If angle A is congruent to itself by the Reflexive Property, which transformation could be used to prove ΔABC ~ ΔADE by AA similarity postulate? triangles ABC and ADE, in which point B is between points A and D and point C is between points A and E

Translate triangle ABC so that point B lies on point E to confirm ∠B ≅ ∠E.
Translate triangle ABC so that point C lies on point E to confirm ∠C ≅ ∠E.
Dilate ΔABC from point A by the ratio segment AD over segment AB to confirm segment AD ~ segment AB.
Dilate ΔABC from point A by the ratio segment AE over segment AC to confirm segment AE ~ segment AC.

Each equation given below describes a parabola. which statement best compares their graphs? x = 2y^2 x = 8y^2

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.)

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?