Answer: 18/5
Step-by-step explanation: hope this helps pls mark me brainliest
Answer:
B. Every 16 minutes, 22 more pizzas were set out on the buffet.
Step-by-step explanation:
At 11:00 am, x would be equal to 0, and there would be 15 pizzas on the buffet line. Then, every 8 minutes, 11 more pizzas are added to the buffet line. So in 16 minutes, 22 pizzas will be added to the buffet.
![\frac{16}{8} =2\\(11)(2) = 22](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B8%7D%20%3D2%5C%5C%2811%29%282%29%20%3D%2022)
Answer:
![x = 3 + 4\sqrt{3}](https://tex.z-dn.net/?f=x%20%3D%203%20%2B%204%5Csqrt%7B3%7D)
Step-by-step explanation:
OPQ is a right angle triangle.
<u>Using Pythagoras</u>
![x^{2} + (x+5)^{2} = (x+8)^{2}\\x^{2} + x^{2} + 10x +25 = x^{2} + 16x + 64\\x^{2} + x^{2} - x^{2} + 10x - 16x + 25 - 64 = 0\\x^{2} - 6x -39 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%20%28x%2B5%29%5E%7B2%7D%20%3D%20%28x%2B8%29%5E%7B2%7D%5C%5Cx%5E%7B2%7D%20%2B%20x%5E%7B2%7D%20%2B%2010x%20%2B25%20%3D%20x%5E%7B2%7D%20%2B%2016x%20%2B%2064%5C%5Cx%5E%7B2%7D%20%2B%20x%5E%7B2%7D%20-%20x%5E%7B2%7D%20%2B%2010x%20-%2016x%20%2B%2025%20-%2064%20%3D%200%5C%5Cx%5E%7B2%7D%20-%206x%20-39%20%3D%200)
<u>Using quadratic formula</u>
<u />![x = \frac{-b \± \sqrt{b^{2}-4ac}}{2a}\\x = \frac{-(-6) \± \sqrt{(-6)^{2}-4(1)(-39)}}{2(1)}\\x = \frac{6}{2} \± \frac{\sqrt{192}}{2}\\x = 3 \± \frac{8\sqrt{3}}{2}\\x = 3 \± 4\sqrt{3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%20%5C%C2%B1%20%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%5C%5Cx%20%3D%20%5Cfrac%7B-%28-6%29%20%5C%C2%B1%20%5Csqrt%7B%28-6%29%5E%7B2%7D-4%281%29%28-39%29%7D%7D%7B2%281%29%7D%5C%5Cx%20%3D%20%5Cfrac%7B6%7D%7B2%7D%20%5C%C2%B1%20%5Cfrac%7B%5Csqrt%7B192%7D%7D%7B2%7D%5C%5Cx%20%3D%203%20%5C%C2%B1%20%5Cfrac%7B8%5Csqrt%7B3%7D%7D%7B2%7D%5C%5Cx%20%3D%203%20%5C%C2%B1%204%5Csqrt%7B3%7D)
![x = 3 + 4\sqrt{3} = 9.928(4s.f.)](https://tex.z-dn.net/?f=x%20%3D%203%20%2B%204%5Csqrt%7B3%7D%20%3D%209.928%284s.f.%29)
OR
(Length can't be negative)
∴ ![x = 3 + 4\sqrt{3}](https://tex.z-dn.net/?f=x%20%3D%203%20%2B%204%5Csqrt%7B3%7D)
X + 13 = -4
x = -4 - 13
x = - 17
I am thinking it is the first one..solution is -17
Answer:
A
Step-by-step explanation:
if (x1,y1) and (x2,y2) are the extremities of diameter,then eq. of circle is
(x-x1)(x-x2)+(y-y1)(y-y2)=0
reqd. eq. is (x+1)(x-5)+(y+9)(y-1)=0
![x^{2} +x-5x-5+y^2+9y-y-9=0\\x^{2} -4x+y^2+8y-14=0\\compare with x^2+y^2+2gx+2fy+c=0\\center (-g,-f) \\radius r=\sqrt{g^2+f^2-c}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2Bx-5x-5%2By%5E2%2B9y-y-9%3D0%5C%5Cx%5E%7B2%7D%20-4x%2By%5E2%2B8y-14%3D0%5C%5Ccompare%20with%20x%5E2%2By%5E2%2B2gx%2B2fy%2Bc%3D0%5C%5Ccenter%20%28-g%2C-f%29%20%5C%5Cradius%20r%3D%5Csqrt%7Bg%5E2%2Bf%5E2-c%7D)
center is (2,-4)
r=√(2²+(-4)²-(-14))
=√(4+16+14)
=√(34)
eq. of circle is (x-2)²+(y+4)²=34
or
(x²-4x)+(y²+8y)=14
(x²-4x+4)+(y²+8y+16)=14+4+16
(x-2)²+(y+4)²=34