Answer:
(a) The sum of the previous term and 9
(b) 36, 45, 54
Step-by-step explanation:
Given
Sequence: Arithmetic Progression

Solving (a): Describe the relationship in each term
First, we calculate the common difference (d)
In arithmetic progression:

Take n as 2


Where



<em>The relationship is: The sum of the previous term and 9</em>
Solving (b): The next three terms
As said in (a) each term is derived from a sum of 9 and the previous term
So, we have:



Hence, the next three terms are: 36, 45 and 54
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: Use the formula (base1+base2)/2 multiplied by height(3 in)
Step-by-step explanation: I can't see what the bottom base is, but lets say it is 12. 5+12=17, and 17/2=8.5. 8.5*3=25.5
Answer:25.5
Answer: 6 if by whole number or 6.25 for decimals
Step-by-step explanation:
Answer:
a = 28°
Step-by-step explanation:
62°+a° = 90°
a = 90 - 62
a = 28°