Answer:
30+4?
Step-by-step explanation:
It looks like you have the domain confused for the range! You can think of the domain as the set of all "inputs" for a function (all of the x values which are allowed). In the given function, we have no explicit restrictions on the domain, and no situations like division by 0 or taking the square root of a negative number that would otherwise put limits on it, so our domain would simply be the set of all real numbers, R. Inequality notation doesn't really use ∞, so you could just put an R to represent the set. In set notation, we'd write

and in interval notation,

The <em>range</em>, on the other hand, is the set of all possible <em>outputs</em> of a function - here, it's the set of all values f(x) can be. In the case of quadratic equations (equations with an x² term), there will always be some minimum or maximum value limiting the range. Here, we see on the graph that the maximum value for f(x) is 3. The range of the function then includes all values less than or equal to 3. As in inequality, we can say that
,
in set notation:

(this just means "f(x) is a real number less than or equal to 3")
and in interval notation:
![(-\infty,3]](https://tex.z-dn.net/?f=%20%28-%5Cinfty%2C3%5D%20)
Answer:
Felipe = 23 messages
Keisha = 31 messages
Manuel = 46 messages
Step-by-step explanation:
Keisha = K
Felipe = F
Manuel = M
=> There are a total of 100 messages.
=> K sent 8 +F => K = 8 + F
=> M sent 2 * F => M = 2F
=> F = F
=> 8 + F + 2F + F = 100
=> 8 + 4F = 100
=> 8 - 8 +4F = 100 -8
=> 4F = 92
=> 4F/4 = 92/4
=> F = 23
So, Felipe = 23 messages.
Keisha = 8 + F = 8 + 23 = 31 messages.
Manuel = 2F = 2* 23 = 46 messages.
46 + 31 + 23 = 77 + 23 = 100 messages.
So, the answer is correct.
The two angles are verticals angles so they are congruent, so you can solve for x by writing and solving an equation
6x-82=3x-23
Combine like terms
3x=105
And simplify to get x=35
Answer: choice C) 19/60
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Explanation:
Add up the minute values: 19+4+37 = 60
We have a total of 60 minutes. Of that total, 19 minutes is dedicated to news.
Divide the two values (19 and 60) to get the fraction 19/60. We can't reduce from here so we leave it like that.