Answer:
Below in bold.
Step-by-step explanation:
First term a1 = 13
11th term a11 = a1 + 10d = 83
So a1 + 10d - a1 = 83 - 13
10d = 70
d = 10
The common difference d = 7.
Sum of n terms = (n/2)[2a1 + (n - 1)d]
Sum of the first 20 terms:
S20 = (20/2)[2*13 + (20-1)7]
S20 = 10 *(26 + 19*7)
S20 = 10*159 = 1590.
Answer:
The three given points are the vertices of a right triangle.
Step-by-step explanation:
To determine that the three points are the vertices of a right triangle let us find the distance between each two points
The formula of the distance is
∵ = 6 and = -6
∵ = 9 and = -6
∴ =
∴ = 3
∵ = 6 and = -6
∵ = 9 and = 1
∴ =
∴ =
∵ = 9 and = 1
∵ = 9 and = -6
∴ =
∴ = 7
<em>Let us use the fact that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle at the vertex which opposite to the longest side</em>
∵ The longest side is
∵ The other two sides are 3 and 7
∵ ( )² = 58
∵ (3)² + (7)² = 9 + 49 = 58
∴ ( )² = (3)² + (7)²
- By using the fact above
∴ The triangle is a right triangle
The three given points are the vertices of a right triangle.
Answer:
6.2
Step-by-step explanation:
because 1 2/3 times 3 1/3 is 6.2
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Solution:
Your problem → x + 45 = 97x
x+45=97x
⇒-96x+45=0
⇒96x=45
⇒x=45/96
⇒x=15/32
The answer to your question is a = 2.25