Kevin drove 95 miles to meet his friend amanda at an
amusement park amanda drove 125 miles to get to the
same amusement park. given that kevin's truck uses one
gallon of gasoline every 15 miles and amanda's hybrid car
uses one gallon of gasoline every 40 miles, approximately
how many more gallons of gasoline did kevin's truck use
than amanda's car to reach the amusement park?

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?

Tod does not have any cookies. david gives jeff 8 cookies. then he splits half of the cookies he has left with tod. david let’s c represent the number of cookies that he starts with. he finds the number of cookies that tod has is 1/2 the difference of c and 8. write an expression to represent the number of cookies that tod has.

Have you ever been in the middle of telling a story and had to use hand gestures or even a drawing to make your point? in algebra, if we want to illustrate or visualize a key feature of a function, sometimes we have to write the function in a different form—such as a table, graph, or equation—to determine the specific key feature we’re looking for. think about interactions with others and situations you’ve come across in your own life. how have you had to adjust or change the way you represented something based on either the concept you were trying to describe or the person you were interacting with? explain how the complexity or layout of the concept required you to change your style or presentation, or how the person’s unique learning style affected the way you presented the information.