Answer by JKismyhusbandbae: The mean is the average of all the numbers. You add all the numbers and divide by how many numbers you added to get the mean.
Answer:
54÷9 = 6 so for the second box is 6 hot dogs per person
54÷27= 2 third box is 2 hot dogs per person
54÷54= 1 fourth box is 1 hot dog per person
Answer:
<h3> 1)
![x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2](https://tex.z-dn.net/?f=x_1%3D%5Cdfrac%7B7%2B%5Csqrt%7B13%7D%7D2%5C%2C%2C%5Cquad%20x_2%3D%5Cdfrac%7B7-%5Csqrt%7B13%7D%7D2)
</h3><h3> 2)
![x_1=-\dfrac13\,,\quad x_2=-3](https://tex.z-dn.net/?f=x_1%3D-%5Cdfrac13%5C%2C%2C%5Cquad%20x_2%3D-3)
</h3>
Step-by-step explanation:
<h3>1)</h3>
![x^2 - 7x + 9 = 0\quad\implies\quad a=1\,,\ b = -7\,,\ c=9\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot1\cdot9}}{2\cdot1}=\dfrac{7\pm\sqrt{49-36}}2\\\\x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2](https://tex.z-dn.net/?f=x%5E2%20-%207x%20%2B%209%20%3D%200%5Cquad%5Cimplies%5Cquad%20a%3D1%5C%2C%2C%5C%20b%20%3D%20-7%5C%2C%2C%5C%20c%3D9%5C%5C%5C%5Cx%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%3D%5Cdfrac%7B-%28-7%29%5Cpm%5Csqrt%7B%28-7%29%5E2-4%5Ccdot1%5Ccdot9%7D%7D%7B2%5Ccdot1%7D%3D%5Cdfrac%7B7%5Cpm%5Csqrt%7B49-36%7D%7D2%5C%5C%5C%5Cx_1%3D%5Cdfrac%7B7%2B%5Csqrt%7B13%7D%7D2%5C%2C%2C%5Cquad%20x_2%3D%5Cdfrac%7B7-%5Csqrt%7B13%7D%7D2)
<h3>2)</h3><h3>
![3x^2 + 10x=-3\\\\3x^2+10x+3=0\quad\implies\quad a=3\,,\ b =10\,,\ c=3\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-10\pm\sqrt{10^2-4\cdot3\cdot3}}{2\cdot3}= \dfrac{-10\pm\sqrt{100-36}}6\\\\x_1=\dfrac{-10+\sqrt{64}}6=\dfrac{-10+8}6=-\dfrac13\,,\qquad x_2=\dfrac{-10-8}6=-3](https://tex.z-dn.net/?f=3x%5E2%20%2B%2010x%3D-3%5C%5C%5C%5C3x%5E2%2B10x%2B3%3D0%5Cquad%5Cimplies%5Cquad%20a%3D3%5C%2C%2C%5C%20b%20%3D10%5C%2C%2C%5C%20c%3D3%5C%5C%5C%5Cx%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%3D%5Cdfrac%7B-10%5Cpm%5Csqrt%7B10%5E2-4%5Ccdot3%5Ccdot3%7D%7D%7B2%5Ccdot3%7D%3D%20%5Cdfrac%7B-10%5Cpm%5Csqrt%7B100-36%7D%7D6%5C%5C%5C%5Cx_1%3D%5Cdfrac%7B-10%2B%5Csqrt%7B64%7D%7D6%3D%5Cdfrac%7B-10%2B8%7D6%3D-%5Cdfrac13%5C%2C%2C%5Cqquad%20x_2%3D%5Cdfrac%7B-10-8%7D6%3D-3)
</h3>