Answer:
See explanation
Step-by-step explanation:
The given circle has center O.
A, B,C, and D are points on the circumference of the circle.
We want to prove that: 
We need to join to B and C as shown in the attachment.
Recall that angle subtended by arc BC at the center is twice the angle subtended at the circumference by the same arc.
This implies that:


The LHS of equation (1) and (2) are equal. Therefore the RHS are also equal.
This implies that:


Answer:
3n + 5 =60
Step-by-step explanation:
Answer : n=55/3
Answer:
Step-by-step explanation:
The equation for an arithmetic sequence is
where n is the position of the number in the sequence, a1 is the first number in the sequence, and d is the difference between the numbers in the sequence.
Our first number is 2, so a1 = 2; to get from 2 to 5 we add 3, to get from 5 to 8 we add 3. That means that d = 3. Filling in the standard form of the equation:
which simplifies to
and a bit more to
(which should tell you that arithmetic sequences are lines!)
Finding the 13th number simply requires that we replace n with 13 and solve:
so

Answer
Let f(x) = ax + b
Then
f(x + 1) = a(x + 1) + b
= ax + a + b
Hence, a = 3, and a + b = 5, b = 2
f(-2) = 3(-2) + 2
= -6 + 2
= - 4
f(2x) = 3(2x ) + 2
= 6x + 2