25 point for this question:

for which values of a and b the following is true for any real number x?

The values of a and b are and respectively.

Step-by-step explanation:

Given that

We solve this by partial fraction method.

Taking L.C.M. in the RHS, we get

To find the value of 'b', substitute x = 2. This would make 'a' vanish leaving an equation with 'b'.

Therefore, 2 - 4 = a(2 - 2) + b(2 + 9)

⇒ -2 = 0 + b(11)

Similarly, substitute x = -9 to find the value of 'a'.

⇒ -9 - 4 = a(7) + b(0)

.

Therefore, the values of 'a' and 'b'b are: =-13/7 and -2/11 respectively.

50.6

step-by-step explanation:

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

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