Answer: 94 child tickets
<u>Step-by-step explanation:</u>
Let x represent child tickets
Let y represent adult tickets
Cost Equation: 5.70x + 9.75y = 1306.10
Quantity Equation: x + y = 173
Solve the system of equations using the elimination method:
Multiply the Quantity Equation by -5.70
5.70x + 9.75y = 1306.10
<u> -5.70x - 5.70y</u> = <u>-986.10</u>
4.05y = 320.00
<u> ÷4.05 </u> <u>÷4.05 </u>
y = 79
x + y = 173
x + 79 = 173
x = 94
To find the zeros of a quadratic fiunction given the equation you can use the next quadratic formula after equal the function to 0:
![\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20ax%5E2%2Bbx%2Bc%3D0%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5Cend%7Bgathered%7D)
For the given function:

![x=\frac{-(-10)\pm\sqrt[]{(-10)^2-4(2)(-3)}}{2(2)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-10%29%5Cpm%5Csqrt%5B%5D%7B%28-10%29%5E2-4%282%29%28-3%29%7D%7D%7B2%282%29%7D)
![x=\frac{10\pm\sqrt[]{100+24}}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B10%5Cpm%5Csqrt%5B%5D%7B100%2B24%7D%7D%7B4%7D)
![\begin{gathered} x=\frac{10\pm\sqrt[]{124}}{4} \\ \\ x=\frac{10\pm\sqrt[]{2\cdot2\cdot31}}{4} \\ \\ x=\frac{10\pm\sqrt[]{2^2\cdot31}}{4} \\ \\ x=\frac{10\pm2\sqrt[]{31}}{4} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D%5Cfrac%7B10%5Cpm%5Csqrt%5B%5D%7B124%7D%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B10%5Cpm%5Csqrt%5B%5D%7B2%5Ccdot2%5Ccdot31%7D%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B10%5Cpm%5Csqrt%5B%5D%7B2%5E2%5Ccdot31%7D%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B10%5Cpm2%5Csqrt%5B%5D%7B31%7D%7D%7B4%7D%20%5C%5C%20%20%5Cend%7Bgathered%7D)
![\begin{gathered} x_1=\frac{10}{4}+\frac{2\sqrt[]{31}}{4} \\ \\ x_1=\frac{5}{2}+\frac{\sqrt[]{31}}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x_1%3D%5Cfrac%7B10%7D%7B4%7D%2B%5Cfrac%7B2%5Csqrt%5B%5D%7B31%7D%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20x_1%3D%5Cfrac%7B5%7D%7B2%7D%2B%5Cfrac%7B%5Csqrt%5B%5D%7B31%7D%7D%7B2%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} x_2=\frac{10}{4}-\frac{2\sqrt[]{31}}{4} \\ \\ x_2=\frac{5}{2}-\frac{\sqrt[]{31}}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x_2%3D%5Cfrac%7B10%7D%7B4%7D-%5Cfrac%7B2%5Csqrt%5B%5D%7B31%7D%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20x_2%3D%5Cfrac%7B5%7D%7B2%7D-%5Cfrac%7B%5Csqrt%5B%5D%7B31%7D%7D%7B2%7D%20%5Cend%7Bgathered%7D)
Then, the zeros of the given quadratic function are:
![\begin{gathered} x=\frac{5}{2}+\frac{\sqrt[]{31}}{2} \\ \\ x_{}=\frac{5}{2}-\frac{\sqrt[]{31}}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D%5Cfrac%7B5%7D%7B2%7D%2B%5Cfrac%7B%5Csqrt%5B%5D%7B31%7D%7D%7B2%7D%20%5C%5C%20%20%5C%5C%20x_%7B%7D%3D%5Cfrac%7B5%7D%7B2%7D-%5Cfrac%7B%5Csqrt%5B%5D%7B31%7D%7D%7B2%7D%20%5Cend%7Bgathered%7D)
Answer: Third option
Answer:
The radius of the balloon is increasing at a rate of 4 feet per minute.
Step-by-step explanation:
We are given the following in the question:

Volume of sphere is given by

where r is the radius of the balloon.
Instant radius, r = 2 ft
Rate of change of volume =

Putting values, we get,

Thus, the radius of the balloon is increasing at a rate of 4 feet per minute.
Answer:3
Step-by-step explanation:
(2,-2) would be the answer I think