Answer:
<u><em>85 degrees</em></u>
Step-by-step explanation:
A triangle's angles must add up to 180 degrees.
50 + 45 = 95
180 - 95 = 85
x = 85
4x^2 + 5x - 6 = (4x - 3) (x + 2)
You can do it by using the quadratic function to solve 4x^2 + 5x - 6 = 0; the result will be x = 3/4 and x = -2
Then you have to make (x- 3/4) = 0 and (x +2 ) = 0
When you develop x - 3/4 = 0 you get 4x -3 = 0, which means that 4x - 3 is a factor. The other factor is directly x + 2.
Answer: option b: (4x -3)(x + 2)
Using it's formula, the surface area of the figure is:
A. S=2332 m²
<h3>What is the surface area of a rectangular prism?</h3>
The surface area of a rectangular prism of dimensions l, w and h is given by:
S = 2(lw + lh + wh)
In this problem, the dimensions are:
35m, 9m, 16m
Hence the surface area of the rectangular prism is:
S = 2(35 x 9 + 35 x 16 + 16 x 9) = 2038 m².
<h3>What is the surface area of a cube?</h3>
The surface area of a cube of side length l is given by:
S = 6l².
In this problem, we have that l = 7 m, hence the surface area is:
S = 6 x 7² = 294 m².
<h3>What is the total surface area?</h3>
The total surface area is the sum of the surface areas, hence:
T = 2038 m² + 294 m² = 2332 m².
Which means that option A is correct.
More can be learned about surface area at brainly.com/question/13030328
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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
