What is the remainder when f(x) = x3 + 3x2 + 6x + 9 is divided by x + 2? A. −7 B. 1 C. 17 D. 41

B.1

Step-by-step explanation:

when f(x) is divided by (x+2).

The remainder,

f(-2) = -8 + 12 - 12 + 9

f(-2) = 1

The remainder is 1.

Arc AD = 43°

Step-by-step explanation:

Image is attached.

When an angle subtends from an Arc to the center, the measure of the Arc and the Angle are same. Now, looking at the figure,

Arc AB = 180 (since this is an Arc subtending the diameter)

Arc DC = 90 degrees since the central angle is 90

So,

Arc AD + Arc CB = 180 - 90 = 90

Arc AD and Arc CB have the same measures as the central angle it created (terms in x). So we can write:

Arc AD + Arc CB = 90

7x + 1 + 9x - 7 = 90

We can solve for x:

The central angle AD is:

AD = 7x + 1 = 7(6) + 1 = 43

Also, Arc AD is same, thus:

Arc AD = 43°