Answer:
The perimeter of the original octagon is:
The perimeter of the new octagon is:
Step-by-step explanation:
When it is mentioned that an octagon is regular, it means that all its sides are equal, therefore, each side of the original octagon has a length of 9 units, considering the formula of the octagon's perimeter:
- Perimeter of an octagon = 8 * length.
By replacing you get:
- Perimeter of the original octagon = 8 * 9 = 72 units.
For the new octagon, it is mentioned that each side increases by 27 units, therefore:
- New length = 27 + 9 = 36 units.
Applying the formula of perimeter of an octagon with the new values we obtain:
- <u>Perimeter of the new octagon = 8 * 36 = 288 units.</u>
Answer: 20/12
Step-by-step explanation: In order to get a 12 in the denominator
of 5/3, we multiply top and bottom of 5/3 by 4 to get 20/12.
So 20/12 is an equivalent fraction.
There is no question or picture.
Answer:
(3, 1.7)
Step-by-step explanation:
The point at which the vertices of a triangle meet is known as the orthocenter of the triangle. The orthocenter passes through the vertex of the triangle and is perpendicular to the opposite sides.
Two lines are perpendicular if the product of their slopes is -1.
The slope of the line joining D(0,0), F(3,7) is:
![m_1=\frac{7-0}{3-0}=\frac{7}{3}](https://tex.z-dn.net/?f=m_1%3D%5Cfrac%7B7-0%7D%7B3-0%7D%3D%5Cfrac%7B7%7D%7B3%7D)
The slope of the line perpendicular to the line joining D and F is -3/7. The orthocenter is perpendicular to the line joining D and F and passes through vertex E(7, 0). The equation is hence:
![y-y_1=m(x-x_1)\\\\y-0=-\frac{3}{7} (x-7)\\\\y=-\frac{3}{7}x+3 \ .\ .\ .\ (1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29%5C%5C%5C%5Cy-0%3D-%5Cfrac%7B3%7D%7B7%7D%20%28x-7%29%5C%5C%5C%5Cy%3D-%5Cfrac%7B3%7D%7B7%7Dx%2B3%20%5C%20.%5C%20.%5C%20.%5C%20%281%29)
The slope of the line joining E(7,0), and F(3,7). is:
![m_1=\frac{7-0}{3-7}=-\frac{7}{4}](https://tex.z-dn.net/?f=m_1%3D%5Cfrac%7B7-0%7D%7B3-7%7D%3D-%5Cfrac%7B7%7D%7B4%7D)
The slope of the line perpendicular to the line joining E and F is 4/7. The orthocenter is perpendicular to the line joining E and F and passes through vertex D(0, 0). The equation is hence:
![y-y_1=m(x-x_1)\\\\y-0=\frac{4}{7} (x-0)\\\\y=\frac{4}{7} x\ .\ .\ .\ (2)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29%5C%5C%5C%5Cy-0%3D%5Cfrac%7B4%7D%7B7%7D%20%28x-0%29%5C%5C%5C%5Cy%3D%5Cfrac%7B4%7D%7B7%7D%20x%5C%20.%5C%20.%5C%20.%5C%20%282%29)
The point of intersection of equation 1 and equation 2 is the orthocenter. Solving equation 1 and 2 simultaneously gives:
x = 3, y = 1.7
The area of the circle is equal to the area of the polygon