1.
{3x+9y=75
{8x+5y=67
2. elmination
{24x+72y=600
-
{24x+15y=201
57y=399
y=7
8x=67-35
x=4
Senior citizen ticket cost $4
child ticket cost $7
I love these. It's often called the Shoelace Formula. It actually works for the area of any 2D polygon.
We can derive it by first imagining our triangle in the first quadrant, one vertex at the origin, one at (a,b), one at (c,d), with (0,0),(a,b),(c,d) in counterclockwise order.
Our triangle is inscribed in the rectangle. There are three right triangles in that rectangle that aren't part of our triangle. When we subtract the area of the right triangles from the area of the rectangle we're left with the area S of our triangle.
That's the cross product in the purest form. When we're away from the origin, a arbitrary triangle with vertices will have the same area as one whose vertex C is translated to the origin.
We set
That's a perfectly useful formula right there. But it's usually multiplied out:
That's the usual form, the sum of cross products. Let's line up our numbers to make it easier.
(1, 2), (3, 4), (−7, 7)
(−7, 7),(1, 2), (3, 4),
[tex]A = \frac 1 2 ( 1(7)-2(-7) + 3(2)-4(1) + -7(4) - (7)(3)
Answer:
28 miles per gallon
Step-by-step explanation:
The correct option will be: A. 67%
<em><u>Explanation</u></em>
Given equation is: , where is the length of the film in minutes and is the percentage of people finish watching the film.
Here, the length of the documentary is given as 95 minutes. So, we will <u>plug into the above equation</u> and get....
<em>(Rounded to the nearest percent)</em>
So, the percentage of people in an audience who will finish watching a documentary that is 95 minutes long will be 67%