What is the partial fraction decomposition of
7x squared- 6x +9/
3x(4x squared +9)

9514 1404 393

  1/(3x) =(x -2)/(4x^2 +9)

Step-by-step explanation:

The denominator cannot be factored further, so the final form will be ...

  A/(3x) + (Bx +C)/(4x^2 +9)

The value of this is ...

  (A(4x^2 +9) +(3x)(Bx +C))/(3x(4x^2 +9))

  = ((3B+4A)x^2 +3Cx +9A)/(3x(4x^2 +9))

Equating coefficients gives ...

  3B+4A = 7

  3C = -6   ⇒   C = -2

  9A = 9   ⇒   A = 1

Using the found value of A, we find ...

  3B +4 = 7   ⇒   B = 1

Then the decomposition is ...

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

answer: it is d

step-by-step explanation: