Consider the diagram below. Which of the following represents the values of x and y?

[tex]Consider the diagram below. Which of the following represents the values of x and y?[/tex]

[tex]Consider the diagram below. Which of the following represents the values of x and y?[/tex]

[tex]x=4\sqrt{6}\ units[/tex]

[tex]y=4\sqrt{2}\ units[/tex]

[tex]z=4\sqrt{3}\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

In the right triangle ABD

Applying the Pythagorean Theorem

[tex]x^2=y^2+(12-4)^2[/tex]

[tex]x^2=y^2+64[/tex]

[tex]y^2=x^2-64[/tex] ----> equation A

step 2

In the right triangle BDC

Applying the Pythagorean Theorem

[tex]z^2=y^2+4^2[/tex]

[tex]z^2=y^2+16[/tex]

[tex]y^2=z^2-16[/tex] ----> equation B

step 3

In the right triangle ABC

Applying the Pythagorean Theorem

[tex]12^2=x^2+z^2[/tex]

[tex]144=x^2+z^2[/tex] ----> equation C

step 4

Equate equation A and equation B

[tex]x^2-64=z^2-16[/tex]

[tex]x^2=z^2+48[/tex] -----> equation D

step 5

substitute equation D in equation C

[tex]144=z^2+48+z^2[/tex]

solve for z

[tex]2z^2=144-48[/tex]

[tex]2z^2=96[/tex]

[tex]z^2=48[/tex]

[tex]z=\sqrt{48}\ units[/tex]

simplify

[tex]z=4\sqrt{3}\ units[/tex]

Find the value of x

[tex]x^2=z^2+48[/tex]

[tex]x^2=48+48=96[/tex]

[tex]x=\sqrt{96}\ units[/tex]

[tex]x=4\sqrt{6}\ units[/tex]

Find the value of y

[tex]y^2=z^2-16[/tex]

[tex]y^2=48-16[/tex]

[tex]y^2=32[/tex]

[tex]y=\sqrt{32}\ units[/tex]

[tex]y=4\sqrt{2}\ units[/tex]

[tex]Consider the diagram below. which of the following represents the values x,y and z?[/tex]

See the attached figure to better understand the problem

we know that

in the triangle BCD

y²+5.66²=z²-------> y²=z²-5.66²------> equation 1

in the triangle ABC

y²+5.66²=x²-------> y²=x²-5.66²------> equation 2

equals 1 and 2

z²-5.66²=x²-5.66²--------> z²=x²---------> z=x

if z=x then

angle A=45°

angle D=45°

in the triangle ABD

cos 45=z/(5.66*2)-------> z=11.32*cos 45-----> 11.32*√2/2----> 8

z=8

x=8

y²=z²-5.66²------> 8²-5.66²-----> y²=31.96------> y=5.65

the answer is

the value of x is 8

the value of z is 8

the value of y=5.65

[tex]Consider the diagram below. which of the following represent the values of x,y, and z to the nearest[/tex]

I took the same test, its B, I got it right.

For proof, I solved y for 4sqrt2. A says x=y which cant be true, so it has to be B, the only other option with y=4sqrt2 in which x=4sqrt6

(sqrt means square root)

Y=5.6568 without rounding, in this case I'm rounding to 6

X=7.211 without rounding, in this case I'm rounding to 7

Z= 10 however answers may vary depending on how you round

Step-by-step explanation:

You subtract 4 from 12 to get 8

for y, you use a formula, 4/x=x/8 and cross multiply giving you x^2=32. then get square root of 32 to get 5.7 (rounded up) therefore Y=5.6568 or 6 or however you round it

then use Pythagorean theorem for the others

X: 4^2+6^2=x^2 then getting 7.211 rounding down to 7

Z: 8^2+6^2=x^2 then getting 10

Option A; x=44 and y=43

Step-by-step explanation:

we know that

In an inscribed quadrilateral, opposite angles are supplementary

step 1

Find the value of x

2x°+(2x+4)°=180°

4x=180°-4°

4x=176°

x=44°

step 2

Find the value of y

(3y+8)°+(y)°=180°

4y=180°-8°

4y=172°

y=43°

See the attached figure to better understand the problem

we know that

in the triangle BCD

y²+5.66²=z²-------> y²=z²-5.66²------> equation 1

in the triangle ABC

y²+5.66²=x²-------> y²=x²-5.66²------> equation 2

equals 1 and 2

z²-5.66²=x²-5.66²--------> z²=x²---------> z=x

if z=x then

angle A=45°

angle D=45°

in the triangle ABD

cos 45=z/(5.66*2)-------> z=11.32*cos 45-----> 11.32*√2/2----> 8

z=8

x=8

y²=z²-5.66²------> 8²-5.66²-----> y²=31.96------> y=5.65

the answer is

the value of x is 8

the value of z is 8

the value of y=5.65

[tex]Consider the diagram below. which of the following represent the values of x,y, and z to the nearest[/tex]