Identify the equation of the circle that has its center at (-16,30) and passes through the origin

(x+16)²+(y-30)²=1156

Step-by-step explanation:

We have given:

center at (-16,30). It means h = -16 and k=30

and it passes through the origin (0,0)

Thus the  radius will be distance between (-16,30) and (0,0)

r=√(-16 - 0)²+(30-0)²

r=√256+900

r²=(√1156)²

r²=1156

Now apply standard equation of circle:

(x-h)²+(y-k)² = r²

(x+16)²+(y-30)²=1156

Thus the equation is (x+16)²+(y-30)²=1156

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

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step-by-step explanation: