Answer:
The first statement is true.
Step-by-step explanation:
The function is f(x) = - (x + 6)(x + 2)
⇒ f(x) = - x² - 8x - 12
Now, condition for a function f(x) to be increasing at x = a is f'(a) > 0.
Now, f(x) = - x² - 8x - 12
⇒ f'(x) = -2x - 8 {Differentiating with respect to x}
Now, f'(a) = -2a - 8 {Here a can be any real value}
And, the condition for increasing function at x = a is
- 2a - 8 > 0
⇒ - 2a > 8
⇒ a < - 4
Therefore, the first statement is true i.e. the function is increasing for all real values of x where x < – 4. (Answer)
Answer:
-2x+1
Step-by-step explanation:
9514 1404 393
Answer:
reflection across the line y = x
Step-by-step explanation:
The orientation of the triangle has changed from CW to CCW (considering sides in order least-to-greatest). This means a reflection is involved.
In order for this to be a single transformation, we need to know the line or point of reflection.
Each point is reflected about the point that is the midpoint joining an image point and the corresponding preimage point. Here, the points of reflection of the vertices all lie on the line y = x. So we can say ...
the transform is reflection across the line y = x
For this case we have a function of the form:
Where,
m: slope of the line
b: cutting point with the y axis.
The line cuts to the y-axis at the point:
Therefore, the value of b is given by:
We now look for the slope of the line.
For this, we use the following equation:
Substituting values we have:
Rewriting:
Then, the equation of the line is:
Answer:
the rule that matches the function shown in the graph is:
64% as fraction = 64/100 4 into 64 is 16 and 4 into 100 is 25.
= 16 / 25
= 16 / 25 in simplest form.
