9514 1404 393
Answer:
B. Two
Step-by-step explanation:
There are two points that are 4 inches from A and 6 inches from B.
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<em>Additional comment</em>
They are at the intersection points of circle A with radius 4 inches and circle B with radius 6 inches.
Answer:
False.
The vertex is at (-7, 4).
Step-by-step explanation:
f(x) = (x + 7)^2 + 4
The minimum value of (x + 7)^2 = 0 (as it's a perfect square) , so minimum of f(x) is 4 when x = -7.
The answer is seven, 7+7=14+6+20
Answer:
See explanation.
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Functions
- Function Notation
<u>Calculus</u>
Limits
- Right-Side Limit:
![\displaystyle \lim_{x \to c^+} f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%20c%5E%2B%7D%20f%28x%29)
- Left-Side Limit:
![\displaystyle \lim_{x \to c^-} f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%20c%5E-%7D%20f%28x%29)
Limit Rule [Variable Direct Substitution]: ![\displaystyle \lim_{x \to c} x = c](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%20c%7D%20x%20%3D%20c)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
![\displaystyle f(x) = \left \{ {{\sqrt{x + 1}, \ x < 3} \atop {5 - x, \ x \geq 3}} \right.](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cleft%20%5C%7B%20%7B%7B%5Csqrt%7Bx%20%2B%201%7D%2C%20%5C%20x%20%3C%203%7D%20%5Catop%20%7B5%20-%20x%2C%20%5C%20x%20%5Cgeq%203%7D%7D%20%5Cright.)
<u>Step 2: Find Right Limit</u>
- Substitute in variables [Right-Side Limit]:
![\displaystyle \lim_{x \to 3^+} 5 - x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%203%5E%2B%7D%205%20-%20x)
- Evaluate limit [Limit Rule - Variable Direct Substitution]:
![\displaystyle \lim_{x \to 3^+} 5 - x = 5 - 3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%203%5E%2B%7D%205%20-%20x%20%3D%205%20-%203)
- Subtract:
![\displaystyle \lim_{x \to 3^+} 5 - x = 2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%203%5E%2B%7D%205%20-%20x%20%3D%202)
∴ the right-side limit equals 2.
<u>Step 3: Find Left Limit</u>
- Substitute in variables [Left-Side Limit]:
![\displaystyle \lim_{x \to 3^-} \sqrt{x + 1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%203%5E-%7D%20%5Csqrt%7Bx%20%2B%201%7D)
- Evaluate limit [Limit Rule - Variable Direct Substitution]:
![\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{3 + 1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%203%5E-%7D%20%5Csqrt%7Bx%20%2B%201%7D%20%3D%20%5Csqrt%7B3%20%2B%201%7D)
- [√Radical] Add:
![\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%203%5E-%7D%20%5Csqrt%7Bx%20%2B%201%7D%20%3D%20%5Csqrt%7B4%7D)
- [√Radical] Evaluate:
![\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = 2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%203%5E-%7D%20%5Csqrt%7Bx%20%2B%201%7D%20%3D%202)
∴ the left-side limit equals 2.
<u>Step 4: Find Limit</u>
<em>The right and left-side limits are equal.</em>
∴ ![\displaystyle \lim_{x \to 3} f(x) = 2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%203%7D%20f%28x%29%20%3D%202)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
Hope this Helps with your Math Problem :D