A bedroom is 15 ft long and 12 ft wide. How much carpet is needed to cover the floor

180 ft squared

Step-by-step explanation:

You need to find the area of the room. The equation for area is length × width. 12×15=180

No, Lydia's assertion is not correct

Step-by-step explanation:

Plot three Lydia's points D(-2, -1) , E (-2, 2), and F (0, 0) on the coordinate plane (see attached diagram).

Triangle DEF will be right triangle if one of its angle is right angle. If one angle is right angle, then adjacent sides are prependicular. If two sides are perpendicular, then the dot product is equal to 0.

1. Dot product between vectors DE and DF:

So, DE and DF are not perpendicular, and angle D is not right angle.

2.  Dot product between vectors ED and EF:

So, ED and EF are not perpendicular, and angle E is not right angle.

3. Dot product between vectors FD and FE:

So, FD and FE are not perpendicular, and angle F is not right angle.