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.....
Pretty sure that's right.
We can write a system of equations:
1x + 10y = 182
x + y = 56
Where 'x' is the number of $1 bills, and 'y' is the number of $10 bills.
To find this we can solve using substitution.
Re-arrange the 2nd equation:
x + y = 56
Subtract 'y' to both sides:
x = -y + 56
Now we can plug in '-y + 56' for 'x' in the first equation.
1x + 10y = 182
1(-y + 56) + 10y = 182
-y + 56 + 10y = 182
Subtract 56 to both sides:
-y + 10y = 126
Combine like terms:
9y = 126
Divide 9 to both sides:
y = 14
Now we can plug this into any of the two equations to find the 'x' value.
x + y = 56
x + 14 = 56
Subtract 14 to both sides:
x = 42
So our final answer is (42, 14).
This means that the motel clerk had 42 $1 bills, and 14 $10 bills.
Answer:
see explanation
Step-by-step explanation:
the perimeter is the sum of the 3 sides of the triangle
add the parts of the ratio 21 + 8 + 14 = 43
divide the perimeter by 43 to find the value of one part of the ratio
= 5 ft ← 1 part of the ratio, hence
21 parts = 21 × 5 = 105 ft
8 parts = 8 × 5 = 40 ft
14 parts = 14 × 5 = 70 ft
the 3 sides of the triangle are 105 ft, 40 ft and 70 ft
