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shutvik [7]
3 years ago
12

Thank you very much for your help!

Mathematics
1 answer:
Kobotan [32]3 years ago
5 0
For a.
x^2+y^2=25

For b.
(x-4)^2+(y-3)^2=25

For c.
(x-5)^2+(y-4)^2=9


Hope that helps
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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
Kenny weight is 6/7 times Melvin weight. What is the ratio of Kenny weight to Melvin weight? Give answer in fraction form
SOVA2 [1]

-- Kenny's weight is 6/7 of Melvin's weight.

-- Melvin's weight is 7/7 of Melvin's weight.

-- The ratio of Kenny's weight to Melvin's weight is  (6/7) / (7/7)  =  6/7 .
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9r+7+3(8p+7r)+15 simplify the expression
Lynna [10]
30 r + 22 + 24 p .....
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Find the area and the circumference of a circle with diameter 9 yards using the value 3.14 for pi
Ray Of Light [21]
Area of circle = pi r^, (r)radius is half the diameter so 9÷2=4.5 so in this scenario it would be 3.14×4.5^
3.14×4.5×4.5=63.6

circumference of circle= diameter×pi (3.14)
so 9×3.14=28.3
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3 years ago
HELP <br> what is the equation of the lines in slope - intercept form
34kurt

Answer:

y=7x

Step-by-step explanation:

slope intercept form is y=mx+b.

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