Answer with explanation:
We have to prove that, For any integer m, 2 m×(3 m + 2) is divisible by 4.
We will prove this result with the help of Mathematical Induction.
⇒For Positive Integers
For, m=1
L HS=2×1×(3×1+2)
=2×(5)
=10
It is not divisible by 4.
⇒For Negative Integers
For, m= -1
L HS=2×(-1)×[3×(-1)+2]
=-2×(-3+2)
= (-2)× (-1)
=2
It is not divisible by 4.
False Statement.
Basically Samantha makes six bracelets per hour, so:
After 1 hour she makes 6
After 2 hours she makes 12
After 3 hours she makes 18
After 4 hours she makes 24, therefor the answer is B
This can also be modelled by the equation B = 6t, where B is the number of bracelets and t is the number of hours, so:
B = 6(4) = 24
Domain restrictions are what x values make the denominator zero.
a² + 5a - 36 = (a + 9)(a - 4)
a ≠ -9 ; a ≠ 4
use midpoint equation
radius = distance between midpoint and one of the endpoints.
midpoint: (3+5)/2, (2+6)/2, (5+7)/2 = (4,4,6)
equation of sphere: (x-4)^2 + (y-4)^2 + (z-6)^2 = r^2
square distance between midpoint and one of the endpoints.
r^2 = 6
Equation: (x-4)^2 + (y-4)^2 + (z-6)^2 = 6
8 ÷ (7 - 9) * ( 4 + (-4) ) <--- notice that bolded part.
4 + (-4) = 4 - 4 = 0.
after that, you're pretty much dividing and multiplying by 0, so
whatever ÷ whatever * whatever * 0 = 0.
