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]