Answer:
<u>e</u>
Step-by-step explanation:
According to Angle Sum Property :
<u>∠A + ∠B + ∠C = 180°</u>
<u />
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Given :
⇒ ∠A = 50°
⇒ ∠B = 32°
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Solving :
⇒ 50° + 32° + ∠C = 180°
⇒ ∠C + 82° = 180°
⇒ ∠C = <u>98°</u>
<h3>
Answer: True</h3>
Explanation:
Technically you could isolate any variable you wanted, from either equation. However, convention is to pick the variable in which isolating it is easiest, and most efficient.
The key thing to look for is if there's a coefficient of 1. This is found in the second equation for the y term. Think of -4x+y = -13 as -4x+1y = -13. Due to the coefficient of 1, when solving for y we won't involve messy fractions.
If you were to solve for y, then you'd get y = 4x-13, which is then plugged in (aka substituted) into the first equation. That allows you to solve for x. Once you know x, you can determine y.
Answer:
![f'(x) = \frac{4x}{2x^2+1}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B4x%7D%7B2x%5E2%2B1%7D)
Domain: All Real Numbers
General Formulas and Concepts:
<u>Algebra I</u>
- Domain is the set of x-values that can be inputted into function f(x)
<u>Calculus</u>
The derivative of a constant is equal to 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Chain Rule: ![\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Derivative: ![\frac{d}{dx} [ln(u)] = \frac{u'}{u}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bln%28u%29%5D%20%3D%20%5Cfrac%7Bu%27%7D%7Bu%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = ln(2x² + 1)
<u>Step 2: Differentiate</u>
- Derivative ln(u) [Chain Rule/Basic Power]:
![f'(x) = \frac{1}{2x^2+1} \cdot 2 \cdot 2x^{2-1}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2x%5E2%2B1%7D%20%5Ccdot%202%20%5Ccdot%202x%5E%7B2-1%7D)
- Simplify:
![f'(x) = \frac{1}{2x^2+1} \cdot 4x](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2x%5E2%2B1%7D%20%5Ccdot%204x)
- Multiply:
![f'(x) = \frac{4x}{2x^2+1}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B4x%7D%7B2x%5E2%2B1%7D)
<u>Step 3: Domain</u>
We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.
Therefore, our domain would be all real numbers.
We can also graph the differential function to analyze the domain.
Answer:
option c is the correct answer
All are correct
Explanation:since in none of the answers share the same the same X value and since the graph passes the vertical line test it is a function