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:
t=√d-12/4 and t=√-d-12/4, d≥12
Step-by-step explanation:
Hope this helps.
This is basically saying how much of the pizza did Tashia and Jay both ate, thus combining their portions together.
1/3 + 3/8 = fraction of pizza eaten
To add fractions, you must have a common denominator. Which is 24 in this case because 3*8 = 24.
So you multiply 1/3 with 8 and multiply 3/8 with 3.
1/3*8= 8/24
3/8*3= 9/24
Now you add the fractions.
8/24+9/24= 17/24. You add the numerator, the denominator stays the same.
17/24 of the pizza was eaten.
Answer:
81y^2+36y+4
Step-by-step explanation:
First: 9y^2= 81y
Next: 2^2= 4
Then: 9y times 2= 18
Last: 18 times 2= 36y
(this : ^2 means squared in case you did not know)
Answer: H - 50%
Step-by-step explanation:
