Read the word problem below. Chan rows at a rate of eight miles per hour in still water. On Wednesday, it takes him three hours to row upstream from his house to the park. He rows back home, and it takes him two hours. What is the speed of the current?

1 3/5 miles/hr

Step-by-step explanation:

Let C be the speed of the current

Let D be the distance between Chan's house and the park

We know that Distance, D, is = Speed x Time

Chan's speed going upstream is (8 - C)mph.

That gives us:

D = (8-C)(3 hr)

Chan's speed going downstream is (8+C)mph

So we have:

D = (8+C)(2 hr)

We know that the d is the same for these two equations, so:

(8-C)(3 hr)  = (8+C)(2 hr)

24 - 3C = 16 + 2C

5C = 8

C = (8/5) or 1 3/5 mph

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: