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!!!
Answer:
The diameter will increase at a rate of 1/30π cm/min
Step-by-step explanation:
Here we want to calculate the rate at which the diameter will increase
Mathematically, the area of a sphere is given as;
A = 4πr^2
But r = d/2
so A = 4 * π * d/2 * d/2 = πd^2
dA/d(d) = 2πd
Thus dd/dA = 1/2πd = 1/2 * π * 15 = 1/30π
Given dA/dt = 10
Mathematically;
d(d)/dt = d(d)/dA * dA/dt
dd/dt = 1/30π * 10 = 10/30π = 1/3π cm/min
Answer:
Triangles A & C are right triangles.
Step-by-step explanation:
Triangles A & C are right triangles because they make a 90 degree angle were a pair of legs intersect. That box in the corner of each triangle indicates that the triangle is 90 degrees, therefore a right triangle.
Answer:
The ratio children to adult is 9:3
In reduced form, the ratio is 3:1
