[algebra 2] find the quotient with the necessary restrictions.

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!!!

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

35-60 students are taking math.