First let's figure out the angle of the green beans section - this would be 360 minus the total of the other two angles:
360 - (98 + 195)
= 360 - 293
= 67°
Now the formula for the circumference of a circle is circumference = πd, but since we have only a section of the circle we need to multiply this by the angle of our section/the sum of angles in a circle, ie.:
Circumference = 12π*(67/360)
= 67π/30
= 7 inch (to the nearest whole number)
Therefor F is the correct answer
Answer:
<em>-26 or 14</em>
Step-by-step explanation:
Given that
Coordinate of point A is -6.
Length of AB = 20
To find:
Coordinates for the point B = ?
Solution:
We are given that:
AB = 20
In other words, we can use modulus function to define the distance between A and B:
|Coordinates of B - Coordinates of A| = 20
Let the coordinates of B = ![x](https://tex.z-dn.net/?f=x)
Kindly refer to the attached image for the given situation.
Point B might be either on the left or on the right side of A.
That means:
![|x-(-6)| = 20\\\Rightarrow |x+6|=20](https://tex.z-dn.net/?f=%7Cx-%28-6%29%7C%20%3D%2020%5C%5C%5CRightarrow%20%7Cx%2B6%7C%3D20)
Now, let us have a look at the modulus function:
![|y|=\left \{ {-{y}\ if\ y0} \right.](https://tex.z-dn.net/?f=%7Cy%7C%3D%5Cleft%20%5C%7B%20%7B-%7By%7D%5C%20if%5C%20y%3C0%20%5Catop%20%7By%7D%5C%20if%5C%20y%3E0%7D%20%5Cright.)
So,
![|x+6|=\left \{ {-{(x+6)}\ if\ (x+6)0} \right.](https://tex.z-dn.net/?f=%7Cx%2B6%7C%3D%5Cleft%20%5C%7B%20%7B-%7B%28x%2B6%29%7D%5C%20if%5C%20%28x%2B6%29%3C0%20%5Catop%20%7B%28x%2B6%29%7D%5C%20if%5C%20%28x%2B6%29%3E0%7D%20%5Cright.)
![(x+6 ) =20\\\Rightarrow x =14](https://tex.z-dn.net/?f=%28x%2B6%20%29%20%3D20%5C%5C%5CRightarrow%20x%20%3D14)
![-(x+6 ) =20\\\Rightarrow x =-26](https://tex.z-dn.net/?f=-%28x%2B6%20%29%20%3D20%5C%5C%5CRightarrow%20x%20%3D-26)
Therefore, the answer is:
<em>-26 or 14</em>
Answer: The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.
Explanation:
It is given that coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .
The distance formula for two points is given below,
![D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=D%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}](https://tex.z-dn.net/?f=DE%3D%5Csqrt%7B%282%2B2%29%5E2%2B%284-5%29%5E2%7D%3D%5Csqrt%7B17%7D)
![EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}](https://tex.z-dn.net/?f=EF%3D%5Csqrt%7B%280-2%29%5E2%2B%280-4%29%5E2%7D%3D%5Csqrt%7B20%7D)
![FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}](https://tex.z-dn.net/?f=FG%3D%5Csqrt%7B%28-4-0%29%5E2%2B%281-0%29%5E2%7D%3D%5Csqrt%7B17%7D)
![DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}](https://tex.z-dn.net/?f=DG%3D%5Csqrt%7B%28-4%2B2%29%5E2%2B%281-5%29%5E2%7D%3D%5Csqrt%7B20%7D)
Slope formula,
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Slope of DE,
![m_1=\frac{4-5}{2+2}= \frac{-1}{4}](https://tex.z-dn.net/?f=m_1%3D%5Cfrac%7B4-5%7D%7B2%2B2%7D%3D%20%5Cfrac%7B-1%7D%7B4%7D)
Slope of EF,
![m_2=\frac{0-4}{0-2}= 2](https://tex.z-dn.net/?f=m_2%3D%5Cfrac%7B0-4%7D%7B0-2%7D%3D%202)
Slope of FG,
![m_3=\frac{1-0}{-4-0}= \frac{-1}{4}](https://tex.z-dn.net/?f=m_3%3D%5Cfrac%7B1-0%7D%7B-4-0%7D%3D%20%5Cfrac%7B-1%7D%7B4%7D)
Slope of DG,
![m_4=\frac{1-5}{-4+2}= 2](https://tex.z-dn.net/?f=m_4%3D%5Cfrac%7B1-5%7D%7B-4%2B2%7D%3D%202)
The slope of opposite sides are equal, it means the opposite sides are parallel.
All four sides do not have the same length. It means it is not a rhombus.
From the figure it is noticed that the opposite sides are parallel.
Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.
(-7,3) here is the answer, easy one