Solve for x. Leave your answer in simplest radical form

x = √35

Step-by-step explanation:

Please see attached photo for explanation.

We'll begin calculating the value of y. This can be obtained as follow:

10² = y² + 4²

100 = y² + 16

Collect like terms

100 – 16 = y²

84 = y²

Take the square root of both side

y = √84

Finally, we shall determine the value of x. This can be obtained as follow:

y² = x² + 7²

(√84)² = x² + 49

84 = x² + 49

Collect like terms

84 – 49 = x²

35 = x²

Take the square root of both side

x = √35

180

step-by-step explanation:

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'.