Geometry Help please

Select the correct answer from each drop-down menu.

In the figure, all, and both lines are intersected by transversal Complete the statements to prove that m<1=m<5

allb (given)

m21 + m23 = 180° (Linear Pair Theorem)
m25+ m26 = 180° (Linear Pair Theorem)
m21 + m23 = 25+ 26(blank)
m 23 = m26 (blank)
m21 = m 25 (Subtraction Property of Equality

Options (for both blanks)

A) Transitive property of equality quality
B) Alternative interior angles theorem
C) Alternate exterior ankles theorem
D)Vertical angles theorem

If a particle moves along a path such that r : (3 sin t) m and ? : 2t rad, where t is in seconds. what is the particle's acceleration in m/s in 4 seconds? a)- 16.43 b)- 16.29 c)- 15.21 d)- 13.79

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

Aplate clutch has a single pair of mating friction surfaces 250-mm od by 175-mm id. the mean value of the coefficient of friction is 0.30, and the actuating force is 4 kn. a) find the maximum pressure and the torque capacity using the uniform-wear model. b) find the maximum pressure and the torque capacity using the uniform-pressure model.