8x + 3 = -39
8x + 3 -3 = -39 - 3
8x = -42
8x/8 = -42/8
x = -5.25
The slope is the value in the term with "x". That is 2/9x has "x".
In this case, the slope will be 2/9
Information about concavity is contained in the second derivative of a function. Given f(x) = ax² + bx + c, we have
f'(x) = 2ax + b
and
f''(x) = 2a
Concavity changes at a function's inflection points, which can occur wherever the second derivative is zero or undefined. In this case, since a ≠ 0, the function's concavity is uniform over its entire domain.
(i) f is concave up when f'' > 0, which occurs when a > 0.
(ii) f is concave down when f'' < 0, and this is the case if a < 0.
In Mathematica, define f by entering
f[x_] := a*x^2 + b*x + c
Then solve for intervals over which the second derivative is positive or negative, respectively, using
Reduce[f''[x] > 0, x]
Reduce[f''[x] < 0, x]
The equivalent expression on expanding -1/4 (-8x + 12y) is 2x - 3y
<h3>Expansion of expression</h3>
Expansion of expression can be carried out using the distributive rule a shown:
A(B + C) = AB + AC
Note that <u>A is distributed over B and C</u>
Given the expression
-1/4 (-8x + 12y)
-1/4(-8x) - 1/4(12y)
2x - 3y
Hence the equivalent expression on expanding -1/4 (-8x + 12y) is 2x - 3y
Learn more on expansion here: brainly.com/question/26430239
#SPJ1
Answer:
b. Alberto can go to the movies if he washes the car.
Step-by-step explanation:
a. A triangle with all angles congruent <u><em>is</em></u> equilateral.
b. Alberto can go to the movies <u><em>if</em></u> he washes the car.
