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!!!
Use Pythagorean's Theorem to solve for the missing leg length.
with a being the length of the missing leg. Simplifying we have
and
. If we are told to express our answer to the nearest tenth of an inch, then we are simply plugging that into our calculator to get 26.45 or, rounded correctly, 26.5
The conversions factors needed are 1 mile= 5280 feet and 1 hour = 3600 seconds, speed in ft/s = 14.67 ft/s
<u>Solution:
</u>
Given, A runner is running 10 miles per hour.
We have to find what conversion factors should be used to convert 10 mi/hr to ft/s?
Now, speed of runner = 10 miles per hour.
But we need the units to be in ft / s.
Then, conversion factors are miles to feet and hours to seconds.
Now, miles to feet ⇒ 1 mile = 5280 feet.
Now, hours to seconds ⇒ 1 hour = 3600 seconds
Hence, the conversions needed are 1 mile = 5280 feet and 1 hour = 3600 seconds, speed in ft/s = 14.67 ft/s
