Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side: Given: ΔABC Prove: The midsegment between sides Line segment AB and Line segment BC is parallel to side Line segment AC. Draw ΔABC on the coordinate plane with point A at the origin (0, 0). Let point B have the ordered pair (x1, y1) and locate point C on the x-axis at (x2, 0). Point D is the midpoint of Line segment AB with coordinates at Ordered pair the quantity 0 plus x sub 1, divided by 2. The quantity 0 plus y sub 1, divided by 2 by the Midpoint Formula. Point E is the midpoint of Line segment BC with coordinates of Ordered pair the quantity x sub 1 plus x sub 2, divided by 2. The quantity 0 plus y sub 1, divided by 2 by the Midpoint Formula. The slope of Line segment DE is found to be 0 through the application of the slope formula: The difference of y sub 2 and y sub 1, divided by the difference of x sub 2 and x sub 1 is equal to the difference of the quantity 0 plus y sub 1, divided by 2, and the quantity 0 plus y sub 1, divided by 2, divided by the difference of the quantity x sub 1 plus x sub 2, divided by 2 and the quantity 0 plus x sub 1, divided by 2 is equal to 0 divided by the quantity x sub 2 divided by 2 is equal to 0 When the slope formula is applied to Line segment AC the difference between y sub 2 and y sub 1, divided by the difference of x sub 2 and x sub 1 is equal to the difference of 0 and 0, divided by the difference of x sub 2 and 0 is equal to 0 divided by x sub 2 is equal to 0, its slope is also 0. Since the slope of Line segment DE and Line segment AC are identical, Line segment DE and Line segment AC are parallel by the Parallel Postulate. Which statement corrects the flaw in Gina's proof? The coordinates of D and E were found using the slope formula. Segments DE and AC are parallel by definition of parallel lines. The coordinates of D and E were found using the Distance between Two Points Postulate The slope of segments DE and AC is not 0.

Question
solved
general 9 months ago 3460

Sal exercised by stretching and jogging 5 days last week. He stretches for a total of 25 minutes during the week. He jogged for an equal number of minutes each of the 5 days. He exercised for a total of 240 minutes. Elena also exercised by stretching and jogging 5 days last week. She stretched for 15 minutes each day. She jogged for an equal number of minutes each of the 5 days. She exercised for a total of 300 minutes Determine the number of minutes Sal jogged each day last week and the number of minutes Elena jogged each day last week.

Question
solved
general 9 months ago 7294

50 points!!!A system of equations is shown below:6x − 2y = 3 (equation 1)5x + 3y = 4 (equation 2)A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof? Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 10x − 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x − y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

Question
solved
general 9 months ago 4751