Situation 1:

f
(
x
)
=
14
x
−
12
f(x)=14x−12
g
(
x
)
=
7
x
2
−
3
x
−
11
g(x)=7x2−3x−11

mark is asked to find
(
g
−
f
)
(
x
)
.
(g−f)(x).
this is his work:

14
x
−
12
−
7
x
2
−
3
x
−
11
−
7
x
2
+
11
x
+
23
14x−12−7x2−3x−11−7x2+11x+ 23

find mark's mistakes (there are more than one). explain what he did wrong and how to fix it.

Manuela claims that and are congruent. which statement best describes her claim? she is incorrect because the segments do not have the same orientation. she is incorrect because the segments do not have the same length. she is correct because the segments have the same length. she is correct because the segments have the same orientation.

Solve the system of equations using the substitution method. {y=−3x+7x=−2y−16 enter your answers in the boxes.

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.)