Answer:
(A)-494
Step-by-step explanation:
Given the arithmetic series
The terms in the sequence are:
- When k=1, 4-3k=4-3(1)=1
- When k=2, 4-3k=4-3(2)=-2
- When k=3, 4-3k=4-3(3)=-5
Therefore, the terms in the sequence are: 1, -2, -5, ...
First term, a =1
Common difference, d=-2-1=-3
The sum of an arithmetic series, ![S_n=\dfrac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%3D%5Cdfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
Therefore:
![S_{19}=\dfrac{19}{2}[2(1)+(19-1)(-3)]\\=9.5[2+18*-3]\\=9.5[2-54]\\=9.5*-52\\=-494](https://tex.z-dn.net/?f=S_%7B19%7D%3D%5Cdfrac%7B19%7D%7B2%7D%5B2%281%29%2B%2819-1%29%28-3%29%5D%5C%5C%3D9.5%5B2%2B18%2A-3%5D%5C%5C%3D9.5%5B2-54%5D%5C%5C%3D9.5%2A-52%5C%5C%3D-494)
The correct option is A.
Answer:
cot(x)
Step-by-step explanation:
Recall the Pythagorean Identity 
A^2 + b^2 = c^2
C is your hypotenuse or the longest side of the triangle; you plug in your values and solve for the missing side:
15^2 + b^2 = 17^2
225 + b^2 = 289
*-225 on both sides to get b by itself*
B^2 = 64
*to get rid of the ^2; you take the square root*
B = sqrt 64
B= 8 <— final answer
Point AAA is at {(-6,-5)}(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and point CCC is at {(4,0)}(4,0)l
Anarel [89]
Answer:
(0, 2)
Step-by-step explanation:
Given the following
coordinate A (-6, 5)
Coordinate C (4, 0)
Ratio is 2:3
Required
Coordinate of B
Using the midpoint formula expressed as;
M(X,Y) = [(ax1+bx2/a+b), ay1+by2/a+b]
x1 = -6, y1 = 5, x2 = 4 and y2 = 0
a = 2 b = 3
Get X;
X = ax1+bx2/a+b
X = 2(-6)+3(4)/2+3
X = -12+12/5
X = 0/5
X = 0
Get Y;
Y = ay1+by2/a+b
Y= 2(5)+3(0)/2+3
Y = 10/5
Y = 2
Hence the coordinate of B is at (0, 2)
