What is the measure of angle M?

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

nataly862011 [7]

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

Leah walks 40 yards south. $B = (0, 0 - 40) = (0, -40)$
Leah walks 60 yards west. $B = (0 - 60, -40) = (-60, -40)$
Leah walks 10 yards north. $B = (-60, -40 + 10) = (-60, -30)$
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.

5 0

3 years ago

The ages of five friends are 20,31,28,31 and 25. How many of the friends are older than the average (arithmetic mean) age?

FromTheMoon [43]

Answer:

3 friends

Step-by-step explanation:

The mean age is 27 so 3 friends are above that age.

7 0

2 years ago

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulati

horrorfan [7]

The answer is x≥0 y≥0 x+y≤6 2x+3y≤15

5 0

2 years ago

Which expression shows how to multiply 5x381 by using place value and exxpanded form?

Dovator [93]

<span><span>1. </span>We have the given number = 5 x 381
Let’s show how to multiply this given equation using its expanded form and place value
=> 5 x 381
since we’re multiplying, we will start with the ones value which is 1
=> 5 x 1 = 5
Second is on the tens value
=> 5 x 80 = 400
Third is the hundreds value
=> 5 x 300 = 1 500
Now, we already have the answer to each values. Add
=> 1 500 + 400 + 5
=> 1 905</span>

5 0

2 years ago

Does anyone know what to fill in?

riadik2000 [5.3K]

Answer:

$36.69

Step-by-step explanation:

Okay, so let's first write the equation:

2.59*10 + 3d = 135.97

Now, let's work on isolating d by first simplifying the equation:

25.9 + 3d = 135.97

25.9 + 3d - 25.9 = 135.97 - 25.9

3d = 110.07

3d/3 = 110.07/3

d = 36.69

Okay, now let's check:

2.59*10 + 3*36.69 = 135.97

25.9 + 110.07 = 135.97

135.97 = 135.97

Okay, so so it costs $36.69 per pair of shoe.

4 0

2 years ago