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
Answer: n = 6
Step-by-step explanation:
First lets combine like terms
(3 + n) + 7 = 3 + (6 + 7)
10 + n = 16
Now let’s subtract 10 on each side to isolate x
N = 6
Now let’s check our work by inputting x just to make sure
(3 + 6) + 7 = 3 + (6 + 7)
9 + 7 = 3 + 13
16 = 16
So we are right!
Answer:
34:51
Step-by-step explanation:
There are 34 zombies and 51 living humans
Answer: B
I hope this helped
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R1 ÷ 2 = ![\left[\begin{array}{ccc}1&3&1.5\\-5&1&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%261.5%5C%5C-5%261%264%5Cend%7Barray%7D%5Cright%5D)
R2 ÷ -5 = ![\left[\begin{array}{ccc}1&3&1.5\\1&-0.2&-0.8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%261.5%5C%5C1%26-0.2%26-0.8%5Cend%7Barray%7D%5Cright%5D)
R2: R1 - R2 = ![\left[\begin{array}{ccc}1&3&1.5\\0&3.2&2.3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%261.5%5C%5C0%263.2%262.3%5Cend%7Barray%7D%5Cright%5D)
R2 ÷ 3.2 = ![\left[\begin{array}{ccc}1&3&1.5\\0&1&0.71875\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%261.5%5C%5C0%261%260.71875%5Cend%7Barray%7D%5Cright%5D)
R1: R1 - 3R2 = ![\left[\begin{array}{ccc}1&0&0.65625\\0&1&0.71875\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260.65625%5C%5C0%261%260.71875%5Cend%7Barray%7D%5Cright%5D)
Answer: x = 0.65625, y = 0.71875
