Answer:
The area of the circle is equal to
.
Step-by-step explanation:
Given that,
The area of sector is, ![\dfrac{17}{2}\pi](https://tex.z-dn.net/?f=%5Cdfrac%7B17%7D%7B2%7D%5Cpi)
The central angle is ![\dfrac{17}{9}\pi](https://tex.z-dn.net/?f=%5Cdfrac%7B17%7D%7B9%7D%5Cpi)
We need to find the area of circle.
We know that,
![\text{Area of sector}=\dfrac{\text{central angle}}{2\pi}\times \text{Area of circle}\\\\\text{Area of circle}=\dfrac{2\pi \times \text{Area of sector}}{\text{central angle}}\\\\=\dfrac{2\pi \times \dfrac{17\pi}{2}}{\dfrac{17\pi }{9}}\\\\=9\pi](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20sector%7D%3D%5Cdfrac%7B%5Ctext%7Bcentral%20angle%7D%7D%7B2%5Cpi%7D%5Ctimes%20%5Ctext%7BArea%20of%20circle%7D%5C%5C%5C%5C%5Ctext%7BArea%20of%20circle%7D%3D%5Cdfrac%7B2%5Cpi%20%5Ctimes%20%5Ctext%7BArea%20of%20sector%7D%7D%7B%5Ctext%7Bcentral%20angle%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B2%5Cpi%20%5Ctimes%20%5Cdfrac%7B17%5Cpi%7D%7B2%7D%7D%7B%5Cdfrac%7B17%5Cpi%20%7D%7B9%7D%7D%5C%5C%5C%5C%3D9%5Cpi)
So, the area of the circle is equal to
.
Answer:
y= -4/9 + 1/9
Step-by-step explanation:
Answer: 0.0004951
Step-by-step explanation:
Given
Five cards are from the deck
The total number of cards in the deck is 52
total spades card is ![13](https://tex.z-dn.net/?f=13)
We have to choose 5 cards out of 13, this can be done in
![\Rightarrow ^{13}C_5](https://tex.z-dn.net/?f=%5CRightarrow%20%5E%7B13%7DC_5)
The probability of choosing 5 spade cards is
![\Rightarrow P=\dfrac{^{13}C_5}{^{52}C_5}\\\\\Rightarrow P=\dfrac{1287}{2598960}=0.0004951](https://tex.z-dn.net/?f=%5CRightarrow%20P%3D%5Cdfrac%7B%5E%7B13%7DC_5%7D%7B%5E%7B52%7DC_5%7D%5C%5C%5C%5C%5CRightarrow%20P%3D%5Cdfrac%7B1287%7D%7B2598960%7D%3D0.0004951)
ANSWER
![x = - 11\: or \: x = 3](https://tex.z-dn.net/?f=x%20%3D%20%20%20-%2011%5C%3A%20or%20%5C%3A%20x%20%3D%20%203)
EXPLANATION
The quadratic equation given to us is
![{x}^{2} + 8x = 33](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%208x%20%3D%2033)
We add half the square of the coefficient of
![x](https://tex.z-dn.net/?f=x)
to both sides of the equation to obtain,
![{x}^{2} + 8x + {(4)}^{2} = 33 + {(4)}^{2}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%2B%208x%20%2B%20%20%7B%284%29%7D%5E%7B2%7D%20%20%3D%2033%20%2B%20%20%7B%284%29%7D%5E%7B2%7D)
This implies that,
![{x}^{2} + 8x + {(4)}^{2} = 33 + 16](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%2B%208x%20%2B%20%20%7B%284%29%7D%5E%7B2%7D%20%20%3D%2033%20%2B%2016)
The right hand side simplifies to
![{x}^{2} + 8x + {(4)}^{2} = 49](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%2B%208x%20%2B%20%20%7B%284%29%7D%5E%7B2%7D%20%20%3D%2049)
The left hand side is a perfect square.
This gives us
![{(x + 4)}^{2} = 49](https://tex.z-dn.net/?f=%20%7B%28x%20%2B%204%29%7D%5E%7B2%7D%20%20%3D%2049)
We take the square root of both sides
![x + 4 = \pm \sqrt{49}](https://tex.z-dn.net/?f=x%20%2B%204%20%3D%20%20%5Cpm%20%5Csqrt%7B49%7D%20)
This evaluates to
![x + 4 = \pm 7](https://tex.z-dn.net/?f=x%20%2B%204%20%3D%20%20%5Cpm%207)
We make x the subject.
![x = - 4\pm 7](https://tex.z-dn.net/?f=x%20%3D%20%20%20-%204%5Cpm%207)
We now split the square root sign to get
.
![x = - 4 - 7 \: or \: x = - 4 + 7](https://tex.z-dn.net/?f=x%20%3D%20%20%20-%204%20-%207%20%5C%3A%20or%20%5C%3A%20x%20%3D%20%20-%204%20%2B%207)
![x = - 11\: or \: x = 3](https://tex.z-dn.net/?f=x%20%3D%20%20%20-%2011%5C%3A%20or%20%5C%3A%20x%20%3D%20%203)
The correct answer is A.
24/22,000=916.6666666 so assuming this is how you do it, it would be 916 rounded up 917 hope this helps