Answer:
The correct answer is: 3x² (4x - 1) / (x - 4) (x - 3) ∧ restriction x ≠ 3, x ≠ 4, x ≠ 0 and x ≠ 1/4
Step-by-step explanation:
Given:
((16x² - 8x + 1) / (x² - 7x + 12)) : ((20x² - 5x) / 15x³) =
dividing with one fraction is the same as multiplying with its reciprocal value
((16x² - 8x + 1) / (x² - 7x + 12)) · (15x³ / (20x² - 5x))
First we need to factorize both numerators and denominators
16x² - 8x + 1 = (4x - 1)² This is square binomial
x² - 7x + 12 = x² - 4x - 3x + 12 = x (x - 4) - 3 (x - 4) = (x - 4) ( x - 3)
20x² - 5x = 5x (4x - 1)
(4x - 1)² / (x - 4) (x - 3) · 15x³ / 5x (4x - 1)
The existence of this rational algebraic expression is possible only if it is:
x - 4 ≠ 0 and x - 3 ≠ 0 and x ≠ 0 and 4x - 1 ≠ 0 =>
x ≠ 4 and x ≠ 3 and x ≠ 0 and x ≠ 1/4 This is restriction
Finally we have:
3 x² (4x - 1) / (x - 4) (x - 3)
God with you!!!
The answer would be 11 gallons.
The tub starts with 32 gallons. Every minute it loses 3 gallons.
So after 1 minute it has lost 3 gallons. For example:
32-3= 29 Meaning that after 1 minute the tub has 29 gallons left.
Now you have to remember that the tub is draining for 7 minutes. So it is losing 3 gallons 7 times, because it loses 3 gallons each minute and there are 7 minutes.
We can use multiplication to find how many gallons the tub loses after 7 minutes. This sign “X” basically means “groups of”. We have 7 groups of 3, or
7 X 3
This is the same as saying we have 3, 7 times. Written like this:
3+3 +3 +3 +3 +3 +3 = 21
So after 7 minutes the tub has lost 21 gallons.
Now we take the original number of gallons and take away what was lost:
32-21=11
So there are 11 gallons left after 7 minutes.
Please let me know if you need any further explanation. Hope this helped.
Twenty-two million two hundred and twenty-two thousand two hundred and twenty-two
Answer:
Step-by-step explanation:
For any prism or cylinder for that matter, you can find the volume by multiplying the area of the base times the height. So this problem just becomes simple algebra.
B * h = V
25 * h = 80
h = 80/25
h = 3.2
If you don't get why it's the area of the base let me know and I can try to explain it.
Using y=Mx+b, the answer is y=10x-4.
