Answer:
The value of x = 4
Step-by-step explanation:
In this question, we are asked to calculate the value of the angle x
Here the ray cuts the angle into half.
Since the total of the angle was 120, half of this would be 120/2 = 60
Now, it is this value of 60, that our new angle equals to
Mathematically;
3x + 48 = 60
3x = 60-48
3x = 12
x = 12/3
x = 4
<span>
This arithmetic sequence has a common difference of 4, meaning that we add 4 to a term in order to get the next term in the sequence.
The recursive formula for an arithmetic sequence is written in the form
For our particular sequence, since the common difference (d) is 4, we would write
So once you know the common difference in an arithmetic sequence you can write the recursive form for that sequence.
However, the recursive formula can become difficult to work with if we want to find the 50th term. Using the recursive formula, we would have to know the first 49 terms in order to find the 50th. This sounds like a lot of work. There must be an easier way. And there is!
Rather than write a recursive formula, we can write an explicit formula. The explicit formula is also sometimes called the closed form. To write the explicit or closed form of an arithmetic sequence, we use
<span><span>an</span> is the nth term of the sequence. When writing the general expression
for an arithmetic sequence, you will not actually find a value for
this. It will be part of your formula much in the same way x’s and y’s
are part of algebraic equations.
a1
is the first term in the sequence. To find the explicit formula, you
will need to be given (or use computations to find out) the first term
and use that value in the formula.
n is treated like the variable in a sequence. For example, when writing the general explicit formula, n is the variable and does not take on a value. But if you want to find the 12th term, then n does take on a value and it would be 12.
d is the common difference
for the arithmetic sequence. You will either be given this value or be
given enough information to compute it. You must substitute a value for d
into the formula. </span> You must also simplify your formula as much as possible. </span>
Answer:
A pair of friends are walking around outside and come across an unknown object. They are not sure if it is a living or a non-living thing. The friends decide to do a quick investigation to determine if it is alive.
Step-by-step explanation:
Answer:
5.946 cm
Step-by-step explanation:
Using the Pythagorean Theorem, we know that in a right angle triangle to find the longest side we must use the equation a^2 = b^2 + c^2
A is the longest side while b and c are the other two sides
To find one side we must use
b^2 = a^2 - c^2
a squared = 6.9 squared - 3.5 squared
a^2 = 35.36
square root 35.36 to get a
a = 5.946427499
a (3 d.p.) = 5.946
Plug in the expressions where the letters say for example the first problem would be set up as “4( x-5 )- 4( 2x+5 ). distribute and solve the equation.