Answer:
Given
x+y+z=0
⟹x+y=−z
Cubing on both sides
(x+y) 3 =(−z) 3
⟹x 3 +y 3 +3x 2y+3xy 2 =−z 3
⟹x 3 +y 3 +3xy(x+y)=−z 3
⟹x 3+y 3+3xy(−z)=−z 3
⟹x 3 +y 3−3xyz=−z 3
⟹x 3 +y 3 +z 3 =3xyz
Step-by-step explanation:
Hope it is helpful.....
Answer:
The relationship between the circumference of a circle and its diameter represent a direct variation and the constant of proportionality is equal to the constant 
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form 
where K is the constant of proportionality
In this problem we know that
The circumference of a circle is equal to
therefore
the relationship between the circumference of a circle and its diameter is a direct variation and the constant of proportionality is equal to the constant
First, factor out 5:
5 (x² -x -20)
We need two numbers that add to -1 and multiply to -20. -5 and 4 satisfy this.
5(x-5)(x+4)
8/185 = 4.3 %
That is the number of days she missed so she was in attendance
100-4 = 96%
Answer:
D) 20°
Step-by-step explanation:
Using the triangle sum theorem, you know that every triangle's interior angles add up to 180°. Therefore the bottom triangle's missing angle can be found by giving it the variable x.
57° + 30° + x = 180°
Simplify: 87° + x =180°
x=93°
By the vertical angles theorem, the vertical angle directly across this angle is congruent to this one. Meaning that the top triangle's angle are 67°, 93°, and unknown, which we can assign y. We can use the same method from above here.
67° + 93° + y = 180°
Simplify: 160° + y = 180°
y=20°
