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MrRa [10]
3 years ago
15

from point a leah walked 40 yards south, 60 yards west, 10 yards north, and 20 yards east to point b. what is the length, in yar

ds, of ab?
Mathematics
1 answer:
nataly862011 [7]3 years ago
5 0

Let's say A = (0, 0). Let's find point B so that we can find \overline{AB}.


  1. Leah walks 40 yards south. B = (0, 0 - 40) = (0, -40)
  2. Leah walks 60 yards west. B = (0 - 60, -40) = (-60, -40)
  3. Leah walks 10 yards north. B = (-60, -40 + 10) = (-60, -30)
  4. Leah walks 20 yards east. B = (-60 + 20, -30) = (-40, -30)

We have found that B = (-40, -30).


Now think about this scenario visually. We started at the center of something, which we call point A, and then started moving around until we got to point B. We can then form line \overline{AB} between the points. However, realize that we can actually make a triangle. Just think of one of the legs as part of the x-axis and the other leg as part of the y-axis.


We can find the length of these parts, which is simply the absolute value of the coordinates of point B. It may be a little hard to think about, but essentially, we can form a triangle with sides that consist of part of the x-axis, part of the y-axis, and \overline{AB}. We also know that the lengths of the legs are 40 and 30.


Since we are given the two lengths of the legs on the triangle and trying to find the length of the hypotenuse, we can use the Pythagorean Theorem. This states:

a^2 + b^2 = c^2

  • a and b are the lengths two legs of the triangle
  • c is the length of the hypotenuse

Thus, substituting in our values, we find:

40^2 + 30^2 = (\overline{AB})^2

\overline{AB} = \sqrt{40^2 + 30^2} = \sqrt{2500} = 50


The length of \overline{AB} is 50.

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Answer:

m∡A = 14

m∡B = 76

Step-by-step explanation:

Two Angles are Complementary when they add up to 90 degrees.

So 3x -7 + 11x - 1 = 90, which we can solve.

14x - 8 = 90

14x = 98

x = 98/14 = 7

with the knowledge of x=7, we can find the angles:

m∡A = 3·7 - 7 = 14

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Answer:

y = -948

Step-by-step explanation:

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3 years ago
Find the area of the shaded region.
lbvjy [14]

Answer:

48\pi\\\approx 150.796

Step-by-step explanation:

1.Approach

To solve this problem, find the area of the larger circle, and the area of the smaller circle. Then subtract the area of the smaller circle from the larger circle to find the area of the shaded region.

2.Find the area of the larger circle

The formula to find the area of a circle is the following,

A=(\pi)(r^2)

Where (r) is the radius, the distance from the center of the circle to the circumference, the outer edge of the circle. (\pi) represents the numerical constant (3.1415...). One is given that the radius of (8), substitute this into the formula and solve for the area,

A_l=(\pi)(r^2)\\A_l=(\pi)(8^2)\\A_l=(\pi)(64)

3.Find the area of the smaller circle

To find the area of the smaller circle, one must use a very similar technique. One is given the diameter, the distance from one end to the opposite end of a circle. Divide this by two to find the radius of the circle.

8 ÷2 = 4

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Substitute into the formula,

A_s=(\pi)(r^2)\\A_s=(\pi)(4^2)\\A_s=(\pi)(16)

4.Find the area of the shaded region

Subtract the area of the smaller circle from the area of the larger circle.

A_l-A_s\\=64\pi - 16\pi\\=48\pi

\approx150.796

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