EXPLANATION
If the first two terms of an arithmetic sequence are 7 and 4, then we know that an arithmetic sequence has a constant difference d and is defined by
Check wheter the difference is constant:
Compute the differences of all the adjacent terms:
Replacing terms:
4-7 = -3
The difference between all of the adjacent terms is the same and equal to
d = -3
The first element of the sequence is
Therefore, the nth term is computed by
d= -3
Refine
d= -3 ,
Now, replacing n=7
So, the answer is -11.
Answer:
9) 6.3 units
11) n=6√2 and m=12,
10) m=6√3, n=6
12) 330.6 ft
Step-by-step explanation:
1) The Pythagoras Theorem says that, the square of the hypotenuse is the sum of the squares of the two shorter legs.
Let the missing side, which is the hypotenuse be x.
Then
The missing side is 6.3 units to the nearest tenth.
2) This is an isosceles right triangle.
This implies that, the two legs are equal.
The hypotenuse can be found using Pythagoras Theorem.
3) The side lengths of 30°-60°-90° are in the ratio, 2x,x√3,x
From the diagram, the hypotenuse is 12, therefore the other two legs are
and
4) The height of the monument is 115 feet, the hypotenuse is 350.
By Pythagoras Theorem,
