Answer
Find out the which system of equations could be used to determine the number of hours charged at the day rate (d) and at the night rate (n) .
To proof
As given in the question
Let us assume that the number of hours charged at the day rate = d
Let us assume that the number of hours charged at the night rate = n
An online data base charges $25 an hour during the day and $12.50 an hour at night. If a research company paid $250 for 12 hours of use.
Total working hour in a company including day and night be 12 hours .
than the equation become in the form
d + n = 12
also
An online data base charges $25 an hour during the day
$12.50 an hour at night.
If a research company paid $250 for 12 hours of use.
than the equation becomes
25d + 12.50n = 250
than the two equation are
d + n = 12 , 25d + 12.50n = 250
multiply first by 25 and subtracted from 25d + 12.50n = 250
25d - 25d + 12.50n - 25n = 250 - 300
12.5 n = 50
n = 4hours
put this in the d + n = 12
d + 4 =12
d = 12-4
d = 8 hours
Therefore the number of hours charged at the day rate is 8 hours and at the night rate is 4hours .
Hence proved
Answer:
a
Step-by-step explanation:
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
