Select the correct answer. Given: ∆ABC Prove: A midsegment of ∆ABC is parallel to a side of ∆ABC. Statement Reason 1. Define the vertices of ∆ABC to have unique points A(x1, y1), B(x2, y2), and C(x3, y3). given 2. Let D be the midpoint of and E be the midpoint of . defining midpoints 3. definition of midpoints 4. slope of slope of definition of slope 5. slope of = slope of Transitive Property of Equality 6. definition of parallel lines 7. Let F be the midpoint of . defining a midpoint 8. definition of midpoint 9. slope of slope of definition of slope 10. 11. definition of parallel lines 12. Similarly, is parallel to . steps similar to steps 1−11 What is the missing step in this proof? A. Statement: slope of = slope of Reason: definition of slope B. Statement: slope of = slope of Reason: Transitive Property of Equality C. Statement: DF = BC Reason: Corresponding sides of congruent triangles are congruent. D. Statement: ∆ADF ≅ ∆ABC Reason: ASA

Darian wants to build a regulation size pool table that is 9 feet in length. he plans he ordered are 18 by 36 inches. what is the scale factor of the dilation he must use to build a regulation pool table

Janie has $3. she earns $1.20 for each chore she does and can do fractions of chores. she wants to earn enough money to buy a cd for $13.50. write an inequality to determine the number of chores, c, janie could do to have enough money to buy the cd.

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.