Relations are subsets of products <span><span>A×B</span><span>A×B</span></span> where <span>AA</span> is the domain and <span>BB</span> the codomain of the relation.
A function <span>ff</span> is a relation with a special property: for each <span><span>a∈A</span><span>a∈A</span></span> there is a unique <span><span>b∈B</span><span>b∈B</span></span> s.t. <span><span>⟨a,b⟩∈f</span><span>⟨a,b⟩∈f</span></span>.
This unique <span>bb</span> is denoted as <span><span>f(a)</span><span>f(a)</span></span> and the 'range' of function <span>ff</span> is the set <span><span>{f(a)∣a∈A}⊆B</span><span>{f(a)∣a∈A}⊆B</span></span>.
You could also use the notation <span><span>{b∈B∣∃a∈A<span>[<span>⟨a,b⟩∈f</span>]</span>}</span><span>{b∈B∣∃a∈A<span>[<span>⟨a,b⟩∈f</span>]</span>}</span></span>
Applying that on a relation <span>RR</span> it becomes <span><span>{b∈B∣∃a∈A<span>[<span>⟨a,b⟩∈R</span>]</span>}</span><span>{b∈B∣∃a∈A<span>[<span>⟨a,b⟩∈R</span>]</span>}</span></span>
That set can be labeled as the range of relation <span>RR</span>.
To solve any equation, we have to get the variables and the constants (numbers) on opposite sides of the equals sign.
First, we have to combine the like terms on the left side of the equation, resulting in
7a - 9 = 30
Then, because we want the constants on the right side of the equation, we have to +9 to cancel out the -9 on the left side.
7a=39
Next, the a has a coefficient of 7, which it is multiplied by. To undo multiplication, you have to divide. Therefore, we should divide both sides by 7.
a= 5 4/7 or 5.57142857143
In improper fraction form, a = 39/7, as this fraction cannot be simplified any farther.
Answer:
- Both are terminating decimals
Step-by-step explanation:
<u>Answer to your questions:</u>
- First of all, both A and B are correct and both quotients are terminating decimals.
- To find out if the decimal is terminating or not, multiply the quotient by divisor. If you get exactly the same number as dividend, then it is terminating otherwise it is non-terminating.
- The fraction may have greater numerator than denominator, in this case the quotient will be greater than one.
- Now regarding simplification. You would be asked to give an answer rounded to some extend. One decimal place, two decimal places, 3 significant numbers etc. For the first operation you would get 34.8 (rounded to nearest tenth).
- Or you may be asked to have a best estimated result. In this case you would round the initial numbers and find results. 205/714 ≈ 0.29
Answer:
B. negative infinity < x < positive infinity
Step-by-step explanation:
When a question asks for the domain of a function, it is asking for all possible x-values, so we can rule out choice A since there are clearly x-values greater than 1. This graph shows arrows pointing left and downward, indicating that the graph continues past what we can see. This tells us that even though the x-values look like they end at -10 and 2, they continue further, so we can also rule out option C and option D. After these eliminations, we are left with choice B, which is a way of writing "All real numbers," and is the domain for <u>all</u> exponential functions, including this one.
lmk if im incorrect about anything, hope this helps :)
Answer:
The correct system of inequalities is b.
