Joey has a square piece of paper with edges that are 8 inches long. he cuts the paper along a diagonal to make two congruent triangles. which measurement is closest to the length in inches of the hypotenuse of each triangle?
a. 11.3
b. 13.9
c. 8
d. 16

Step-by-step explanation:

If we have a square measuring 8 inches along every side, when we cut from corner to corner, we have 2 congruent triangles with base measures of 8 inches and height measures of 8 inches.  We need to find the measure of the hypotenuse which we can find using Pythagorean's Theorem:

and

and

s0

c = 11.3

the hypotenuse of each triangle is 11.3

Step-by-step explanation:

The paper that Joey had is a square. All sides are equal in a square. The length of the given sides are 8 inches each. He cuts the paper along a diagonal to make two congruent triangles. This means that the square is divided equally.

Each part is a right angle triangle whose hypotenuse is the diagonal of the square and the length of each side of the square forms the opposite site and adjacent side of the triangle. Applying Pythagoras theorem,

Hypotenuse^2 = opposite side^2 + adjacent side^2

Hypotenuse^2 = 8^2 + 8^2 = 64 + 64 = 128

Hypotenuse = √128 = 11.3

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'.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is