Most quadratic functions(which is what you have there, to a degree of 2) are solved using factoring and the zero product law. If you can not factor then you have to use the quadratic formula or graph it. However this one can be factored.
It's pretty simple to just factor it by inspection but I use the chart method, if you know decomposition that works as well.
Factoring gives us,
Then you set each factor to 0 and solve for x,
And the second one,
The solutions to this equation are
x = -1/2, 3
There are two cases to consider.
A) The removed square is in an odd-numbered column (and row). In this case, the board is divided by that column and row into parts with an even number of columns, which can always be tiled by dominos, and the column the square is in, which has an even number of remaining squares that can also be tiled by dominos.
B) The removed square is in an even-numbered column (and row). In this case, the top row to the left of that column (including that column) can be tiled by dominos, as can the bottom row to the right of that column (including that column). The remaining untiled sections of the board have even numbers of rows, so can be tiled by dominos.
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Perhaps the shorter answer is that in an odd-sized board, the corner squares are the ones that there is one of in excess. Cutting out one that is of that color leaves an even number of squares, and equal numbers of each color. Such a board seems like it <em>ought</em> to be able to be tiled by dominos, but the above shows there is actually an algorithm for doing so.
thanks for the fact, that was really helpful !!!
Answer:
Inside the triangle - Acute Triangle
Outside the triangle - Obtuse Triangle
On the hypotenuse - Right Triangle
Step-by-step explanation:
The <u>circumcenter</u> is the point where the perpendicular bisectors of a triangle intersect.
In the special case of a right triangle, the circumcenter lies exactly at the midpoint of the hypotenuse.
The circumcenter of an acute triangle lies inside the triangle.
The circumcenter of an obtuse triangle lies outside the triangle.
8x - 2y = -8
-5x + 2y = -1
3x = -9
x = -3
