Answer:
4x+20=
6x-10
Step-by-step explanation:
Simplifying: 4x + 20 = 6x + -10
Reorder the terms: 20 + 4x = 6x + -10
Reorder the terms: 20 + 4x = -10 + 6x
Solving: 20 + 4x = -10 + 6x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6x' to each side of the equation: 20 + 4x + -6x = -10 + 6x + -6x
Combine like terms: 4x + -6x = -2x: 20 + -2x = -10 + 6x + -6x
Combine like terms: 6x + -6x = 0: 20 + -2x = -10 + 0: 20 + -2x = -10
Add '-20' to each side of the equation: 20 + -20 + -2x = -10 + -20
Combine like terms: 20 + -20 = 0: 0 + -2x = -10 + -20: -2x = -10 + -20
Combine like terms: -10 + -20 = -30: -2x = -30
Divide each side by '-2': x = 15
Simplifying: x = 15
Answer:
V = 15 in.³
Step-by-step explanation:
The original cylinder has radius r and height h.
V = πr²h
Its volume is 30 in.³, so
πr²h = 30 in.³
The new cylinder has radius (1/2)r and height 2h.
Its volume is
V = π(r/2)²(2h)
V = πr² × 2h/4
V = πr²h/2
πr²h is the volume of the original cylinder, and it is 30 in.³.
V = 30 in.³/2
V = 15 in.³
Answer:
False
Step-by-step explanation:
Lets call the three prime divisors of n p, q, and r, being r the largest, we know:
Now, if
then
So:
Also, for every natural greater than one, we know:
![\sqrt[3]{n}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bn%7D%3C%5Csqrt%7Bn%7D)
so
![\sqrt[3]{n}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bn%7D%3C%5Csqrt%7Bn%7D%20%3C%20r)
from which:
![\sqrt[3]{n} < r](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bn%7D%20%3C%20r)
So, we see, this means the preposition is false, we can find a particular counterexample:
q=2
p=3
p*q = 6
We need to choose a prime greater than 6
r=7
n= 2 * 3 *7 = 42
![\sqrt[3]{42} = 3.4760 < 7](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B42%7D%20%3D%203.4760%20%3C%207)
hope it will help u......
