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:
54°
Step-by-step explanation:
Since the radius is not given, i'm going to assume that you are being asked for the measure of Arc FE, which is the angle the arc makes on the circumference when measured from the center of the circle.
Please refer to attached.
We can observe that FG and GE are both radii of the circle, hence they will have the same length. This also means that triangle FGE is an isosceles triangle. Which in turn means that ∠GFE = ∠GEF = 63°.
With this we can find the measure of arc FE
= ∠FGE
= 180° - 63° - 63°
= 54°
Hope this helps!
Answer: f(x) = a*x^5 + b*x^3 + c*x^2 + 12.
Step-by-step explanation:
The degree is 5, so we will have a term like:
a*x^5
it crosses the vertical axis at y = 12, then we will have a constant term equal to 12.
The polynomial has 4 terms, and we already defined two, so we can invent two more, such that the exponent must be between 1 and 4
This polynomial can be something like:
f(x) = a*x^5 + b*x^3 + c*x^2 + 12.
where a, b and c are real numbers.
Has 4 terms, f(0) = 12, then it intersects the y-axis at y = 12, and the maximum exponent is 5, then the degree of f(x) is 5.
The answer to this equation would be 3.
