keep change flip. You would keep 5/6, change the division sign to multiplication, then flip the 5/16 to 16/5 (the reciprocal)
7 0
3 years ago
Why might working with n a commission basis make dealing with finances more difficult?
Lady_Fox [76]

Answer: The commission is paid according to sales amounts that are likely to vary from month to month.

Step-by-step explanation: Instead of a salary that is paid in the same amount on a schedule, the commission may be very large one month and very small or zero at other times.

Financial planning usually includes monthly payments that and predictable expenses for food, transportation, utilities, etc. The person who earns a commission must remember to set aside some of the "extra" to cover these expenses. And be prepared to work more or harder at some times to make sales when they don't come easily.

8 0
3 years ago
Find the center of mass of a thin plate of constant density covering the given region bounded by lines thru the following points
goldenfox [79]

Answer:

center of mass = ( 1 ,2 )

Step-by-step explanation:

attached below is the detailed solution of the problem

first we have to determine the value of m

M = ∫∫ dA

   = 6

Mx = 12

attached solution below

My = 6

hence center of mass of a thin plate

   x       ,    y

= My/m , Mx/m

= 6/6  ,   12/6

= ( 1, 2 )

4 0
3 years ago
The length of a rectangular garden is 5 meters long. The area of the garden is 10 square meters.
tatuchka [14]

length=5 meters

area=10meters squared

area=length times width

10=L*W

10=5L

Length=2meters

7 0
3 years ago
Read 2 more answers
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