A) if c is the line segment connecting the point (x1, y1) to the point (x2, y2), find the following. x dy − y dx c correct: your answer is correct. (b) if the vertices of a polygon, in counterclockwise order, are (x1, y1), (x2, y2), , (xn, yn), find the area of the polygon. a = 1 2 (x1y2 − x2y1) − (x2y3 − x3y2) − − (xn − 1yn − xn n − 1) + (xny 1 − x1yn) a = 1 2 (x1y2 + x2y1) + (x2y3 + x3y2) + + (xn − 1yn + xn n − 1) + (xny 1 + x 1 yn) a = 1 2 (x2y1 − x1y2) + (x3y2 − x2y3) + + (xnyn−1 − xn−1yn) + (x1yn − xny1) a = (x1y2 − x2y1) + (x2y3 − x3y2) + + (xn − 1yn − xnyn − 1) + (xny1 − x1yn) a = 1 2 (x1y2 − x2y1) + (x2y3 − x3y2) + + (xn − 1yn − xnyn − 1) + (xny1 − x1yn) correct: your answer is correct. (c) find the area of the pentagon with vertices (0, 0), (4, 1), (1, 3), (0, 1), and (−2, 1).

the speed is   miles per hour > is false

step-by-step explanation:

we know that  

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

for the point

substitute the values of x and y

the linear equation is equal to

statements

case a) it takes hours to go miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct

case b) the speed is   miles per hour

the statement is false

because the speed is

case c) the unit rate for the trip is

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took minutes to go the first miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct