Answer:
B. f(x) = -x^3 - x^2 + 7x - 4
Step-by-step explanation:
For this problem, we want to find the fastest-growing term in our given expressions and equate them when x is - infinite and when x is infinite to see the given trends.
For each of these equations, we will simply take the terms with the highest power and consider those. The two cases we need to consider is + infinite for x and - infinite for x. Let's check each of these equations.
Note, any value raised to an even power will be positive. Any negative value raised to an odd power will be negative.
<u>[A] - x^4</u>
<em>When x is +∞ --> - (∞)^4 --> f(x) is -∞</em>
<em>When x is -∞ --> - (-∞)^4 --> f(x) is -∞</em>
<em />
<u>[B] - x^3</u>
<em>When x is +∞ --> - (∞)^3 --> f(x) is -∞</em>
<em>When x is -∞ --> - (-∞)^3 --> f(x) is ∞</em>
<em />
<u>[C] 2x^5</u>
<em>When x is +∞ --> 2(∞)^5 --> f(x) is ∞</em>
<em>When x is -∞ --> 2(-∞)^5 --> f(x) is -∞</em>
<em />
<u>[D] x^4</u>
<em>When x is +∞ --> (∞)^4 --> f(x) is ∞</em>
<em>When x is -∞ --> (-∞)^4 --> f(x) is ∞</em>
<em />
Notice how only option B, when looking at asymptotic (fastest-growing) values, satisfies the originally given conditions for the relation of x to f(x).
Cheers.
Answer:
... knows they will need cash in the near future.
Step-by-step explanation:
An investment with more liquidity would be ideal for someone who knows they will need cash in the near future.
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The meaning of "high liquidity" is that it can be easily converted to cash. If you know you need cash, then you need high liquidity.
If m and n are parallel, then that's like saying 3x-10 is equal to 5x-30 (or 3x-10 = 5x-30).
If that's the case, then You'll need to format the problem so you can solve for x. In order to solve this equation, we need to group all the variable terms on one side, and all of the constant terms on the other side of the equation.
So the -10, will be moved to the right side and the 5x will be moved to the left side. Also as each term that moves, it causes their signs to change.
So we now have the problem of 3x-5x=10-30. Now we can start to simplify the problem by combining like terms.
So 3x-5x = -2x and 10-30=-20 or more simply -2x=-20
Now we need to isolate the variable x so it's on a side by itself.
The easiest way to do this is simply divide both sides by 2, which gives us 2x/2=20/2 or more simply, x=20/2.
So we're down to the simple problem of x=20/2 which equals 10. So x=10.
Answer:
Age of teacher = 32 years
Step-by-step explanation:
Average age of 15 students = 16 years
Sum of age of 15 students = 16 * 15 = 240 years
Average of age 15 students and a teacher = 17 years
Sum of age 15 students and a teacher = 17 * 16 = 272 years
Age of teacher = 272 - 240 = 32 years