Explain how to use the midpoint formula to prove or disprove that abcd is a parallelogram. a) prove that ac and bd do not have the same midpoint. the diagonals of a parallelogram cannot have the same midpoint. b) prove that ad and bc have the same midpoint. all sides of a parallelogram are congruent; therefore, they have the same midpoint. c) prove that ac and bd have the same midpoint. the diagonals of a parallelogram bisect each other; therefore, they have the same midpoint. d) prove that ab and cd do not have the same midpoint. all sides of a parallelogram are congruent; therefore, they have different midpoints.

The birth weights of newborn babies in the unites states follow in a normal distrubution with a mean of 3.4 kg and standard deviation of 0.6 kg. reaserches interested in studying how. children gain weights decide to take random samples of 100 newborn babies and calculate the sample mean birth weights for each sample

Joyce deposited $5000 in an account with an annual interest rate of 6%, compounded annually. how much money will be in the account 10 years later

Xtax=1. determine their canon- 1. write the following quadratic forms as v(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical coordinates (y1, 2, y3) in terms of the original coordinates (x1, x2, x3). state what surfaces these quadratic forms correspond to: = > (a) -a x + 4x12 4x1x38x231; (b) 3-33 + 4xrj224x3122a3= 1; (c) 4a7 2x1 2x1x36x2a3 = 1. 2. solve the following systems of differential equations using the matrix exponential technique 3x 4 (a) x(0) = 5, y(0) = 1; 4x-3y 3.x y(0) = 9, y(0) = 3; -2x 6x2y