Answer:
(6, -3)
Step-by-step explanation:
The actual coordinates are x = -6 and y = 3
If we rotate 180 degrees and the center of rotation is at (0,0), all we need to do is invert the signal of each axis, that is, we invert the sign of the original x-coordinate and invert the signal of the original y-coordinate.
So the final x-coordinate is - (-6) = 6
And the final y-coordinate is - (3) = -3
So the coordinates will be (6, -3).
Answer:
Center of dilation origin, The scale factor is 4, The dilation mapping is (x, y) → (4x,4y) and The image represents the shape of the triangle.
Step-by-step explanation:
Given Hector is making an art project by cutting and gluing fabric shapes to a wooden board. His design includes two similar triangles, with one 4 times the size of the other. He cuts the smaller fabric triangle and traces it onto grid paper. we have to tell how he can use the tracing to make a pattern for the larger fabric triangle.
Apply the center of dilation origin.
The scale factor is 4
The dilation mapping is (x, y) → (4x,4y)
The image represents the shape of the triangle.
It is the division property of equality. You divide by 5 each side of the equation to isolate x.
<span>The derivative here is easy enough to find, first expand the equation into:
</span><span> g(x) = 3 - (x^2 - 10x + 25) = -x^2 + 10x - 22
Take the derivative: g'(x) = -2x +10
</span><span> Now, we have to find when the equation equals zero. So, we set g'(x) = 0. 0 = -2x + 10, 2x = 10, x = 5. When x is 5, this derivative will be zero, and that is the one and only time when the function is constant. When x is less than 5, you can plug in and see that the derivative will be positive, so the function is increasing when x is less than 5. When x is greater than 5, you can plug in and see that the derivative will be negative, so the function decreasing at x is greater than 5. Hope this helped :) have a good day!!!!!!!!!!!!!!!!!!!!!!!! </span>
Okay so when finding the area of an irregular figure, you break it up into regular shapes(like the square, rectangles, etc). Here you could separate this figure into a rectangle and two squares. After finding the area of these shapes, you add them up to get the total area of the figure.
