Which of the following is a result of shifting a circle with equation (x + 3)2 + (y - 2)2 = 36 up 3 units? a. the x-coordinate of the center of the circle increases by 3. b. the y-coordinate of the center of the circle decreases by 3. c. both the x- and y-coordinates of the center of the circle increase by 3. d. the y-coordinate of the center of the circle increases by 3.

D. (y-2) becomes (y-5) and -5 < -2

Step-by-step explanation:

When transforming functions, the following applies:

•Adding/subtracting inside the parenthesis to the input shifts the function left(+) and right(-).

•Adding/subtracting outside the parenthesis to the output shifts the function up(+) and down(-).

•Multiplying the function by a number less than 1 compresses it towards the x-axis.

•Multiplying the function by a number greater than 1 stretches it away from the x-axis.

In this situation, the circle is shifted up 3 units and the variable y which controls this is in the function. To move it up you will subtract 3 in the parenthesis for (y-2) so it becomes (y-5). This will move the vertex 3 units higher.

b

step-by-step explanation:

given

- 2 (3x + 12y - 5 - 17x - 16y + 4 )

simplify the parenthesis by collecting like terms

= - 2 (- 14x - 4y - 1) ← distribute the parenthesis by - 2

= 28x + 8y + 2 → b

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.