The numerator and denominator of a fraction are in the ratio of 3 to 5. if the numerator and denominator are both increased by 2, the fraction is now equal to 2/3 . if n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

The two equation which can be used to solve the problem are:

5n - 3d = 0 and 3n - 2d = -2

The numerator of the fraction is "n" and the denominator of the fractions is "d"

The numerator and denominator of a fraction are in the ratio of 3 to 5

numerator : denominator = 3 : 5

On cross-multiplication we get,

5n = 3d

This is our first equation

The numerator and denominator are both increased by 2, the fraction is now equal to 2/3

The new numerator will be n + 2 and denominator will be d + 2

On cross multiplication we get,

3(n + 2) = 2(d + 2)

3n + 6 = 2d + 4

This is our second equation

Thus the two equation which can be used to solve the problem are:

5n - 3d = 0 and 3n - 2d = -2

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4