The answer is (3600 - 900π) ft²
Step 1. Find the radius r of circles.
Step 2. Find the area of the portion of the field that will be watered by the sprinklers (A1)
Step 3. Find the total area of the field (A2)
Step 4. Find the area of the portion of the field that will not be watered by the sprinklers (A)
Step 1. Find the radius r of circles
r = ?
According to the image, radius of a square is one fourth of the field side length:
r = s/4
s = 60 ft
r = 60/4 = 15 ft
Step 2. Find the area of the portion of the field that will be watered by the sprinklers.
The area of the field that will be watered by the sprinklers (A1) is actually total area of 4 circles with radius 15 ft.
Since the area of a circle is π r², then A1 is:
A1 = 4 * π r² = 4 * π * 15² = 900π ft²
Step 3. Find the total area of the field (A2)
The field is actually a square with side s = 60 ft.
A2 = s² = 60² = 3600 ft²
Step 4. Find the area of the portion of the field that will not be watered by the sprinklers (A).
To get the area of the portion of the field that will not be watered by the sprinklers (A) we need to subtract the area of 4 circles from the total area:
A = A2 - A1
A = (3600 - 900π) ft²
Answer:
The triangles ABE and MNP are similar because the three corresponding angles are equal (AAA Criteria)
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides and two equal angles. The two equal angles are called the base angles and the third angle is called the vertex angle
The triangle ABE is an isosceles triangle with the vertex angle m∠ABE equal to 
so
m∠BAE=m∠AEB-------> base angles
m∠BAE+m∠AEB+m∠ABE= 
------> sum of internal angles of triangle
Find m∠BAE
2m∠BAE=
m∠BAE=
The measure of the angles of triangle ABE are 
The triangle MNP is an isosceles triangle with the base angle m∠NMP and m∠NPM equal to 
so
m∠MNP+m∠NMP+m∠NPM= ------> sum of internal angles of triangle
Find m∠MNP (vertex angle)
m∠MNP=
m∠MNP=
The measure of the angles of triangle MNP are
therefore
The triangles ABE and MNP are similar because the three corresponding angles are equal (AAA Criteria)
Answer:
y = -4x + 2
Step-by-step explanation:
To figure out the slope, plug the coordinates in the formula.
y2 - y1 / x2 - x1
= 6 - (-6) / -1 -2
= -4
Now you need to find the y-intercept, take the coordinates and plug them into your equation so far, which is y = -4x + b
y = -4x + b
-6 = -4(2) +b
-6 = -8 + b
2 = b
Answer:
Step-by-step explanation:
To find measures of angles m and n
The triangle to the left has three sides of equal length.
This means that it will also have three angles of equal measure.
The internal angles of a triangle sum to 180°
So the internal angles of the left triangle are 180/3 = 60°
The top right angle is made up of one of the 60° angles and angle n
60 + n = 90
n = 30°
Again the internal angles of a triangle sum to 180°, so the right triangle
m + n + 90 = 180
m = 180 - 90 - 30
m = 60°
or we could realize that the top and bottom horizontal lines are parallel because the vertical line on the right makes right angles to both of them.
Knowing that they are parallel, we also know that angle m and the top right 60° angle of the left triangle are opposite internal angles of a line intersecting parallel lines and must be identical angles, therefore
m = 60°
