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:
Step-by-step explanation:
s=18, t=18 the s gives t x sweets
s=18-x, t=18+x, s eats 5 and t eats half
s=18-5-x, t=(18+x)/2
Reamining sweets is
R=s+t
R=18-5-x+(18+x)/2
R=13-x+(18+x)/2
R=(26-2x+18+x)/2
R=(44-x)/2
Answer:
C
Step-by-step explanation:
So we need to understand what is rational numbers?
Rational number which can be written under this form: 
when x any are both integers and y
The question here is : Which property would be useful in proving that the product of two rational numbers. In math, when we talk about the product of at least two number, it implies to the multiplication in the operation.
Here, only answer C: 
with the condition 
and a, b, c and d are integers. Product of two integers is always an integer..
Answer:
P = 309.35 + 2.31t
Step-by-step explanation:
The relation between the population of the USA and the time in years after 2010 will be linear as the increase in population is constant for every year since 2010 which is 2.31 million.
So, we can model the population P in million as a function of time(t) in years since 2010 as
P = 309.35 + 2.31t ....... (1)
Now, for t = 0 i.e. in the year 2010, the population will be obtained from equation (1) to be 309.35 million.
(Answer)
Its False. addition and subtraction, Multiplication and division are inverse operations.
