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liubo4ka [24]
3 years ago
8

Lucy is a dress maker. She sews 4/7 of a dress in 3/4 hour. Lucy sews at a constant rate. At this rate, how many dresses does Lu

cy sew in one hour?
Include fractions of dresses if applicable.
Mathematics
1 answer:
MAVERICK [17]3 years ago
7 0

Answer:

16/21 dresses

Step-by-step explanation:

3/4 · k hours: 4/7 · k dresses for any constant k

If we want 1 hour, then k will need to be 4/3

4/3 × 4/3 hours: 4/7 × 4/3

1 hour = 16/21 dresses

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(x+2)^2 + (y-3)^2 = 10

Step-by-step explanation:

The standard equation for circle is

(x-a)^2 + (y-b)^2 = r^2

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______________________________________________________

Given

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let r be the radius of circle

Plugging in this value of center in standard equation for circle given above we have

(x-a)^2 + (y-b)^2 = r^2    \ substitute (a,b) \ with (-2,3) \\=>(x-(-2))^2 + (y-3)^2 = r^2  \\=>(x+2)^2 + (y-3)^2 = r^2    (1)

Given that point (1,2 ) passes through circle. Hence this point will satisfy the above equation of circle.

Plugging in the point (1,2 )  in equation 1 we have

\\=>(x+2)^2 + (y-3)^2 = r^2    \\=> (1+2)^2 + (2-3)^2 = r^2\\=> 3^2 + (-1)^2 = r^2\\=> 9 + 1 = r^2\\=> 10 = r^2\\=>  r^2  = 10\\

now we have value of r^2 = 10, substituting this in equation 1 we have

Thus complete equation of circle is =>(x+2)^2 + (y-3)^2 = r^2\\=>(x+2)^2 + (y-3)^2 = 10

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