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!!!
Box-and-whisker plot
We are given the box-and-whisker plot that summarizes the magnitude of earthquakes.
The minimum value of the dataset is 2,5
The maximum value of the dataset is 8.5
The range is the difference:
Range = 8.5 - 2.5 = 6
Range = 6
The decrease was 27%.
Step-by-step explanation:
Old value = $980
New value = $720
Decrease = Old value - New value
Percent decrease = 
Rounding off to near whole percent
Percent decrease = 27%
The decrease was 27%.
Keywords: Percentage, subtraction
Learn more about subtraction at:
#LearnwithBrainly
(f ° g) (x) means the composition of the two functions in this order f (g (x) )
So, given f(x) = - 9x + 9 and g(x) = √(x + 1), you must do this:
f(g(x)) = - 9 [ g(x) ] + 9 = - 9 [√(x+1) ] + 9 => f(g(24) = - 9 √(24 + 1) + 9 = - 9√25 + 9 =
= -9(5) + 9 = -45 + 9 = - 36
Answer: - 36
