Hiep is writing a coordinate proof to show that the midsegment of a trapezoid is parallel to its bases. he starts by assigning coordinates as given, where rs is the midsegment of trapezoid klmn .

trapezoid k l m n on the coordinate plane. the vertices of the trapezoid are k begin ordered pair 0 comma 0 end ordered pair, l begin ordered pair 2a comma 0 end ordered pair, m begin ordered pair 2d comma 2c end ordered pair, and n begin ordered pair 2b comma 2c end ordered pair. segment r s is drawn with point r on segment k n and point s on segment l m.

drag and drop the correct answers to complete the proof.

since rs is the midsegment of trapezoid klmn , the coordinates of r are (b,) and the coordinates of s are (, c).

the slope of kl is .

the slope of rs is 0.

the slope of nm is 0.

the slope of each segment is 0; therefore, the midsegment is parallel to the bases.

Aline has a slope of 1/4 and passes through point (0.4,-1/2). what is the value of the y-intercept?

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.

Select the correct answer from each drop-down menu. the length of a rectangle is 5 inches more than its width. the area of the rectangle is 50 square inches. the quadratic equation that represents this situation is the length of the rectangle is inches.