Answer: n = 42
Step-by-step explanation:
56 - 14 = 42
If + and - are right next to each other, the + cancels out.
Answer: lim as x → -5 of f(x) and g(x) = 300
Domain of f(x) and g(x) is All Real Numbers
f(-5) = 200
g(-5) = 300
<u>Step-by-step explanation:</u>
The limit of f(x) as x approaches -5:
![f(x) =\dfrac{4x^3+500}{x+5}\\\\\\.\qquad =\dfrac{4(x^3+125)}{x+5}\\\\\\.\qquad =\dfrac{4(x^3+5^3)}{x+5}\qquad \text{we can factor the cubic}\\\\\\.\qquad =\dfrac{4(x+5)(x^2-5x+25)}{x+5}\\\\\\.\qquad =4(x^2-5x+25)\\\\\\\text{as x approaches -5, f(x) = }4[(-5)^2-5(-5)+25]\\\\.\qquad \qquad \qquad \qquad \qquad =4(25 + 25 + 25)\\\\.\qquad \qquad \qquad \qquad \qquad =4(75)\\\\.\qquad \qquad \qquad \qquad \qquad =300](https://tex.z-dn.net/?f=f%28x%29%20%3D%5Cdfrac%7B4x%5E3%2B500%7D%7Bx%2B5%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%3D%5Cdfrac%7B4%28x%5E3%2B125%29%7D%7Bx%2B5%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%3D%5Cdfrac%7B4%28x%5E3%2B5%5E3%29%7D%7Bx%2B5%7D%5Cqquad%20%5Ctext%7Bwe%20can%20factor%20the%20cubic%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%3D%5Cdfrac%7B4%28x%2B5%29%28x%5E2-5x%2B25%29%7D%7Bx%2B5%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%3D4%28x%5E2-5x%2B25%29%5C%5C%5C%5C%5C%5C%5Ctext%7Bas%20x%20approaches%20-5%2C%20f%28x%29%20%3D%20%7D4%5B%28-5%29%5E2-5%28-5%29%2B25%5D%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D4%2825%20%2B%2025%20%2B%2025%29%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D4%2875%29%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D300)
The limit of g(x) as x approaches -5:
g(x) = 4x² - 20x + 100
= 4(-5)² - 20(-5) + 100
= 100 + 100 + 100
= 300
There is a restriction at x = -5 for f(x), however, that discontinuity has been filled with the 200 at x = -5. So the domain is ALL REAL NUMBERs.
There are no restrictions on x for g(x) so the domain is ALL REAL NUMBERs.
<span>the answer: the following methods are the main rule according to the convertions
we know this followin table: km hm dam m dm cm mm. if we want to change or convert any value, cm to meters, meters to km, or anything else, just follow this:
converting dm (decimeter) to m, just multiply the number by 0.1,
converting cm (centimeter) to m, just multiply the number by 0.01,
converting mm (millimeter) to m, just multiply the number by 0.001,
in our case, we have:
convert 10.5cm to meters, so it is 10.5 x 0.01 =0.105 meters</span>
The answer is d to the question
Answer:
Step-by-step explanation:
a. The vertex is (1, -9). False. The vertex is (-1, -9).
b. The graph opens upward. True. That coefficient '6' is positive.
c. The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units. False. It's DOWN 9 units.
d. The graph is steeper than the graph of f(x) = x^2. True. The given function increases 6 times faster than does x^2.
e. The graph is the same as the graph of f(x) = 6x2 + 12x - 3.
Let's put f(x) = 6(x + 1)^2 -9 into standard form. Expanding the first term, we get f(x) = 6(x^2 + 2x + 1) - 9, or f(x) = 6x^2 + 12x + 6 - 9. YES, TRUE
