The sum of a series is calculated with the following formula:
n/2(2a+(n-1)d) where n is the number of terms, a is the first term and d is the difference between the terms.
so for this series:
n/2(2*64+(n-1)*-2)=0
n(130-2n)=0
n=0 (not valid because n<1) n=65
so the 65th term gives the sum 0
Answer:
4 triangles and 1 square
Step-by-step explanation:
If we are to make a net of this pyramid, we'd have a net that has 4 triangles, and 1 square.
The base of the pyramid has 4 sides of equal length of 5 in each. A polygon that has 4 right angles and 4 sides that are of equal sizes or lengths is said to be a square.
<em>Therefore, the net of the figure above is made up of 4 triangles and 1 square.</em>
If a system of linear equations has exactly one solution then the slopes of both the lines should be different.
Given A system of linear equations has exactly one solution.
Linear equation is a type of equation when when plotted on the graph gives a straight line. The slope is the ratio of the vertical change to the horizontal change between two distinct points on a line.
let two equations be who have one solution
2x+3y=7
5x+6y=1
solving them
x=7-3y/2
put the value of x in second equation
5(7-3y)/2+6y=1
35-15y/2+6y=1
35-15y+12y=2
-3y=-33
y=11
put the value of y in x=7-3y/2
x=7-3*11/2
x=7-33/2
x=-26/2
x=-13.
There is only one solution which is (-13,11)
Taking equations and convert them into standard form
first
y=7/3-2/3x
second
y=1/6-5/6x
The standard form is y=a+bx where b is slope
from the above equations we can find that the slope of first equation is -2/3 and the slope of second equation is -5/6. In this way we are able to conclude that slopes should be different for one solution.
Learn more about slope here brainly.com/question/3493733
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