For the given functions, the domains are:
1) All real numbers.
2) D: x≥ -3
3) D: set of all real numbers such that x ≠ 0
4) D: 7 ≥ x ≥-7
5) All real numbers.
<h3>
How to get the domain of the given functions?</h3>
For any function, we assume that the domain is the set of all real numbers, and then we remove all the values of x that generate problems (like a denominator equal to zero or something like that).
1) f(x) = x^2 - 4
This is just a quadratic equation, the domain is the set of all real numbers.
2) f(x) = √(x + 3)
Remember that the argument of a square root must be equal to or larger than zero, so here the domain is defined by:
x + 3 ≥ 0
x≥ -3
The domain is:
D: x ≥ -3
3) f(x) = 1/x
We can assume that the domain is the set of all real numbers, but, we can see that when x = 0 the denominator becomes zero, then we need to remove that value from the domain.
Thus, we conclude that the domain is:
D: set of all real numbers such that x ≠ 0
4) f(x) = √(49 - x^2)
Here we must have:
49 - x^2 ≥ 0
49 ≥ x^2
√49 ≥ x ≥-√49
7 ≥ x ≥-7
The domain of this function is:
D: 7 ≥ x ≥-7
5) f(x) = √(x^2 + 1)
Notice that x^2 is always a positive number, then the argument of the above square root is always positive, then the domain of that function is the set of all real numbers.
If you want to learn more about domains:
brainly.com/question/1770447
#SPJ1
x = 83°
Solution:
The reference image to the answer is given below.
Sum of the adjacent angles in a straight line = 180°
⇒ ∠1 + ∠2 + ∠3 = 180° (Refer image)
⇒ 56° + ∠2 + 41° = 180°
⇒ 56° + 41° + ∠2 = 180°
⇒ 97° + ∠2 = 180°
⇒ ∠2 = 180° – 97°
⇒ ∠2 = 83°
In the given image ∠5 and ∠2 are vertically opposite angles.
<u>Vertical angle theorem:</u>
Vertically opposite angles are equal.
⇒ ∠5 = ∠2
⇒ x = ∠2
⇒ x = 83°
Hence the measure of angle x is 83°.
The answer is 126, so it would be D:)
3(8 – 4x) < 6(x – 5)?- 12x + 24 < 6x - 30
- 12x - 6x < - 30 - 24
- 18x < - 54 .(- 1)
18x > 54
x > 54/18
x > 3
Answer:
The triangle is acute because all of the angles are less than 90º
