Matt has to buy a calculator for S100, special graph paper for $9, a textbook for $57, and a notebook for $2. if Matt has $305, how much will he have left after this purchase?

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Which expression is equivalent to the expression below? (6c^2 + 3c) / (-4c + 2) / (2c + 1) / (4c - 1)a. 3c(2c-1) / (2c + 1)b. -3c(2c-1)^2 / (2c + 1)^2c. 3cd. -3c(just took the test its d. -3c)

Is each relation a function? if so, state whether it is one-to-one or many-to-one. 3. (-4,7), (-3,5), (1,4), (3,-8), (5,-11) 4. (-4,8), (-2,4), (0,1), (2,4), (4,8) 5. (-2, 1), (-2,3), (0,-3), (1,4), (3,1)