Determine the domain of the function f(x)=1/3x^2+10x+8
1 answer:
The function is
f(x) = (1/3)x² + 10x + 8
Write the function in standard form for a parabola.
f(x) = (1/3)[x² + 30x] + 8
= (1/3)[ (x+15)²- 225] + 8
= (1/3)(x+15)² -75 + 8
f(x) = (1/3)(x+15)² - 67
This is a parabola with vertex at (-15, -67).
The axis of symmetry is x = -15
The curve opens upward because the coefficient of x² is positive.
As x -> - ∞, f -> +∞.
As x -> +∞, f -> +∞
The domain is all real values of x (see the graph below).
Answer: The domain is (-∞, ∞)
f(x) = (1/3)x² + 10x + 8
Write the function in standard form for a parabola.
f(x) = (1/3)[x² + 30x] + 8
= (1/3)[ (x+15)²- 225] + 8
= (1/3)(x+15)² -75 + 8
f(x) = (1/3)(x+15)² - 67
This is a parabola with vertex at (-15, -67).
The axis of symmetry is x = -15
The curve opens upward because the coefficient of x² is positive.
As x -> - ∞, f -> +∞.
As x -> +∞, f -> +∞
The domain is all real values of x (see the graph below).
Answer: The domain is (-∞, ∞)
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Answer:
<em>Riley has 72 tokens</em>
Step-by-step explanation:
<u>System of Equations </u>
We have two conditions for the tokens Riley and Erik have earned. Let's call x and y to the number of tokens of Riley and Erik respectively. The first condition states that
Solving for y
The second condition is that the ratio of the number of tokens that Riley had to the number of tokens that Erik has is 8 to 7. It's written as
Or equivalently
Replacing y from the first equation
Operating
Simplifying
Riley has 72 tokens
Answer:
4032 different tickets are possible.
Step-by-step explanation:
Given : At a race track you have the opportunity to buy a ticket that requires you to pick the first and second place horses in the first two races. If the first race runs 9 horses and the second runs 8.
To find : How many different tickets are possible ?
Solution :
In the first race there are 9 ways to pick the winner for first and second place.
Number of ways for first place -
Number of ways for second place -
In the second race there are 8 ways to pick the winner for first and second place.
Number of ways for first place -
Number of ways for second place -
Total number of different tickets are possible is
Therefore, 4032 different tickets are possible.