What is the angle of rotation from figure D to figure D’ ? Assume that the center of rotation is the origin. A. 270° clockwise
B. 90° clockwise
C. 90° counterclockwise
D. 180° counterclockwise

Option B.

Step-by-step explanation:

We take a point D from the figure attached,

Coordinates for the point D → (-1.5, 3.5)

And coordinates of D' → (3.5, 1.5)

Coordinates of D when rotated about the origin,

Option A. Rotated by 270° clockwise.

Rule to be followed,

D(x, y) → D'(-y, x)

D(-1.5, 3.5) → D'(-3.5, -1.5)

Therefore, Option A. is incorrect

Option B. rotation by 90° clockwise

Rule to be followed

D(x, y) → D'(y, -x)

D(-1.5, 3.5) → D'(3.5, 1.5)

Therefore, Option B. is correct.

Option C. 90° counterclockwise

Rule to be followed,

D(x, y) → D'(-y, x)

D(-1.5, 3.5) → D'(-3.5, -1.5)

This option C is incorrect.

Option D. 180° counterclockwise

Rule to be followed,

D(x, y) → D'(-x, -y)

D(-1.5, 3.5) → D'(1.5, -3.5)

Therefore, option D is incorrect.

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.