15. Determine and state the coordinates of the center and the length of the radius of a
circle whose equation is x2 + y2 – 6x = 56 - 8y.
PLEASEEE HELP!!!

(3, - 4 ), r = 9

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 6x = 56 - 8y ( add 8y to both sides )

x² + y² - 6x + 8y = 56 ( collect x and y terms together )

x² - 6x + y² + 8y = 56

Use the method of completing the square

add ( half the coefficient of the x/y term )² to both sides

x² + 2(- 3)x + 9 + y² + 2(4)y + 16 = 56 + 9 + 16

(x - 3)² + (y + 4)² = 81 ← in standard form

with centre = (3, - 4 ) and r = = 9

First question

The correct option is  A  

Second question

  The  correct option is  E

Step-by-step explanation:

From the question we are told that

    The  population  mean is  

     The  sample size is  n = 30  

      The population standard deviation is    

      The sample mean is  

        The  level of significance is  

The  null hypothesis is  

The  alternative  hypothesis is  

Generally the test statistics is mathematically represented as

=>    

=>    

Generally the degree of freedom is mathematically represented as

Generally from the student t distribution table the probability corresponding to  -2.38 to  the left  at a degree of freedom of is  

From the value obtained we see that

             hence  

The decision rule  

Reject  the null hypothesis  

The conclusion is  

There evidence to reject the manufacturer's claim because the p-value of  0.0174 is less than the significance level E