The coordinates of the vertices of △abc are a(1,1), b(5,1), and c(5,3). the coordinates of the vertices of △a′b′c′ are a′(−1,−1), b′(−5,−1), and c′(−5,−3)

.

which statement correctly describes the relationship between △abc
and △a′b′c′ ?

a.) △abc is congruent to △a′b′c′ because you can map △abc to △a′b′c′
using a translation 2 units to the left and 2 units down, which is a rigid motion.
b.) △abc is not congruent to △a′b′c′ because there is no sequence of rigid motions that maps △abc to △a′b′c′
.
c.) △abc is congruent to △a′b′c′ because you can map △abc to △a′b′c′
using a rotation of 180° about the origin, which is a rigid motion.
d.) △abc is congruent to △a′b′c′ because you can map △abc to △a′b′c′ using a reflection across the y-axis, which is a rigid motion.

Writing the simplest form of a fraction means the numerator and the denominator have no common factors other than 1.a. trueb. false

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)

Which of the following vectors are orthogonal to (2,1)? check all that apply