For this case we must factor the following polynomial:
![x ^ 3 + 14x ^ 2 + 49x\\](https://tex.z-dn.net/?f=x%20%5E%203%20%2B%2014x%20%5E%202%20%2B%2049x%5C%5C)
We can take common factor x:
![x(x ^ 2+ 14x + 49)](https://tex.z-dn.net/?f=x%28x%20%5E%202%2B%2014x%20%2B%2049%29)
To factor the expression within the parenthesis, we must find two numbers that when multiplied give 49 and when added together, 14 are obtained. These are: 7 and 7.
![7*7=49,7+7=14](https://tex.z-dn.net/?f=7%2A7%3D49%2C7%2B7%3D14)
Thus, the expression is factored as:
![x(x + 7)(x +7)](https://tex.z-dn.net/?f=x%28x%20%2B%207%29%28x%20%2B7%29)
Answer:
![x (x + 7) ^ 2](https://tex.z-dn.net/?f=x%20%28x%20%2B%207%29%20%5E%202)
Answer:
B
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A =
bh ( b is the base and h the perpendicular height )
here b = 4 and h = 6, thus
A =
× 4 × 6 = 2 × 6 = 12 in² → B
You have to find the circumference of both circles.
B= 25.12
Y= 87.92
I think this is right.
The reason the scientific community initially dismissed Higgs' idea was that it seemed to have little empirical basis. The correct option is d.
Given the passage is shown in the attached images.
The fourth paragraph of the passage explains why Higgs' idea of the Higgs field was initially rejected by the scientific community: “The article has been rejected. Not because it contained a technical error, but because the premise of something invisible that enters space and interacts with particles to provide their mass, well, it all looked like a bunch of exaggerated speculation. In other words, the scientific community was skeptical of Higgs' idea because it appeared to be mere theoretical speculation without any empirical evidence.
Option A is incorrect because the passage makes it clear that Higgs' idea addressed a theoretical problem already recognized by scientists, rather than a problem that has yet to be realized by them.
Option B is incorrect because the fourth paragraph implies that Higgs' work was rigorous (free from "technical errors") and not problematic at the level of their equations.
Option C is incorrect because the passage never indicates that acceptance of the Higgs field has rendered other, earlier theories in physics obsolete.
Therefore, the author strongly suggests that the reason the scientific community initially rejected Higgs' idea from the given passage is that it appeared to have little empirical basis.
Learn more about course of passage from here brainly.com/question/1290055
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Part A:
To find the average rate of change, let us first write out the equation to find it.
Δy/Δx = average rate of change.
Finding average rate of change for Section A
Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5
Δx = 1- 0 = 1
Plug the numbers in: Δy/Δx = 5/1 = 5
Therefore, the average rate of change for Section A is 5.
Finding average rate of change for Section B
Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36
Δx = 3 - 2 = 1
Plug the numbers in: Δy/Δx = 36/1 = 36
Therefore, the average rate of change for Section B is 36.
Part B:
(a) How many times greater is the average rate of change of Section B than Section A?
If Section B is on the interval [2,3] and Section A is on the interval [0,1].
For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.
(b) Explain why one rate of change is greater than the other.
Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.