40g+300 is less than or equal to 5000
g is less than or equal to 117.5
So that is 117 guests max can be invited
Ans. 1 Angle E and angle F are corresponding angles.
Solution 2.
So,
angle E = angle F
=> x + 20 = 5x - 20
=> x + 20 + 20 = 5x
=> x + 40 = 5x
=> 40 = 5x - x
=> 40 = 4x
=> 40/4 = x
=> 10 = x
Solution 3.
E = x + 20
=> E = 10 + 20
=> E = 30
F = 5x - 20
=> F = 5(10) - 20
=> F = 50 - 20
=> F = 30
<em>Again</em><em> </em><em>justified</em><em> </em><em>that </em><em>they </em><em>are </em><em>equal</em><em> (</em><em> </em><em>besides</em><em> </em><em>answer </em><em>1</em><em>)</em><em>.</em>
Given:
The shaded sector above covers
of the circle.
Radius of the circle = 3 cm
To find:
The area of the sector in terms of π.
Solution:
The area of a circle is
![A=\pi r^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2)
Substituting
, we get
![A=\pi (3)^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20%283%29%5E2)
![A=9\pi](https://tex.z-dn.net/?f=A%3D9%5Cpi)
It is given that the shaded sector above covers
of the circle.
The area of shaded sector ![=\dfrac{1}{3}A](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B3%7DA)
![=\dfrac{1}{3}(9\pi)](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B3%7D%289%5Cpi%29)
![=3\pi](https://tex.z-dn.net/?f=%3D3%5Cpi)
Therefore, the area of shaded sector is 3π sq. cm.
Answer:
The value of
. The figure is also attached below.
Step-by-step explanation:
Considering the expression
![5x + 6(x - 2) - 8 (x - 3)](https://tex.z-dn.net/?f=5x%20%2B%206%28x%20-%202%29%20-%208%20%28x%20-%203%29)
If we have to find the vale of
, then
![5x + 6(x - 2) - 8 (x - 3)=0](https://tex.z-dn.net/?f=5x%20%2B%206%28x%20-%202%29%20-%208%20%28x%20-%203%29%3D0)
![5x+6x-12-8\left(x-3\right)=0](https://tex.z-dn.net/?f=5x%2B6x-12-8%5Cleft%28x-3%5Cright%29%3D0)
![5x+6x-12-8x+24=0](https://tex.z-dn.net/?f=5x%2B6x-12-8x%2B24%3D0)
![3x+12=0](https://tex.z-dn.net/?f=3x%2B12%3D0)
![\mathrm{Subtract\:}12\mathrm{\:from\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3A%7D12%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D)
![3x+12-12=0-12](https://tex.z-dn.net/?f=3x%2B12-12%3D0-12)
![3x=-12](https://tex.z-dn.net/?f=3x%3D-12)
![\mathrm{Divide\:both\:sides\:by\:}3](https://tex.z-dn.net/?f=%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D3)
![\frac{3x}{3}=\frac{-12}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B3%7D%3D%5Cfrac%7B-12%7D%7B3%7D)
![x=-4](https://tex.z-dn.net/?f=x%3D-4)
Therefore, the value of
. The figure is also attached below.
Keywords: equation
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