What percent of the figure is shaded? The large figure is a square, and each arc is one-fourth of a circle.

Step-by-step explanation:

Hi there,

To get started, notice there are four sections not shaded. Since the shape is perfectly curved and each point along the arc is equidistant from that arc's corner of the shape, this means each non-shaded section is a quarter of a circle. Since we know the square's full area,

This will be our denominator,  since we are comparing shaded area to total area. The total shaded area is 4 times the area of a quarter-circle:

Notice, this is just the area of a circle! However, keep in mind the radius of one of the quarter circles is half the side length of the square:

Now, we want the shaded area. However, the white area is the non-shaded portion. We know the total area contains both shaded and non shaded:

Solve for area shaded:

Now

A% %  

Now, we can just go ahead and plug in!

A% =  =21.46 %

Thus, the shaded area percent is 21.46%.

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for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1