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:
8 packs of bottled water and 14 packs of candy bars
Step-by-step explanation:
Provided,
Each pack of water bottles = 35 bottles
Each pack of candy = 20 candy
Since quantity of candy in each pack is small than quantity of water bottle in each pack, in order to have same quantity in numbers of both bottles and candies,
Purchase quantity of candy packs shall be more than the pack of water bottles.
Further, with this option 1 and 2 are not valid as candy packs are same or less than packs of water bottle.
In option 3 and 4, option 3 have smaller quantities as provided manager bought the least possible quantity.
Accordingly
Option 3
8 packs of water bottle = 
14 packs of candy = 
Since the quantities of water bottles and candies are same this is an opt answer.
Answer:
(A). y = ( x - 3 ) ( x + 4 )
Step-by-step explanation:
4/5 x 1 1/6
<span>= 4/5 x (6 x 1 + 1)/6 </span>
<span>= 4/5 x 7/6 </span>
<span>= (4 x 7)/(5 x 6) </span>
<span>= 28/30 </span>
<span>= (28 ÷ 2)/(30 ÷ 2) </span>
<span>= 14/15</span>
