1a. If
2 answers:
The function f(g(x)) eventually simplifies to
f(g(x) = (4/3)(x-5)(x-2)/(x² - 6x - 7)
a) The sum of the x-coordinates of the vertical asymptotes is the opposite of the x-coefficient in the denominator: 6.
b) Since the numerator and denominator are of the same degree, the horizontal asymptote is the overall multiplier: y = 4/3.
_____
Consider a quadratic with roots at "a" and "b". Then the factored form is
(x-a)(x-b)
and the expanded form is
(x² - (a+b)x + ab)
That is, the sum of the roots is the opposite of the x-coefficient. For this problem, that sum is the sum that is requested in part A.
f(g(x) = (4/3)(x-5)(x-2)/(x² - 6x - 7)
a) The sum of the x-coordinates of the vertical asymptotes is the opposite of the x-coefficient in the denominator: 6.
b) Since the numerator and denominator are of the same degree, the horizontal asymptote is the overall multiplier: y = 4/3.
_____
Consider a quadratic with roots at "a" and "b". Then the factored form is
(x-a)(x-b)
and the expanded form is
(x² - (a+b)x + ab)
That is, the sum of the roots is the opposite of the x-coefficient. For this problem, that sum is the sum that is requested in part A.
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Answer:
Step-by-step explanation:
we know that
An equilateral triangle has three equal sides and three equal interior angles (the measure of each interior angle is equal to 60 degrees)
see the attached figure to better understand tyhe problem
Let
h ----> the height of an equilateral triangle
b ---> the length side of an equilateral triangle
In the right triangle ABD
Applying the Pythagorean Theorem
substitute the given values
square root both sides
Answer:
y = - 2x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
Calculate m using the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (1,1)
m = = - 2
note the line passes through (0, 3) ⇒ c = 3
y = - 2x + 3 ← equation in slope-intercept form