Amanda's first four test scores are 77, 95, 84, and 69. What does Amanda need to score on the next test to have at least an 82 a
2 answers:
You might be interested in
Answer:
The quadrilateral is not a rectangle
Step-by-step explanation:
we know that
If a quadrilateral ABCD is a rectangle
then
Opposite sides are congruent and parallel and adjacent sides are perpendicular
Remember that
If two lines are parallel, then their slopes are the same
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
The formula to calculate the slope between two points is equal to
we have
A(-5,5), B(1,8), C(4,2), and D(-2,-2)
Plot the figure to better understand the problem
see the attached figure
Find the slope of the four sides and then compare
step 1
Find slope AB
A(-5,5), B(1,8)
substitute in the formula
step 2
Find slope BC
B(1,8), C(4,2)
substitute in the formula
step 3
Find slope CD
C(4,2), and D(-2,-2)
substitute in the formula
step 4
Find slope AD
A(-5,5), D(-2,-2)
substitute in the formula
step 5
Verify if the opposites are parallel
Remember that
If two lines are parallel, then their slopes are the same
The opposite sides are
AB and CD
BC and AD
we have
so
It is not necessary to continue verifying, because two of the opposite sides are not parallel
therefore
The quadrilateral is not a rectangle
Answer:
The route across the park is 40 meter shorter than the route around its edges.
Step-by-step explanation:
We have to calculate the distance for both routes
As the route around the edges is straight, we have to find the sum of length of both edges
Let be the distance of route around edges
Now we know that a diagonal divides a rectangle in two right angled triangles in which the diagonal is the hypotenuse.
We can use Pythagoras theorem to find the length of the diagonal
So,
In the given scenario
P = 60
B = 80
Now
In order to calculate that how much shorter is the path across the park, we have to subtract the distance across park from the distance across edges.
Hence,
The route across the park is 40 meter shorter than the route around its edges.