The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is .

The center of the circle is at the point
, and its radius is
units.

The general form of the equation of a circle that has the same radius as the above circle is
.

Step-by-step explanation:

x² + y² + 42x + 38y - 47 = 0

Put the equation into standard (center-radius) form:

regroup terms

(x²+42x) + (y²+38y) = 47

complete the squares:

(x²+42x+21²) + (y²+38y+19²) = 47 + 21² + 19²

(x+21)² + (y+19)² = 849

center at (-21,-19)

radius = √849 units

The general form of the equation for a circle with radius √849 units is:

(x-h)² + (y-k)² = 849

where the (h,k) is the center.

it would to have a graph or something ! but i had this question so its false

step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places