Answer: 6
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let x represent the number of adult tickets that were sold.
Let y represent the number of children tickets that were sold.
The auditorium can hold no more than 200 audience members. This means that
x + y ≤ 200
An adult ticket costs $9 and a child's ticket costs $4. The students would like ticket sales of at least $1300. This means that
9x + 4y ≥ 1300
These are the set of inequalities that represents the situation.
16
find the absolute values ie. 9 and 2
multiply 9 by 2 and subtract 2 by 18
Answer:
Step-by-step explanation:
If you want to factor this, you have to use the quadratic formula to do so.
![x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%2B%2F-%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
For us, it looks like this:
![x=\frac{-3+/-\sqrt{(-3)^2-4(5)(4)} }{2(5)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-3%2B%2F-%5Csqrt%7B%28-3%29%5E2-4%285%29%284%29%7D%20%7D%7B2%285%29%7D)
which simplifies to
![x=\frac{-3+/-\sqrt{-71} }{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-3%2B%2F-%5Csqrt%7B-71%7D%20%7D%7B10%7D)
Since it breaks every mathematical rule to have a negative number under an even index radical, we have to deal with that using the imaginary "i". You should know at this point that ![i^2=-1](https://tex.z-dn.net/?f=i%5E2%3D-1)
so we will do a rewrite on that equation above:
![x=\frac{-3+/-\sqrt{i^2*71} }{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-3%2B%2F-%5Csqrt%7Bi%5E2%2A71%7D%20%7D%7B10%7D)
which simplifies further to
![x=\frac{-3+/-i\sqrt{71} }{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-3%2B%2F-i%5Csqrt%7B71%7D%20%7D%7B10%7D)
This is the answer but we can separate it into its proper standard form which is
and ![x=-\frac{3}{10}-\frac{\sqrt{71} }{10}i](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B3%7D%7B10%7D-%5Cfrac%7B%5Csqrt%7B71%7D%20%7D%7B10%7Di)
Answer:
Percentage profit = 11.3%
Step-by-step explanation:
<u>Given the following data;</u>
- Vat = 13% = 13/100 = 0.13
- Cost price = 10,000
- Selling price = Rs 12430
To calculate the profit percentage on the article;
First of all, we would determine the value-added (vat) tax levy;
Vat levy = 0.13 * 10000
Vat levy = Rs. 1300
Profit = selling price - cost price
Profit = 12430 - 10000
Profit = 2430
Profit after vat;
Profit after vat = Profit - Vat levy
Profit after vat = 2430 - 1300
Profit after vat = 1130
Next, we would calculate the profit percentage on the article;
![Percentage \; profit = \frac {Profit \; after \; vat}{Cost \; price} * 100](https://tex.z-dn.net/?f=%20Percentage%20%5C%3B%20profit%20%3D%20%5Cfrac%20%7BProfit%20%5C%3B%20after%20%5C%3B%20vat%7D%7BCost%20%5C%3B%20price%7D%20%2A%20100%20)
Substituting the values into the formula, we have;
![Percentage \; profit = \frac {1130}{10000} * 100](https://tex.z-dn.net/?f=%20Percentage%20%5C%3B%20profit%20%3D%20%5Cfrac%20%7B1130%7D%7B10000%7D%20%2A%20100%20)
![Percentage \; profit = \frac {113000}{10000}](https://tex.z-dn.net/?f=%20Percentage%20%5C%3B%20profit%20%3D%20%5Cfrac%20%7B113000%7D%7B10000%7D%20)
<em>Percentage profit = 11.3%</em>