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

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step-by-step explanation:

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a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!