Which of the following when added to 4a^2+9 will result in a perfect square for all integer values of a?

(A) 0
(B) 3a
(C) 6a
(D) 9a
(E) 12a

(D) 9a

Step-by-step explanation:

Given

4a^2 + 9

Add 9a to the expression

4a^2 + 9 + 9a

This can be written as

(2a)^2 + (3)^2 + (3)^2 a

she will travel a distance in the range of 3 - 11 miles

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.