Express your answer in scientific notation. 2.3 \cdot 10^8 + 4.7 \cdot 10^7 =2.3⋅10 8 +4.7⋅10 7 =2, point, 3, dot, 10, start superscript, 8, end superscript, plus, 4, point, 7, dot, 10, start superscript, 7, end superscript, equals

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?

Fredrick designed an experiment in which he spun a spinner 20 times and recorded the results of each spin

The rumpart family is building a new room onto their house. the width of the new room will be 16 feet. the length of the room will be 4% greater than the width. write an expression to find the length of the new room. what will be the area of this new room?