Answer:
![(-7,4]\text{ or }\{x|-7](https://tex.z-dn.net/?f=%28-7%2C4%5D%5Ctext%7B%20or%20%7D%5C%7Bx%7C-7%3Cx%5Cleq%204%5C%7D)
Step-by-step explanation:
The domain is the span of x-values covered by the function.
From the graph, we can see that the graph covers all the x-values from x=-7 to x=4.
However, note that closed and open circles. There is an open circle at x=-7, which means that the domain excludes x=-7. However, the circle at x=4 is closed, meaning it is included in the domain.
Therefore, the domain is, in interval notation:
![(-7,4]](https://tex.z-dn.net/?f=%28-7%2C4%5D)
We use parentheses on the left because we do not include -7. And we use brackets on the right because we <em>do </em>include the 4.
And in set notation, this is:

Answer:
388.5yd²
Step-by-step explanation:
We have Triangle TUV
In the question, we are given already
Angle U = 32°
Angle T = 38°
Angle V = ???
Side t = 31yd
Side u = ?
Side v = ?
Area of the triangle= ?
Step 1
We find the third angle = Angle V
Sum of angles in a triangle = 180°
Third angle = Angle V = 180° - (32 + 38)°
= 180° - 70°
Angle V = 110°
Step 2
Find the sides u and v
We find these sides using the sine rule
Sine rule or Rule of Sines =
a/ sin A = b/ Sin B
Hence for triangle TUV
t/ sin T = u/ sin U = v/ sin V
We have the following values
Angle T = 38°
Angle U = 32°
Angle V = 110°
We are given side t = 31y
Finding side u
u/ sin U= t/ sin T
u/sin 32 = 31/sin 38
Cross Multiply
sin 32 × 31 = u × sin 38
u = sin 32 × 31/sin 38
u = 26.68268yd
u = 26.68yd
Finding side x
v / sin V= t/ sin T
v/ sin 110 = 31/sin 38
Cross Multiply
sin 110 × 31 = v × sin 38
v = sin 110 × 31/sin 38
v = 47.31573yd
v = 47.32yd
To find the area of triangle TUV
We use heron formula
= √s(s - t) (s - u) (s - v)
Where S = t + u + v/ 2
s = (31 + 26.68 + 47.32)/2
s = 52.5
Area of the triangle = √52.5× (52.5 - 31) × (52.5 - 26.68 ) × (52.5 - 47.32)
Area of the triangle = √150967.6032
Area of the triangle = 388.5454973359yd²
Approximately to the nearest tenth =388.5yd²

Here, we want to find the diagonal of the given solid
To do this, we need the appropriate triangle
Firstly, we need the diagonal of the base
To get this, we use Pythagoras' theorem for the base
The other measures are 6 mm and 8 mm
According ro Pythagoras' ; the square of the hypotenuse equals the sum of the squares of the two other sides
Let us have the diagonal as l
Mathematically;
![\begin{gathered} l^2=6^2+8^2 \\ l^2\text{ = 36 + 64} \\ l^2\text{ =100} \\ l\text{ = }\sqrt[]{100} \\ l\text{ = 10 mm} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20l%5E2%3D6%5E2%2B8%5E2%20%5C%5C%20l%5E2%5Ctext%7B%20%3D%2036%20%2B%2064%7D%20%5C%5C%20l%5E2%5Ctext%7B%20%3D100%7D%20%5C%5C%20l%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7B100%7D%20%5C%5C%20l%5Ctext%7B%20%3D%2010%20mm%7D%20%5Cend%7Bgathered%7D)
Now, to get the diagonal, we use the triangle with height 5 mm and the base being the hypotenuse we calculated above
Thus, we calculate this using the Pytthagoras' theorem as follows;