<em><u>The solution is (4, 4)</u></em>
<em><u>Solution:</u></em>
<em><u>Given system of equations are:</u></em>
<em><u>Substitute eqn 2 in eqn 1</u></em>
Make the right side of equation 0
<em><u>Solve by quadratic equation</u></em>
<em><u>Substitute x = 4 in eqn 2</u></em>
y = 2(4) - 4
y = 8 - 4
y = 4
Thus solution is (4, 4)
Answer:
The number of tickets they have sold in advance are summed up with the following equation and solution:
Equation: [the final answer should be in dollars]
Solution: The Opera sold 391 tickets in advance.
Step-by-step explanation:
First: Review some background information:
Let's see what the problem gives us to answer it. I'll bold out the important parts:
The Opera is collecting monies in advance for ticket sales. The tickets cost $17.50 each. If they have collected $6842.50 already, then how many tickets have they sold in advance?
We know how much the tickets cost and how much money they have earned from selling tickets, we can find out how much tickets they have sold.
Second: Solve the problem:
We can solve this problem using many ways, but I'm just going to pick one. We will use proportions to answer this. Now thoughts might be going through your head like this: What is this guy saying? What in the world is proportions? Well hopefully you learn from this example (Please don't take offense if you <em>do</em> know how to do proportions).
First we set up two fractions. One ticket costs $17.50, so we will use it to set up our first fraction: . We don't know how many tickets all together cost $6842.50 so we will use the variable: x. Now, we can set up our second fraction. x tickets costs $6842.50 so our second fraction will be:
. Now we must use cross multiplication. We multiply the numerator of the first fraction times the denominator of the second fraction, and then we multiply the denominator o the first fraction times the numerator of the second fraction. That's what we would do usually. But now, since we have a variable, we must use cross multiplication to solve for this variable. So we multiply the the numerator of the first fraction times the denominator of the other fraction and then we divide that answer times the denominator of the first fraction (You don't have to set it up like this).So let's solve this question:
1 x 17.50 = 17.50
6842.50 ÷ 17.50 = 391
So our equation is 6842.50 ÷ 17.50, and our solution is 391 tickets
Topic: Proportions
a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is
b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so
c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so
Then by linearity, we have