Answer:
A rule of polygons is that the sum of the exterior angles always equals 360 degrees. Since it is a regular octagon, so each of the interior angles of octagon are equal. ((n-2)*180)/n where n is the number of sides of the polygon.for example in case n=8 for an octagon, so we get:
((8-2)*180)/8 => (6*180)/8 => 1080/8 = 135 degrees. This means that each interior angle of the regular octagon is equal to 135 degrees.
Each exterior angle is the supplementary angle to the interior angle at the vertex of the polygon, so in this case each exterior angle is equal to 45 degrees. (180 - 135 = 45). Remember that supplementary angles add up to 180 degrees.
And since there are 8 exterior angles, we multiply 45 degrees * 8 and we get 360 degrees.
This technique works for every polygon, as long as you are asked to take one exterior angle per vertex.
Answer:
B. y-300=4(x-100)
Step-by-step explanation:
Answer:How often does Old Faithful blow?
The world's most famous geyser, Old Faithful in Yellowstone, currently erupts around 20 times a day. These eruptions are predicted with a 90 percent confidence rate, within a 10 minute variation, based on the duration and height of the previous eruption.
Step-by-step explanation:
How often does Old Faithful blow?
The world's most famous geyser, Old Faithful in Yellowstone, currently erupts around 20 times a day. These eruptions are predicted with a 90 percent confidence rate, within a 10 minute variation, based on the duration and height of the previous eruption.
Answer:
The area of the rectangle is 1222 units²
Step-by-step explanation:
The formula of the perimeter of a rectangle is P = 2(L + W), where L is its length and W is its width
The formula of the area of a rectangle is A = L × W
∵ The length of a rectangle is 5 less than twice the width
- Assume that the width of the rectangle is x units and multiply
x by 2 and subtract 5 from the product to find its length
∴ W = x
∴ L = 2x - 5
- Use the formula of the perimeter above to find its perimeter
∵ P = 2(2x - 5 + x)
∴ P = 2(3x - 5)
- Multiply the bracket by 2
∴ P = 6x - 10
∵ The perimeter of the rectangle is 146 units
∴ P = 146
- Equate the two expression of P
∴ 6x - 10 = 146
- Add 10 to both sides
∴ 6x = 156
- Divide both sides by 6
∴ x = 26
Substitute the value of x in W and L expressions
∴ W = 26 units
∴ L = 2(26) - 5 = 52 - 5
∴ L = 47 units
Now use the formula of the area to find the area of the rectangle
∵ A = 47 × 26
∴ A = 1222 units²
∴ The area of the rectangle is 1222 units²
Answer:
The family donated $52.50
Step-by-step explanation:
Larry's mom donated $7.50 ($15 ÷ $2=$7.50)
Larry's dad donated $25.00 ($5 x $5=$25.00)
Larry's sister donated $5.00 ($15 - $10=$5.00)
Larry donated $15.00
