Tanya and Greg are going skiing. Tanya is a seasoned skier while Greg is a novice, he only skied once before. They have a map that provides the coordinates for the top and bottom of each path. Tanya wants to ski the most challenging path while Greg wants to start off with an easier one. Each coordinate represents 10 feet. Coordinates for each path are as follows: Path A (20, 1),(100,0); Path B (21, 3),(200,1); Path C; ( 21, 6),(300, 2) and Path D (20,8), (400, 0). What path would Tanya want to ski down? Determine what information you need to solve this problem.
a.The length of each path.
b.The path with the highest starting point.
c.The path with the lowest starting point. <--- or D
d.The slope of each path.
Stewart is going to make a flower bed in the shape of an Isosceles Triangle because he already has two pieces of white wood fencing each measuring 10 ft. in length. He plans to put the two pieces of fencing together so that they form a right angle. Then he will purchase a new piece of white fencing to close off the flower bed. What will the other two angles of the flower bed measure? Which step would not be included in a summary of how to solve the problem?
a.Sum the known side lengths of the flower bed.
b. Find the total measure of all the angles in the flower bed.
c. Subtract the known angle measure from the total.
D. Divide the difference between the total and the known angle measure in half. <-- or B?
For the first question about Tanya and Greg going skiing, in order to determine what path Tanya would want to ski down, we need to consider the difficulty of each path. However, the question does not provide any information about the difficulty of the paths. Instead, the given coordinates represent the top and bottom points of each path. Therefore, the correct answer is to determine the slope of each path (option d) because the slope indicates the steepness or difficulty level of a path.
To calculate the slope of a path, we can use the formula: slope = (change in y-coordinates) / (change in x-coordinates). So, we need to find the change in y-coordinates and change in x-coordinates for all the paths and compare the slopes to identify the most challenging path.
For the second question about Stewart and the flower bed, the problem states that Stewart plans to put two pieces of fencing together in a right angle to create an isosceles triangle-shaped flower bed. The two known side lengths of the triangle are both 10 ft. So, to find the other two angles, we don't need to sum the known side lengths (option a) or find the total measure of all the angles in the flower bed (option b).
The correct steps to solve the problem would be:
1. Identify the known angle measure, which is 90 degrees because the two fencing pieces are joined at a right angle.
2. Subtract the known angle measure (90 degrees) from the total angle measure of a triangle (180 degrees).
3. Divide the difference between the total angle measure (180 degrees) and the known angle measure (90 degrees) in half. This will give us each of the remaining angles of the triangle.
Therefore, the step not included in the summary of how to solve the problem is to divide the difference between the total and the known angle measure in half (option D).